Recent Publications

Steven A.Kivelson, Eduardo Fradkin and Victor J.Emery, Electronic Liquid Crystal Phases of a Doped Mott Insulator. Nature 393, 550 (1998). arXiv:cond-mat/9707327 , pdf The character of the ground state of an antiferromagnetic insulator is fundamentally altered upon addition of even a small amount of charge. The added charge is concentrated into domain walls across which a $\pi$ phase shift in the spin correlations of the host material is induced. In two dimensions, these domain walls are ``stripes'' which are either insulating, or conducting, i. e. metallic rivers with their own low energy degrees of freedom. However, in arrays of one-dimensional metals, which occur in materials such as organic conductors, the interactions typically drive a transition to an insulating ordered charge density wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large in comparison to the CDW coupling between stripes. As a consequence, there exist novel electronic quantum liquid crystal phases which constitute new states of matter, and which can be either high temperature superconductors or two-dimensional anisotropic ``metallic'' non-Fermi liquids. Neutron scattering and other experiments in the cuprate superconductor, La_{1.6-x} Nd_{0.4} Sr_x CuO_4, already provide convincing evidence of the existence of these phases in at least one class of materials.
Eduardo Fradkin, Chetan Nayak, Alexei Tsvelik and Frank Wilczek. A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State. Nucl. Phys. B 516, 704 (1998). arXiv:cond-mat/9711087, pdf We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at $\nu=1$ is an SU(2)_2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chern-Simons theory with coupling constant k=2. The effective field theories for other Pfaffian states, such as the fermionic one at $\nu=1/2$ are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.
Nancy P. Sandler, Claudio de C. Chamon and Eduardo Fradkin. Noise measurements and fractional charge in fractional quantum Hall liquids. Phys. Rev. B 59, 12521 (1999). arXiv:cond-mat/9806335, pdf We present a calculation of noise in the tunneling current through junctions between two two-dimensional electron gases (2DEG) in inequivalent Laughlin fractional quantum Hall (FQH) states, as a function of voltage and temperature. We discuss the interpretation of measurements of suppressed shot noise levels of tunneling currents through a quantum point contact (QPC) in terms of tunneling of fractionally charged states. We show that although this interpretation is always possible, for junctions between different FQH states the fractionally charged states involved in the tunneling process are not the Laughlin quasiparticles of the isolated FQH states that make up the junction, and should be regarded instead as solitons of the coupled system. The charge of the soliton is, in units of the electron charge, the harmonic average of the filling fractions of the individual Laughlin states, which also coincides with the saturation value of the differential conductance of the QPC. For the especially interesting case of a QPC between states at filling fractions $\nu=1$ and $\nu=1/3$, we calculate the noise in the tunneling current exactly for all voltages and temperatures and investigate the crossovers. These results can be tested by noise experiments on (1,1/3) QPCs. We present a generalization of these results for QPC's of arbitrary Laughlin fractions in their weak and strong coupling regimes. We also introduce generalized Wilson ratios for the noise in the shot and thermal limits. These ratios are universal scaling functions of V/T that can be measured experimentally in a general QPC geometry.
Eduardo Fradkin and Steven Kivelson. Liquid Crystal Phases of Quantum Hall Systems. Phys. Rev. B 59, 8065 (1999). arXiv:cond-mat/9810151, pdf Mean-field calculations for the two dimensional electron gas (2DEG) in a large magnetic field with a partially filled Landau level with index N>1 consistently yield ``stripe-ordered'' charge-density wave ground-states, for much the same reason that frustrated phase separation leads to stripe ordered states in doped Mott insulators. We have studied the effects of quantum and thermal fluctuations about such a state and show that they can lead to a set of electronic liquid crystalline states, particularly a stripe-nematic phase which is stable at T>0. Recent measurements of the longitudinal resistivity of a set of quantum Hall devices have revealed that these systems spontaneously develop, at low temepratures, a very large anisotropy. We interpret these experiments as evidence for a stripe nematic phase, and propose a general phase diagram for this system.
Eduardo Fradkin, Chetan Nayak, and Kareljan Schoutens. Landau-Ginzburg Theories for Non-Abelian Quantum Hall States. Nucl. Phys. B 546, 711 (1999). arXiv:cond-mat/9811005, pdf We construct Landau-Ginzburg effective field theories for fractional quantum Hall states -- such as the Pfaffian state -- which exhibit non-Abelian statistics. These theories rely on a Meissner construction which increases the level of a non-Abelian Chern-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping Abelian theory. We describe this construction in the context of a system of bosons at Landau level filling factor $\nu=1$, where the non-Abelian symmetry is a dynamically-generated SU(2) continuous extension of the discrete particle-hole symmetry of the lowest Landau level. We show how the physics of quasiparticles and their non-Abelian statistics arises in this Landau-Ginzburg theory. We describe its relation to edge theories -- where a coset construction plays the role of the Meissner projection -- and discuss extensions to other states.
Ana Lopez and Eduardo Fradkin, Universal structure of the edge states of the fractional quantum Hall states. Phys. Rev. B 59 , 15323 (1999). arXiv:cond-mat/9810168, pdf We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dimensional electron gas, the edge states for all the Jain filling fractions $\nu=p/(2np+1)$ have only one propagating edge field that carries both energy and charge, and two non-propagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propagators at the edge. We show that these operators create states with the correct charge and statistics. It is found that the electron tunneling density of states for all the Jain states scales with frequency as $|\omega|^{(1-\nu)/\nu}$.
Eduardo Fradkin,Exploring the fractional quantum Hall effect with electron tunneling. Invited talk at the XXXIVth Rencontres de Moriond, Condensed Matter Physics Meeting Quantum Physics at the Mesoscopic Scale, Les Arcs, Haute Savoie, France, January 1999. arXiv:cond-mat/9905218, pdf In this talk I present a summary of recent work on tunnel junctions of a fractional quantum Hall fluid and an electron reservoir, a Fermi liquid. I consider first the case of a single point contact. This is a an exactly solvable problem from which much can be learned. I also discuss in some detail how these solvable junction problems can be used to understand many aspects of the recent electron tunneling experiments into edge states. I also give a detailed picture of the unusual behavior of these junctions in their strong coupling regime. A pedagogical introduction to the theories of edge states is also included.
Eduardo Fradkin, Steven A. Kivelson, Efstratios Manousakis and Kwangsik Nho, Nematic phase of the two-dimensional electron gas in a magnetic field ; Phys. Rev. Lett. 84 , 1982 (2000). arXiv:cond-mat/9906064, pdf The two dimensional electron gas (2DEG) in moderate magnetic fields in ultra-clean AlAs-GaAs heterojunctions exhibits transport anomalies suggestive of a compressible, anisotropic metallic state. Using scaling arguments and Monte Carlo simulations, we develop an order parameter theory of an electron nematic phase. The observed temperature dependence of the resistivity anisotropy behaves like the orientational order parameter if the transition to the nematic state occurs at a finite temperature, Tc ~ 65 mK, and is slightly rounded by a small background microscopic anisotropy. We propose a light scattering experiment to measure the critical susceptibility.
Victor J. Emery, Eduardo Fradkin, Steven A. Kivelson and Tom C. Lubensky, Quantum Theory of the Smectic Metal State in Stripe Phases, Phys. Rev. Lett. 85 , 2160 (2000). arXiv:cond-mat/0001077, pdf We present a theory of the electron smectic fixed point of the stripe phases of doped layered Mott insulators. We show that in the presence of a spin gap three phases generally arise: (a) a smectic superconductor, (b) an insulating stripe crystal and (c) a smectic metal. The latter phase is a stable two-dimensional anisotropic non-Fermi liquid. In the abscence of a spin gap there is also a more conventional Fermi-liquid-like phase. The smectic superconductor and smectic metal phases (or glassy versions thereof) may have already been seen in Nd-doped LSCO.
Mats Granath, Vadim Oganesyan , Steven A. Kivelson, Eduardo Fradkin and Victor J. Emery, Nodal quasi-particles and coexisting orders in striped superconductors, Phys. Rev. Lett. 86, 167011 (2001); arXiv:cond-mat/0010350, pdf We study the properties of a quasi-one dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple charicature of a locally striped high temperature superconductor, and is more generally a theoretically controllable system in which the superconducting state emerges from a non-Fermi liquid normal state. Even in this limit, ``d-wave like'' order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasi-particle spectrum, or gapless ``nodal'' quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity.
Ana Lopez and Eduardo Fradkin, Bulk effective actions and edge states for quantum Hall states in bilayers, Phys. Rev. B 63, 085306 (2001); arXiv:cond-mat/0008219, pdf We present an effective theory for the bulk Fractional Quantum Hall states in spin-polarized bilayer and spin-$1/2$ single layer two-dimensional electron gases (2DEG) in high magnetic fields consistent with the requirement of global gauge invariance on systems with periodic boundary conditions. We derive the theory for the edge states that follows naturally from this bulk theory. We find that the minimal effective theory contains two propagating edge modes that carry charge and energy, and two non-propagating topological modes responsible for the statistics of the excitations. We give a detailed description of the effective theory for the spin-singlet states, the symmetric bilayer states and for the $(m,m,m)$ states. We calculate explicitly, for a number of cases of interest, the operators that create the elementary excitations, their bound states, and the electron. We also discuss the scaling behavior of the tunneling conductances in different situations: internal tunneling, tunneling between identical edges and tunneling into a FQH state from a Fermi liquid.
S.A. Kivelson, E.Fradkin, V.Oganesyan, I.P.Bindloss, J.M.Tranquada, A.Kapitulnik and C.Howald, How to detect fluctuating order in the high-temperature superconductors, Reviews of Modern Physics 75, 1201 (2003); arXiv:cond-mat/0210683, pdf We discuss fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies for extracting information concerning such local order from experiments are derived with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems - the exactly solvable one dimensional electron gas with an impurity, and a weakly-interacting 2D electron gas. We extensively review experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies. We adduce evidence that stripe correlations are widespread in the cuprates. Finally, we compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi liquid state, and strong coupling, in which the magnetism is associated with well defined localized spins, and stripes are viewed as a form of micro-phase separation. We present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.
Eduardo Fradkin, Vishnu Jejjala and Robert G. Leigh, Non-commutative Chern-Simons for the Quantum Hall system and Duality, Nucl. Phys. B 642, 483-500 (2002); arXiv:cond-mat/0205653, pdf. The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of Chern-Simons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized only through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.
Eun-Ah Kim and Eduardo Fradkin, Inter edge tunneling in quantum Hall line junctions, Phys. Rev. B 67, 045317 (2003); arXiv:cond-mat/0205629, pdf. We propose a scenario to understand the puzzling features of the recent experiment by Kang and coworkers on tunneling between laterally coupled quantum Hall liquids by modeling the system as a pair of coupled chiral Luttinger liquid with a point contact tunneling center. We show that for filling factors $\nu\sim1$ the effects of the Coulomb interactions move the system deep into strong tunneling regime, by reducing the magnitude of the Luttinger parameter $K$, leading to the appearance of a zero-bias differential conductance peak of magnitude $G_t=Ke^2/h$ at zero temperature. The abrupt appearance of the zero bias peak as the filling factor is increased past a value $ \nu^* \gtrsim 1$, and its gradual disappearance thereafter can be understood as a crossover controlled by the main energy scales of this system: the bias voltage $V$, the crossover scale $T_K$, and the temperature $T$. The low height of the zero bias peak $\sim 0.1e^2/h$ observed in the experiment, and its broad finite width, can be understood naturally within this picture. Also, the abrupt reappearance of the zero-bias peak for $\nu \gtrsim 2$ can be explained as an effect caused by spin reversed electrons, \textit{i. e.} if the 2DEG is assumed to have a small polarization near $\nu\sim2$. We also predict that as the temperature is lowered $\nu^*$ should decrease, and the width of zero-bias peak should become wider. This picture also predicts the existence of similar zero bias peak in the spin tunneling conductance near for $\nu \gtrsim 2$.
Eun-Ah Kim and Eduardo Fradkin, Double point contact in Quantum Hall Line Junctions, Phys. Rev. Lett. 91, 156801 (2003); arXiv:cond-mat/0305693, pdf. We show that multiple point contacts on a barrier separating two laterally coupled quantum Hall fluids induce Aharonov-Bohm (AB) oscillations in the tunneling conductance. These quantum coherence effects provide new evidence for the Luttinger liquid behavior of the edge states of quantum Hall fluids. For a two point contact, we identify coherent and incoherent regimes determined by the relative magnitude of their separation and the temperature. We analyze both regimes in the strong and weak tunneling amplitude limits as well as their temperature dependence. We find that the tunneling conductance should exhibit AB oscillations in the coherent regime, both at strong and weak tunneling amplitude with the same period but with different functional form.
Ana Lopez and Eduardo Fradkin, Composite Fermions: The Next Generation(s), Phys. Rev. B 69, 155322 (2004); cond-mat/0310128, pdf. We present an effective Chern-Simons theory for the bulk fully polarized fractional quantum Hall (FQH) hierarchical states constructed as daughters of general states of the Jain series, {\it i. e.} as FQH states of the quasi-particles or quasi-holes of Jain states. We discuss the stability of these new states and present two reasonable stability criteria. We discuss the theory of their edge states which follows naturally from this bulk theory. We construct the operators that create elementary excitations, and discuss the scaling behavior of the tunneling conductance in different situations. Under the assumption that the edge states of these fully polarized hierarchical states are unreconstructed and unresolved, we find that the differential conductance $G$ for tunneling of electrons from a Fermi liquid into {\em any} hierarchical Jain FQH states has the scaling behavior $G\sim V^\alpha$ with the universal exponent $\alpha=1/\nu$, where $\nu$ is the filling fraction of the hierarchical state. Finally, we explore alternative ways of constructing FQH states with the same filling fractions as partially polarized states, and conclude that this is not possible within our approach.
Steven A. Kivelson, Eduardo Fradkin and Theodore Geballe, Quasi-1D dynamics and nematic phases in the 2D Emery model Phys. Rev. B 69, 144505 (2004); cond-mat/0302163, pdf. We consider the Emery model of a two dimensional (2D) Cu-O plane of the high temperature superconductors. We show that in a strong-coupling limit, with strong Coulomb repulsions between electrons on nearest-neighbor O sites, the electron-dynamics is strictly one dimensional, and consequently a number of exact results can be obtained concerning the electronic structure. In particular, we show that a nematic phase, which spontaneously breaks the point-group symmetry of the square lattice, is stable at low enough temperatures and strong enough coupling.
Enrico Arrigoni, Eduardo Fradkin and Steven A. Kivelson, Mechanism of High Temperature Superconductivity in a striped Hubbard Model, Phys. Rev. B 69, 214519 (2004); cond-mat/0309572, pdf. It is shown, using asymptotically exact methods, that the two dimensional repulsive Hubbard model with strongly modulated interactions exhibits high temperature superconductivity. Specifically, the explicit modulation, which has the same symmetry as period 4 bond-centered stripes, breaks the system into an alternating array of more and less heavily hole doped, nearly decoupled two-leg ladders. It is shown that this system exhibits a pairing scale determined by the spin-gap of the undoped two-leg ladder, and a phase ordering temperature proportional to a low positive power of the inter-ladder coupling.
Eduardo Fradkin, David Huse, Roderich Moessner, Vadim Oganesyan and Shivaji L. Sondhi, On bipartite Rokhsar-Kivelson points and Cantor deconfinement, Phys. Rev. B 69, 224415 (2004); arXiv:cond-mat/0311353, pdf. Quantum dimer models on bipartite lattices exhibit Rokhsar-Kivelson (RK) points with exactly known critical ground states and deconfined spinons. We examine generic, weak, perturbations around these points. In $d=2+1$ we find a first order transition between a ``plaquette'' valence bond crystal and a region with a devil's staircase of commensurate and incommensurate valence bond crystals. In the part of the phase diagram where the staircase is incomplete, the incommensurate states exhibit a gapless photon and deconfined spinons on a set of finite measure, almost but not quite a deconfined phase in a compact U(1) gauge theory in $d=2+1$! In $d=3+1$ we find a continuous transition between the U(1) resonating valence bond (RVB) phase and a deconfined staggered valence bond crystal. In an appendix we comment on analogous phenomena in quantum vertex models, most notably the existence of a continuous transition on the triangular lattice in $d=2+1$.
Eddy Ardonne, Paul Fendley and Eduardo Fradkin, Topological Order and Conformal Quantum Critical Points, Annals Phys. 310 (2004) 493-551; arXiv:cond-mat/0311466, pdf. We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as two-dimensional quantum critical points separating these phases. All of the ground-state equal-time correlators of these theories are equal to correlation functions of a local two-dimensional classical model. The critical points therefore exhibit a time-independent form of conformal invariance. These theories characterize the universality classes of two-dimensional quantum dimer models and of quantum generalizations of the eight-vertex model, as well as Z_2 and non-abelian gauge theories. The conformal quantum critical points are relatives of the Lifshitz points of three-dimensional anisotropic classical systems such as smectic liquid crystals. In particular, the ground-state wave functional of these quantum Lifshitz points is just the statistical (Gibbs) weight of the ordinary 2D free boson, the 2D Gaussian model. The full phase diagram for the quantum eight-vertex model exhibits quantum critical lines with continuously-varying critical exponents separating phases with long-range order from a Z_2 deconfined topologically-ordered liquid phase. We show how similar ideas also apply to a well-known field theory with non-abelian symmetry, the strong-coupling limit of 2+1-dimensional Yang-Mills gauge theory with a Chern-Simons term. The ground state of this theory is relevant for recent theories of topological quantum computation.
Michael J. Lawler and Eduardo Fradkin, Quantum Hall Smectics, Sliding Symmetry and the Renormalization Group, Phys. Rev. B 70, 165310 (2004); arXiv:cond-mat/0405237, pdf. In this paper we discuss the implication of the existence of a sliding symmetry, equivalent to the absence of a shear modulus, on the low-energy theory of the quantum hall smectic (QHS) state. We show, through renormalization group calculations, that such a symmetry causes the naive continuum approximation in the direction perpendicular to the stripes to break down through infrared divergent contributions originating from naively irrelevant operators. In particular, we show that the correct fixed point has the form of an array of sliding Luttinger liquids which is free from superficially "irrelevant operators". Similar considerations apply to all theories with sliding symmetries.
Eun-Ah Kim, Smitha Vishveshwara and Eduardo Fradkin, Cooper pair tunneling in singlet quantum Hall/superconductor junctions, Phys. Rev. Lett. 92, 266803(2004); arXiv:cond-mat/0405156, pdf. We propose tunnel junctions of a Hall bar and a superconducting lead, for observing Cooper-pair tunneling into singlet fractional quantum Hall edge states. These tunnel junctions provide a natural means of extracting precise information of the spin polarization and the filling factor of the state. The low energy regime one of the set-ups is governed by a novel quantum entangled fixed point.
Paul Fendley and Eduardo Fradkin, Realizing non-Abelian fractional statistics in time-reversal invariant systems, Phys. Rev. B 72, 024412 (2005); arXiv:cond-mat/0502071, pdf. We construct a series of 2+1-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the braid matrix of the particles and the scattering matrix of 1+1-dimensional field theories. We discuss in depth lattice and continuum models whose braiding is that of SO(3) Chern-Simons gauge theory, including the simplest type of non-Abelian statistics, involving just one type of quasiparticle. The ground-state wave function of an SO(3) model is related to a loop description of the classical two-dimensional Potts model. We discuss the transition from a topological phase to a conventionally-ordered phase, showing in some cases there is a quantum critical point.
Eun-Ah Kim, Michael J. Lawler, Smitha Vishveshwara and Eduardo Fradkin, Signatures of fractional statistics in noise experiments in quantum Hall systems, Phys. Rev. Lett. 95, 176402 (2005); arXiv:cond-mat/0507428, pdf. The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a ``bunching'' effect, while for higher states in the Jain sequences they should exhibit an ``anti-bunching'' effect.
Steven A. Kivelson and Eduardo Fradkin, How optimal inhomoheneity produces high temperature superconductivity, to appear as a chapter in Treatise of High Temperature Superconductivity, edited by J. R. Schrieffer and J. Brooks (In press); arXiv:cond-mat/0507459, pdf. Before Vic Emery's untimely death, we had the privilege of working closely with him on the role of Coulomb frustrated phase separation in doped Mott insulators, and on the consequences of the resulting local electronic structures on the ``mechanism'' of high temperature superconductivity. In the present article, we discuss the resulting perspective on superconductivity in the cuprates, and on the more general theoretical issue of what sorts of systems can support high temperature superconductivity. We discuss some of the general, qualitative aspects of the experimental lore which we think should constrain any theory of the mechanism, and show how they are accounted for within the context of our theory.
Michael Lawler, Daniel Barci, Victoria Fernandez, Eduardo Fradkin, and Luis Oxman, Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid, Phys. Rev. B 73, 085101 (2006); arXiv:cond-mat/05087479, pdf. We discuss shape (Pomeranchuk) instabilities of the Fermi surface of a two-dimensional Fermi system using bosonization. We consider in detail the quantum critical behavior of the transition of a two dimensional Fermi fluid to a nematic state which breaks spontaneously the rotational invariance of the Fermi liquid. We show that higher dimensional bosonization reproduces the quantum critical behavior expected from the Hertz-Millis analysis, and verify that this theory has dynamic critical exponent $z=3$. Going beyond this framework, we study the behavior of the fermion degrees of freedom directly, and show that at quantum criticality as well as in the the quantum nematic phase (except along a set of measure zero of symmetry-dictated directions) the quasi-particles of the normal Fermi liquid are generally wiped out. Instead, they exhibit short ranged spatial correlations that decay faster than any power-law, with the law $|x|^{-1} \exp(-\textrm{const.} |x|^{1/3})$ and we verify explicitly the vanishing of the fermion residue utilizing this expression. In contrast, the fermion auto-correlation function has the behavior $|t|^{-1} \exp(-{\rm const}. |t|^{-2/3})$. In this regime we also find that, at low frequency, the single-particle fermion density-of-states behaves as $N^*(\omega)=N^*(0)+ B \omega^{2/3} \log\omega +...$, where $N^*(0)$ is larger than the free Fermi value, N(0), and $B$ is a constant. These results confirm the non-Fermi liquid nature of both the quantum critical theory and of the nematic phase.
Erica Carlson, Karin Dahmen, Eduardo Fradkin and Steven Kivelson, Hysteresis and Noise from Electronic Nematicity in High Temperature Superconductors, Phys. Rev. Lett. 796, 097003 (2006); arXiv:cond-mat/0510259, pdf. An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model (RFIM). Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network, and use what is known about the RFIM to predict new ways to test for electron nematicity using noise and hysteresis. In particular, we have uncovered a remarkably robust linear relation between the orientational order and the resistance anisotropy which holds over a wide range of circumstances.
Antonio H. Castro Neto, Pierre Pujol and Eduardo Fradkin, Ice: a strongly correlated proton system, Phys. Rev. B 74, 024302 (2006); arXiv:cond-mat/0511092, pdf. We discuss the problem of proton motion in Hydrogen bond materials with special focus on ice. We show that phenomenological models proposed in the past for the study of ice can be recast in terms of microscopic models in close relationship to the ones used to study the physics of Mott-Hubbard insulators. We discuss the physics of the paramagnetic phase of ice at 1/4 filling (neutral ice) and its mapping to a transverse field Ising model and also to a gauge theory in two and three dimensions. We show that H3O+ and HO- ions can be either in a confined or deconfined phase. We obtain the phase diagram of the problem as a function of temperature T and proton hopping energy t and find that there are two phases: an ordered insulating phase which results from an order-by-disorder mechanism induced by quantum fluctuations, and a disordered incoherent metallic phase (or plasma). We also discuss the problem of decoherence in the proton motion introduced by the lattice vibrations (phonons) and its effect on the phase diagram. Finally, we suggest that the transition from ice-Ih to ice-XI observed experimentally in doped ice is the confining-deconfining transition of our phase diagram.
Michael J. Lawler and Eduardo Fradkin, Local Quantum Criticality in the Nematic Quantum Phase Transition of a Fermi Fluid, Phys. Rev. B 75, 033304 (2007); arXiv:cond-mat/0605203, pdf. We discuss the finite temperature properties of the fermion correlation function near the fixed point theory of the nematic quantum critical point (QCP) of a metallic Fermi system. We show that though the fixed point theory is above its upper critical dimension, the equal time fermion correlation function takes on a universal scaling form in the vicinity of the QCP. We find that in the quantum critical regime, this equal-time correlation function has an ultra local behavior in space, while the low-frequency behavior of the equal-position auto correlation function is that of a Fermi liquid up to subdominant terms. This behavior should also apply to other quantum phase transitions of metallic Fermi systems.
Eduardo Fradkin and Joel Moore, Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum, Phys. Rev. Lett. 97, 050404 (2006); arXiv:cond-mat/0605683, pdf. The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one dimension have entanglement that diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find the entanglement entropy for a standard class of $z=2$ quantum critical points in two spatial dimensions with scale invariant ground state wave functions: in addition to a nonuniversal ``area law'' contribution proportional to the size of the $AB$ boundary, there is generically a universal logarithmically divergent correction. This logarithmic term is completely determined by the geometry of the partition into subsystems and the central charge of the field theory that describes the equal-time correlations of the critical wavefunction.
Eduardo Fradkin, Steven A. Kivelson and Vadim Oganesyan, Discovery of a Nematic Electron Fluid in a Transition Metal Oxide, Science 315, 196 (2007).

Last updated 1/17/2007