arXiv subjects

S. L. Sondhi

Publications and source records attributed to S. L. Sondhi.

At least 91 records · Page 5Linked to original sources

arXiv2014

Generalizing Quantum Hall Ferromagnetism to Fractional Chern Bands

We study the interplay between quantum Hall ordering and spontaneous sublattice symmetry breaking in multiple Chern number bands at fractional fillings. Primarily we study fermions with repulsive interactions near half filling in a family of square lattice models with flat C=2 bands and a wide band gap. By perturbing about the particularly transparent limit of two decoupled C=1 bands and by exact diagonalization studies of small systems in the more general case, we show that the system generically breaks sublattice symmetry with a transition temperature $T_c>0$ and additionally exhibits a quantized Hall conductance of $e^2/h$ as $T \rightarrow 0$. We note the close analogy to quantum Hall ferromagnetism in the multi-component problem and the connection to topological Mott insulators. We also discuss generalizations to other fillings and higher Chern numbers.

cond-mat.str-el↗

arXiv2014

Eigenstate Thermalization and Representative States on Subsystems

We consider a quantum system A U B made up of degrees of freedom that can be partitioned into spatially disjoint regions A and B. When the full system is in a pure state in which regions A and B are entangled, the quantum mechanics of region A described without reference to its complement is traditionally assumed to require a reduced density matrix on A. While this is certainly true as an exact matter, we argue that under many interesting circumstances expectation values of typical operators anywhere inside A can be computed from a suitable pure state on A alone, with a controlled error. We use insights from quantum statistical mechanics - specifically the eigenstate thermalization hypothesis (ETH) - to argue for the existence of such "representative states".

cond-mat.stat-mech↗

arXiv2014

How universal is the entanglement spectrum?

It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this letter, we show that this belief is false in general. Most significantly, we show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the ES and the Renyi entropies can mislead entirely, while for quantum Hall systems the ES has much less universal content than assumed to date.

cond-mat.str-el↗

arXiv2014

Many-body Localization and Symmetry Protected Topological Order

Recent work shows that highly excited many-body localized eigenstates can exhibit broken symmetries and topological order, including in dimensions where such order would be forbidden in equilibrium. In this paper we extend this analysis to discrete symmetry protected order via the explicit examples of the Haldane phase of one dimensional spin chains and the topological Ising paramagnet in two dimensions. We comment on the challenge of extending these results to cases where the protecting symmetry is continuous.

cond-mat.str-el↗

arXiv2013

Dirty Weyl fermions: rare region effects near 3D Dirac points

We study three-dimensional Dirac fermions with weak finite-range scalar potential disorder. We show that even though disorder is perturbatively irrelevant at 3D Dirac points, nonperturbative effects from rare regions give rise to a nonzero density of states and a finite mean free path, with the transport at the Dirac point being dominated by hopping between rare regions. As one moves in chemical potential away from the Dirac point, there are interesting intermediate-energy regimes where the rare regions produce scattering resonances that determine the DC conductivity. We also discuss the interplay of disorder with interactions at the Dirac point. Attractive interactions drive a transition into a granular superconductor, with a critical temperature that depends strongly on the disorder distribution. In the presence of Coulomb repulsion and weak retarded attraction, the system can be a Bose glass. Our results apply to all 3D systems with Dirac points, including Weyl semimetals, and overturn a thirty year old consensus regarding the irrelevance of weak disorder at 3D Dirac points.

cond-mat.str-el↗

arXiv2013

Field theory of the quantum Hall nematic transition

The topological physics of quantum Hall states is efficiently encoded in purely topological quantum field theories of the Chern-Simons type. The reliable inclusion of low-energy dynamical properties in a continuum description however typically requires proximity to a quantum critical point. We construct a field theory that describes the quantum transition from an isotropic to a nematic Laughlin liquid. The soft mode associated with this transition approached from the isotropic side is identified as the familiar intra-Landau level Girvin-MacDonald-Platzman mode. We obtain z=2 dynamic scaling at the critical point and a description of Goldstone and defect physics on the nematic side. Despite the very different physical motivation, our field theory is essentially identical to a recent "geometric" field theory for a Laughlin liquid proposed by Haldane.

cond-mat.str-el↗

arXiv2013

Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems

We consider the non-equilibrium dynamics of topologically ordered systems driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This dynamics exhibits scaling in the spirit of Kibble and Zurek but now {\it without} the presence of symmetry breaking and a local order parameter. The late stages of the process are seen to exhibit a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase, a potentially interesting signature of topological order. We illustrate these phenomena in the context of particular phase transitions out of the abelian Z_2 topologically ordered phase of the toric code/Z_2 gauge theory, and the non-abelian SU(2)$_k$ ordered phases of the relevant Levin-Wen models.

cond-mat.str-el↗

arXiv2013

Superconductivity of disordered Dirac fermions

We study the effect of disorder on massless, spinful Dirac fermions in two spatial dimensions with attractive interactions, and show that the combination of disorder and attractive interactions is deadly to the Dirac semimetal phase. First, we derive the zero temperature phase diagram of a clean Dirac fermion system with tunable doping level (μ) and attraction strength (g). We show that it contains two phases: a superconductor and a Dirac semimetal. Then, we show that arbitrarily weak disorder destroys the Dirac semimetal, turning it into a superconductor. We discuss the strength of the superconductivity for both long range and short range disorder. For long range disorder, the superconductivity is exponentially weak in the disorder strength. For short range disorder, a uniform mean field analysis predicts that superconductivity should be doubly exponentially weak in the disorder strength. However, a more careful treatment of mesoscopic fluctuations suggests that locally superconducting puddles should form at a much higher temperature, and should establish global phase coherence at a temperature that is only exponentially small in weak disorder. We also discuss the effect of disorder on the quantum critical point of the clean system, building in the effect of disorder through a replica field theory. We show that disorder is a relevant perturbation to the supersymmetric quantum critical point. We expect that in the presence of attractive interactions, the flow away from the critical point ends up in the superconducting phase, although firm conclusions cannot be drawn since the renormalization group analysis flows to strong coupling. We argue that although we expect the quantum critical point to get buried under a superconducting phase, signatures of the critical point may be visible in the finite temperature quantum critical regime.

cond-mat.str-el↗

arXiv2013

Microscopic Theory of a Quantum Hall Ising Nematic: Domain Walls and Disorder

We study the the interplay between spontaneously broken valley symmetry and spatial disorder in multivalley semiconductors in the quantum Hall regime. In cases where valleys have anisotropic electron dispersion a previous long-wavelength analysis [Phys. Rev. B 82, 035428 (2010)] identified two new phases exhibiting the QHE. The first is the quantum Hall Ising nematic (QHIN), a phase with long-range orientational order manifested in macroscopic transport anisotropies. The second is the quantum Hall random-field paramagnet (QHRFPM) that emerges when the Ising ordering is disrupted by quenched disorder, characterized by a domain structure with a distinctive response to a valley symmetry-breaking strain field. Here we provide a more detailed microscopic analysis of the QHIN, which allows us to (i) estimate its Ising ordering temperature; (ii) study its domain-wall excitations, which play a central role in determining its properties; and (iii) analyze its response to quenched disorder from impurity scattering, which gives an estimate for domain size in the descendant QHRFPM. Our results are directly applicable to AlAs heterostructures, although their qualitative aspects inform other ferromagnetic QH systems, such as Si(111) heterostructures and bilayer graphene with trigonal warping.

cond-mat.mes-hall↗

arXiv2013

Approximating random quantum optimization problems

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution space over `classical' product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are: (i) The derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment. (ii) A demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects structure of the solution space of random $k$-QSAT. Simulated annealing exhibits metastability in similar `hard' regions of parameter space. (iii) A generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy `landscape' of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random $k$-QSAT in a two-dimensional energy-density--clause-density space.

cond-mat.stat-mech↗

arXiv2013

On equilibration and coarsening in the quantum O(N) model at infinite $N$

The quantum O(N) model in the infinite $N$ limit is a paradigm for symmetry-breaking. Qualitatively, its phase diagram is an excellent guide to the equilibrium physics for more realistic values of $N$ in varying spatial dimensions ($d>1$). Here we investigate the physics of this model out of equilibrium, specifically its response to global quenches starting in the disordered phase. If the model were to exhibit equilibration, the late time state could be inferred from the finite temperature phase diagram. In the infinite $N$ limit, we show that not only does the model not lead to equilibration on account of an infinite number of conserved quantities, it also does \emph{not} relax to a generalized Gibbs ensemble consistent with these conserved quantities. Nevertheless, we \emph{still} find that the late time states following quenches bear strong signatures of the equilibrium phase diagram. Notably, we find that the model exhibits coarsening to a non-equilibrium critical state only in dimensions $d>2$, that is, if the equilibrium phase diagram contains an ordered phase at non-zero temperatures.

cond-mat.stat-mech↗

arXiv2013

Localization protected quantum order

Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can order in that individual many-body eigenstates can break symmetries or display topological order in the infinite volume limit. Indeed, isolated localized quantum systems can order even at energy densities where the corresponding thermally equilibrated system is disordered, i.e.: localization protects order. In addition, localized systems can move between ordered and disordered localized phases via non-thermodynamic transitions in the properties of the many-body eigenstates. We give evidence that such transitions may proceed via localized critical points. We note that localization provides protection against decoherence that may allow experimental manipulation of macroscopic quantum states. We also identify a `spectral transition' involving a sharp change in the spectral statistics of the many-body Hamiltonian.

cond-mat.stat-mech↗

arXiv2013

Coulomb phase diagnostics as function of temperature, interaction range and disorder

The emergent gauge field characteristic of the Coulomb phase of spin ice betrays its existence via pinch points in the spin structure factor ${\cal{S}}$ in reciprocal space which takes the form of a transverse projector ${\cal{P}}$ at low temperature: ${\cal{S}} (q) \sim {\cal{P}} \sim q^2_\bot/q^2$. We develop a theory which establishes the fate of the pinch points at low and high temperature, for hard and soft spins, for short- and long-ranged (dipolar) interactions, as well as in the presence of disorder. We find that their detailed shape can be used to read off the relative sizes of entropic and magnetic Coulomb interactions of monopoles in spin ice, and we resolve the question why pinch points have been experimentally observed for Ho$_{1.7}$Y$_{0.3}$Ti$_2$O$_7$ even at high temperature in the presence of strong disorder.

cond-mat.str-el↗

arXiv2013

Fractional Quantum Hall Physics in Topological Flat Bands

We present a pedagogical review of the physics of fractional Chern insulators with a particular focus on the connection to the fractional quantum Hall effect. While the latter conventionally arises in semiconductor heterostructures at low temperatures and in high magnetic fields, interacting Chern insulators at fractional band filling may host phases with the same topological properties, but stabilized at the lattice scale, potentially leading to high-temperature topological order. We discuss the construction of topological flat band models, provide a survey of numerical results, and establish the connection between the Chern band and the continuum Landau problem. We then briefly summarize various aspects of Chern band physics that have no natural continuum analogs, before turning to a discussion of possible experimental realizations. We close with a survey of future directions and open problems, as well as a discussion of extensions of these ideas to higher dimensions and to other topological phases.

cond-mat.str-el↗

arXiv2012

Dipolar bogolons: from superfluids to Pfaffians

We study the structure of Bogoliubov quasiparticles, 'bogolons,' the fermionic excitations of paired superfluids that arise from fermion (BCS) pairing, including neutral superfluids, superconductors, and paired quantum Hall states. The naive construction of a stationary quasiparticle in which the deformation of the pair field is neglected leads to a contradiction: it carries a net electrical current even though it does not move. However, treating the pair field self-consistently resolves this problem: In a neutral superfluid, a dipolar current pattern is associated with the quasiparticle for which the total current vanishes. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar charge distribution and consequently to a dipolar current pattern.

cond-mat.str-el↗

arXiv2012

The Kibble-Zurek Problem: Universality and the Scaling Limit

Near a critical point, the equilibrium relaxation time of a system diverges and any change of control/thermodynamic parameters leads to non-equilibrium behavior. The Kibble-Zurek problem is to determine the dynamical evolution of the system parametrically close to its critical point when the change is parametrically slow. The non-equilibrium behavior in this limit is controlled entirely by the critical point and the details of the trajectory of the system in parameter space (the protocol) close to the critical point. Together, they define a universality class consisting of critical exponents-discussed in the seminal work by Kibble and Zurek-and scaling functions for physical quantities, which have not been discussed hitherto. In this article, we give an extended and pedagogical discussion of the universal content in the Kibble-Zurek problem. We formally define a scaling limit for physical quantities near classical and quantum transitions for different sets of protocols. We report computations of a few scaling functions in model Gaussian and large-N problems and prove their universality with respect to protocol choice. We also introduce a new protocol in which the critical point is approached asymptotically at late times with the system marginally out of equilibrium, wherein logarithmic violations to scaling and anomalous dimensions occur even in the simple Gaussian problem.

cond-mat.stat-mech↗

arXiv2012

A Bionic Coulomb Phase on the Pyrochlore Lattice

A class of three dimensional classical lattice systems with macroscopic ground state degeneracies, most famously the spin ice system, are known to exhibit "Coulomb" phases wherein long wavelength correlations within the ground state manifold are described by an emergent Maxwell electrodynamics. We discuss a new example of this phenomenon-the four state Potts model on the pyrochlore lattice-where the long wavelength description now involves three independent gauge fields as we confirm via simulation. The excitations above the ground state manifold are bions, defects that are simultaneously charged under two of the three gauge fields, and exhibit an entropic interaction dictated by these charges. We also show that the distribution of flux loops shows a scaling with loop length and system size previously identified as characteristic of Coulomb phases.

cond-mat.stat-mech↗

arXiv2012

A field trip through spin ice

Fractionalisation -- the breaking up of an apparently indivisible microscopic degree of freedom -- is one of the most counterintuitive phenomena in many-body physics. Here we study its most fundamental manifestation in spin ice, the only known fractionalised magnetic compound in 3D: we directly visualise the $1/r^2$ magnetic Coulomb field of monopoles which emerge as the atomic magnetic dipoles fractionalise. We analyse the internal magnetic field distribution, relevant for local experimental probes. In particular, we present new zero-field NMR measurements which exhibit excellent agreement with the calculated lineshapes, noting that this experimental technique can in principle measure directly the monopole density in spin ice. The distribution of field strengths is captured by a simple analytical form which exhibits a low density of low-field sites---in apparent disagreement with reported $μ$SR results. Counterintuitively, the density of low-field locations decreases as the local ferromagnetic correlations imposed by the ice rules weaken.

cond-mat.str-el↗