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Eduardo Fradkin

Publications and source records attributed to Eduardo Fradkin.

At least 127 records · Page 7Linked to original sources
arXiv2009

Universal entanglement entropy in 2D conformal quantum critical points

We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that, under quite general conditions, the entanglement entropy of a large and simply connected sub-system of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries. The universal finite contribution to the entanglement entropy is computable in terms of the properties of the conformal structure of the wave function of these quantum critical systems. The calculation of the universal term reduces to a problem in boundary conformal field theory.

cond-mat.stat-mech↗
arXiv2009

Theory of the striped superconductor

We define a distinct phase of matter, a "pair density wave" (PDW), in which the superconducting order parameter $ϕ$ varies periodically as a function of position such that when averaged over the center of mass position, all components of $ϕ$ vanish identically. Specifically, we study the simplest, unidirectional PDW, the "striped superconductor," which we argue may be at the heart of a number of spectacular experimental anomalies that have been observed in the failed high temperature superconductor, La$_{2-x}$ Ba$_x$CuO$_4$. We present a solvable microscopic model with strong electron-electron interactions which supports a PDW groundstate. We also discuss, at the level of Landau theory, the nature of the coupling between the PDW and other order parameters, and the origins and some consequences of the unusual sensitivity of this state to quenched disorder.

cond-mat.supr-con↗
arXiv2008

Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids

We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming that the low-energy physics is described by fermionic quasiparticle excitations, we identified an "emergent" local $U(1)^N$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $U(1)^N$ gauge theory associated with this emergent local $U(1)^N$ symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time-reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.

cond-mat.str-el↗
arXiv2008

Local density of states of 1D Mott insulators and CDW states with a boundary

We determine the local density of states (LDOS) of one-dimensional incommensurate charge density wave (CDW) states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the CDW gets pinned at the impurity, which results in a singularity in the Fourier transform of the LDOS at momentum 2k_F. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of one dimensional Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates and 1D Mott insulators.

cond-mat.str-el↗
arXiv2008

Theory of the nodal nematic quantum phase transition in superconductors

We study the character of an Ising nematic quantum phase transition (QPT) deep inside a d-wave superconducting state with nodal quasiparticles in a two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the transition is continuous. To leading order in 1/N, quantum fluctuations enhance the dispersion anisotropy of the nodal excitations, and cause strong scattering which critically broadens the quasiparticle (qp) peaks in the spectral function, except in a narrow wedge in momentum space near the Fermi surface where the qp's remain sharp. We also consider the possible existence of a nematic glass phase in the presence of weak disorder. Some possible implications for cuprate physics are also discussed.

cond-mat.supr-con↗
arXiv2008

Topological phases and topological entropy of two-dimensional systems with finite correlation length

We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $ξ$. Firstly, we suggest that simpler reduced quantities, related to the von Neumann entropy, could be defined to compute the topological entropy. We use our methods to compute the entanglement entropy for the ground state wave function of a quantum eight-vertex model in its topological phase, and show that a finite correlation length adds corrections of the same order as the topological entropy which come from sharp features of the boundary of the region under study. We also calculate the topological entropy for the ground state of the quantum dimer model on a triangular lattice by using a mapping to a loop model. The topological entropy of the state is determined by loop configurations with a non-trivial winding number around the region under study. Finally, we consider extensions of the Kitaev wave function, which incorporate the effects of electric and magnetic charge fluctuations, and use it to investigate the stability of the topological phase by calculating the topological entropy.

cond-mat.str-el↗
arXiv2007

Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models

We study phase diagrams of a class of doped quantum dimer models on the square lattice with ground-state wave functions whose amplitudes have the form of the Gibbs weights of a classical doped dimer model. In this dimer model, parallel neighboring dimers have attractive interactions, whereas neighboring holes either do not interact or have a repulsive interaction. We investigate the behavior of this system via analytic methods and by Monte Carlo simulations. At zero doping, we confirm the existence of a Kosterlitz-Thouless transition from a quantum critical phase to a columnar phase. At low hole densities we find a dimer-hole liquid phase and a columnar phase, separated by a phase boundary which is a line of critical points with varying exponents. We demonstrate that this line ends at a multicritical point where the transition becomes first order and the system phase separates. The first-order transition coexistence curve is shown to become unstable with respect to more complex inhomogeneous phases in the presence of direct hole-hole interactions. We also use a variational approach to determine the spectrum of low-lying density fluctuations in the dimer-hole fluid phase.

cond-mat.str-el↗
arXiv2007

Universality of liquid-gas Mott transitions at finite temperatures

We explain in a consistent manner the set of seemingly conflicting experiments on the finite temperature Mott critical point, and demonstrate that the Mott transition is in the Ising universality class. We show that, even though the thermodynamic behavior of the system near such critical point is described by an Ising order parameter, the global conductivity can depend on other singular observables and, in particular, on the energy density. Finally, we show that in the presence of weak disorder the dimensionality of the system has crucial effects on the size of the critical region that is probed experimentally.

cond-mat.str-el↗
arXiv2007

Dynamical layer decoupling in a stripe-ordered, high T_c superconductor

In the stripe-ordered state of a strongly-correlated two-dimensional electronic system, under a set of special circumstances, the superconducting condensate, like the magnetic order, can occur at a non-zero wave-vector corresponding to a spatial period double that of the charge order. In this case, the Josephson coupling between near neighbor planes, especially in a crystal with the special structure of La_{2-x}Ba_xCuO_4, vanishes identically. We propose that this is the underlying cause of the dynamical decoupling of the layers recently observed in transport measurements at x=1/8.

cond-mat.str-el↗
arXiv2007

Fermi liquid instabilities in the spin channel

We study the Fermi surface instabilities of the Pomeranchuk type in the spin triplet channel with high orbital partial waves ($F_{l}^a ~(l>0)$). The ordered phases are classified into two classes, dubbed the $α$ and $β$-phases by analogy to the superfluid $^3$He-A and B-phases. The Fermi surfaces in the $α$-phases exhibit spontaneous anisotropic distortions, while those in the $β$-phases remain circular or spherical with topologically non-trivial spin configurations in momentum space. In the $α$-phase, the Goldstone modes in the density channel exhibit anisotropic overdamping. The Goldstone modes in the spin channel have nearly isotropic underdamped dispersion relation at small propagating wavevectors. Due to the coupling to the Goldstone modes, the spin wave spectrum develops resonance peaks in both the $α$ and $β$-phases, which can be detected in inelastic neutron scattering experiments. In the p-wave channel $β$-phase, a chiral ground state inhomogeneity is spontaneously generated due to a Lifshitz-like instability in the originally nonchiral systems. Possible experiments to detect these phases are discussed.

cond-mat.str-el↗
arXiv2006

`Local' Quantum Criticality at the Nematic Quantum Phase Transition

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.

cond-mat.str-el↗
arXiv2006

Distinguishing Patterns of Charge Order: Stripes or Checkerboards

In two dimensions, quenched disorder always rounds transitions involving the breaking of spatial symmetries so, in practice, it can often be difficult to infer what form the symmetry breaking would take in the ``ideal,'' zero disorder limit. We discuss methods of data analysis which can be useful for making such inferences, and apply them to the problem of determining whether the preferred order in the cuprates is ``stripes'' or ``checkerboards.'' In many cases we show that the experiments clearly indicate stripe order, while in others (where the observed correlation length is short), the answer is presently uncertain.

cond-mat.str-el↗
arXiv2006

Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments

A central long standing prediction of the theory of fractional quantum Hall (FQH) states that it is a topological fluid whose elementary excitations are vortices with fractional charge and fractional statistics. Yet, the unambiguous experimental detection of this fundamental property, that the vortices have fractional statistics, has remained an open challenge. Here we propose a three-terminal ``T-junction'' as an experimental setup for the direct and independent measurement of the fractional charge and statistics of fractional quantum Hall quasiparticles via cross current noise measurements. We present a non-equilibrium calculation of the quantum noise in the T-junction setup for FQH Jain states. We show that the cross current correlation (noise) can be written in a simple form, a sum of two terms, which reflects the braiding properties of the quasiparticles: the statistics dependence captured in a factor of $\cosθ$ in one of two contributions. Through analyzing these two contributions for different parameter ranges that are experimentally relevant, we demonstrate that the noise at finite temperature reveals signatures of generalized exclusion principles, fractional exchange statistics and fractional charge. We also predict that the vortices of Laughlin states exhibit a ``bunching'' effect, while higher states in the Jain sequences exhibit an ``anti-bunching'' effect.

cond-mat.mes-hall↗
arXiv2006

Fractional statistics and duality: strong tunneling behavior of edge states of quantum Hall liquids in the Jain sequence

While the values for the fractional charge and fractional statistics coincide for fractional Hall (FQH) states in the Laughlin sequence, they do not for more general FQH states, such as those in the Jain sequence. This mismatch leads to additional phase factors in the weak coupling expansion for tunneling between edge states which alter the nature of the strong tunneling limit. We show here how to construct a weak-strong coupling duality for generalized FQH states with simple unreconstructed edges. The correct dualization of quasiparticles into integer charged fermions is a consistency requirement for a theory of FQH edge states with a simple edge. We show that this duality also applies for weakly reconstructed edges.

cond-mat.mes-hall↗
arXiv2006

Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum

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.

cond-mat.str-el↗
arXiv2006

Intermediate Symmetries In Electronic Systems: Dimensional Reduction, Order Out Of Disorder, Dualities, And Fractionalization

We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall systems, transition metal orbital systems, frustrated spin systems, (p+ip) superconducting arrays, and sliding Luttinger liquids. By considering space-time reflection symmetries, we illustrate that several of these systems are dual to each other. In some systems exhibiting these symmetries, low temperature local orders emerge by an "order out of disorder" effect while in other systems, the dimensional reduction precludes standard orders yet allows for multiparticle orders (including those of a topological nature).

cond-mat.str-el↗
arXiv2005

Ice: a strongly correlated proton system

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.

cond-mat.mtrl-sci↗