arXiv subjects

Rahul M. Nandkishore

Publications and source records attributed to Rahul M. Nandkishore.

At least 19 recordsLinked to original sources

arXiv2022

Ergodicity breaking provably robust to arbitrary perturbations

We present a new route to ergodicity breaking via Hilbert space fragmentation that displays an unprecedented level of robustness. Our construction relies on a single emergent (prethermal) conservation law. In the limit when the conservation law is exact, we prove the emergence of Hilbert space fragmentation with an exponential number of frozen configurations. We further prove that every frozen configuration is absolutely stable to arbitrary perturbations, to all finite orders in perturbation theory. In particular, our proof is not limited to symmetric perturbations, or to perturbations with compact support, but also applies to perturbations with long-range tails, and even to arbitrary geometrically nonlocal $k$-body perturbations, as long as $k/L \rightarrow 0$ in the thermodynamic limit, where $L$ is linear system size. Additionally, we identify one-form $U(1)$ charges characterizing some non-frozen sectors, and discuss the dynamics starting from typical initial conditions, which we argue is best interpreted in terms of the magnetohydrodynamics of the emergent one-form symmetry.

cond-mat.stat-mech↗

arXiv2022

Multidome superconductivity in charge density wave kagome metals

Motivated by recent experiments on the kagome metals $A\text{V}_3\text{Sb}_5$ with $A=\text{K}$, $\text{Rb}$, and $\text{Cs}$, which show a charge density wave (CDW) at $\sim100$ K and the superconductivity at $\sim1$ K, we explore the onset of the superconductivity, taking the perspective that it descends from a parent CDW. We argue that viewing the superconductivity as a weak-coupling instability of a reconstructed (by the CDW) Fermi surface naturally explains the experimentally observed 'multidome' nonmonotonic dependence on pressure, with the 'peaks' in the superconducting critical temperature being associated with the Van Hove singularities of the reconstructed Fermi surface. This 'parent-child relationship' also naturally explains the large separation of energy scales between the superconductivity and the CDW. We discuss different possible pairing mechanisms and speculate that the CDW or reconstructed Pomeranchuk fluctuations may mediate the pairing interaction.

cond-mat.str-el↗

arXiv2022

Interplay of Coulomb interactions and disorder in three dimensional quadratic band crossings without time-reversal symmetry and with unequal masses for conduction and valence bands

Coulomb interactions famously drive three dimensional quadratic band crossing semimetals into a non-Fermi liquid phase of matter. In a previous work, Phys. Rev. B 95, 205106 (2017), the effect of disorder on this non-Fermi liquid phase was investigated, assuming that the bandstructure was isotropic, assuming that the conduction and valence bands had the same band mass, and assuming that the disorder preserved exact time-reversal symmetry and statistical isotropy. It was shown that the non-Fermi liquid fixed point is unstable to disorder, and that a runaway flow to strong disorder occurs. In this work, we extend that analysis by relaxing the assumption of time-reversal symmetry and allowing the electron and hole masses to differ (but continuing to assume isotropy of the low energy bandstructure). We first incorporate time-reversal symmetry breaking disorder, and demonstrate that there do not appear any new fixed points. Moreover, while the system continues to flow to strong disorder, time-reversal-symmetry-breaking disorder grows asymptotically more slowly than time-reversal-symmetry-preserving disorder, which we therefore expect should dominate the strong-coupling phase. We then allow for unequal electron and hole masses. We show that whereas asymmetry in the two masses is irrelevant in the clean system, it is relevant in the presence of disorder, such that the 'effective masses' of the conduction and valence bands should become sharply distinct in the low-energy limit. We calculate the RG flow equations for the disordered interacting system with unequal band masses, and demonstrate that the problem exhibits a runaway flow to strong disorder. Along the runaway flow, time-reversal-symmetry-preserving disorder grows asymptotically more rapidly than both time-reversal-symmetry-breaking disorder and the Coulomb interaction.

cond-mat.str-el↗

arXiv2021

Complex charge density waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in kagome metals $\text{AV}_3\text{Sb}_5$

We investigate how the real and imaginary charge density waves interplay at the Van Hove singularity on the hexagonal lattices. A phenomenological analysis indicates the formation of $3Q$ complex orders at all three nesting momenta. Under a total phase condition, unequal phases at the three momenta break the rotation symmetry generally. The $3Q$ complex orders constitute a rich Haldane-model phase diagram. When effective time-reversal symmetries arise under 1-site translations, the Dirac semimetals are protected. The breakdown of these symmetries gaps the Dirac points and leads to the trivial and Chern insulator phases. These phases are deformations of purely real and imaginary orders, which exhibit trivial site and/or bond density and chiral flux orders, respectively. The exotic single-Dirac-point semimetals also appear along the gapless phase boundary. We further show that the theoretical model offers transparent interpretations of experimental observations in the kagome metals $\text{AV}_3\text{Sb}_5$ with $\text{A}=\text{K},\text{Rb},\text{Cs}$. The topological charge density waves may be identified with the complex orders in the Chern insulator phase. Meanwhile, the lower-temperature symmetry-breaking phenomena may be interpreted as the secondary orders from the complex order ground states. Our work sheds light on the nature of the topological charge density waves in the kagome metals $\text{AV}_3\text{Sb}_5$ and may offer useful indications to the experimentally observed charge orders in the future experiments.

cond-mat.str-el↗

arXiv2021

Tunable-spin-model generation with spin-orbit-coupled fermions in optical lattices

We study the dynamical behaviour of ultracold fermionic atoms loaded into an optical lattice under the presence of an effective magnetic flux, induced by spin-orbit coupled laser driving. At half filling, the resulting system can emulate a variety of iconic spin-1/2 models such as an Ising model, an XY model, a generic XXZ model with arbitrary anisotropy, or a collective one-axis twisting model. The validity of these different spin models is examined across the parameter space of flux and driving strength. In addition, there is a parameter regime where the system exhibits chiral, persistent features in the long-time dynamics. We explore these properties and discuss the role played by the system's symmetries. We also discuss experimentally-viable implementations.

cond-mat.quant-gas↗

arXiv2021

Marginally localized edges of time-reversal symmetric topological superconductors

We demonstrate that the one-dimensional helical Majorana edges of two-dimensional time-reversal symmetric topological superconductors (class DIII) can become gapless and insulating by a combination of random edge velocity and interaction. Such a gapless insulating edge breaks time-reversal symmetry inhomogeneously, and the local symmetry broken regions can be regarded as static mass potentials or dynamical Ising spins. In both limits, we find that such glassy Majorana edges are generically exponentially localized and trap Majorana zero modes. Interestingly, for a statistically time-reversal symmetric edge, the low-energy theory can be mapped to a Dyson model at zero energy, manifesting a diverging density of states and exhibiting marginal localization (i.e., a diverging localization length). Although the ballistic edge state transport is absent, the localized Majorana zero modes reflect the nontrivial topology in the bulk. Experimental signatures are also discussed.

cond-mat.str-el↗

arXiv2020

Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone

We analyze the weak-coupling instabilities that may arise when multiple high-order Van Hove points are present inside the Brillouin zone. The model we consider is inspired by twisted bilayer graphene, although the analysis should be more generally applicable. We employ a parquet renormalization group analysis to identify the leading weak-coupling instabilities, supplemented with a Ginzburg-Landau treatment to resolve any degeneracies. Hence we identify the leading instabilities that can occur from weak repulsion with the power-law divergent density of states. Five correlated phases are uncovered along distinct stable fixed trajectories, including $s$-wave ferromagnetism, $p$-wave chiral/helical superconductivity, $d$-wave chiral superconductivity, $f$-wave valley-polarized order, and $p$-wave polar valley-polarized order. The phase diagram is stable against band deformations which preserve the high-order Van Hove singularity.

cond-mat.str-el↗

arXiv2020

Hydrodynamics in lattice models with continuous non-Abelian symmetries

We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles. As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.

cond-mat.stat-mech↗

arXiv2020

Spectroscopic fingerprints of gapped quantum spin liquids, both conventional and fractonic

We explain how gapped quantum spin liquids, both conventional and 'fractonic', may be unambiguously diagnosed experimentally using the technique of multidimensional coherent spectroscopy. 'Conventional' gapped quantum spin liquids (e.g. $Z_2$ spin liquid) do not have clear signatures in linear response, but do have clear fingerprints in non-linear response, accessible through the already existing experimental technique of two dimensional coherent spectroscopy. Type I fracton phases (e.g. X-cube) are (surprisingly) even easier to distinguish, with strongly suggestive features even in linear response, and unambiguous signatures in non-linear response. Type II fracton systems, like Haah's code, are most subtle, and may require consideration of high order non-linear response for unambiguous diagnosis.

cond-mat.str-el↗

arXiv2020

Fracton hydrodynamics

We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter. Fracton phases are characterized by elementary excitations (fractons) with restricted mobility. The hydrodynamic theories we introduce describe thermalization in systems with fracton-like mobility constraints, including fluids where charge and dipole moment are both locally conserved, and fluids where charge is conserved along every line or plane of a lattice. Each of these fluids is subdiffusive, and constitutes a new universality class of hydrodynamic behavior. There are infinitely many such classes, each with distinct subdiffusive exponents, all of which are captured by our formalism. Our framework naturally explains recent results on dynamics with constrained quantum circuits, as well as recent experiments with ultracold atoms in tilted optical lattices. We identify crisp experimental signatures of these novel hydrodynamics, and explain how they may be realized in near term ultracold atom experiments.

cond-mat.str-el↗

arXiv2020

Quantum butterfly effect in polarized Floquet systems

We explore quantum dynamics in Floquet many-body systems with local conservation laws in one spatial dimension, focusing on sectors of the Hilbert space which are highly polarized. We numerically compare the predicted charge diffusion constants and quantum butterfly velocity of operator growth between models of chaotic Floquet dynamics (with discrete spacetime translation invariance) and random unitary circuits which vary both in space and time. We find that for small but finite polarization per length (in the thermodynamic limit), the random unitary circuit correctly predicts the scaling of the butterfly velocity but incorrectly predicts the scaling of the diffusion constant. We argue that this is a consequence of quantum coherence on short time scales. Our work clarifies the settings in which random unitary circuits provide correct physical predictions for non-random chaotic systems, and sheds light into the origin of the slow down of the butterfly effect in highly polarized systems or at low temperature.

cond-mat.stat-mech↗

arXiv2019

Local constraints can globally shatter Hilbert space: a new route to quantum information protection

We show how local constraints can globally "shatter" Hilbert space into subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a "fractonic circuit" - a model of quantum circuit dynamics in one dimension constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic circuit dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. A large number of the emergent subsectors, exponentially many in the size of the system, have dimension one and exhibit strictly localized quantum dynamics---even in the absence of spatial disorder and in the presence of temporal noise. Exponentially large localized subspaces can be proven to exist for any one dimensional fractonic circuit with finite spatial range, and provide a potentially new route for the robust storage of quantum information. Other emergent subsectors display non-trivial dynamics and may be constructed by embedding finite sized non-trivial blocks into the localized subspace. The shattering of a particular symmetry sector into a distribution of dynamical subsectors with varying sizes leads to the coexistence of high and low entanglement states, i.e. this provides a general mechanism for the production of quantum many body scars. We discuss the detailed pattern of fracturing and its implications. We also discuss other mechanisms for similarly shattering Hilbert space.

cond-mat.stat-mech↗

arXiv2019

Superconductor versus insulator in twisted bilayer graphene

We present a simple model that we believe captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary, and arises at generic fillings, but is interrupted by the insulator at commensurate fillings. Importantly, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model is composed of a collection of crossed one-dimensional quantum wires whose intersections form a superlattice. At each superlattice point, we place a locally superconducting puddle which can exchange Cooper pairs with the quantum wires. We analyze this model assuming weak wire-puddle and wire-wire couplings. We show that for a range of repulsive intrawire interactions, the system is superconducting at `generic' incommensurate fillings, with the superconductivity being `interrupted' by an insulating phase at commensurate fillings. We further show that the gapped insulating states at commensurate fillings give way to gapless states upon application of external Zeeman fields. These features are consistent with experimental observations in magic-angle twisted bilayer graphenes despite the distinct microscopic details. We further study the full phase diagram of this model and discover that it contains several distinct correlated insulating states, which we characterize herein.

cond-mat.str-el↗

arXiv2019

Anomalous localization at the boundary of an interacting topological insulator

The boundary of a topological insulator (TI) hosts an anomaly restricting its possible phases: e.g. 3D strong and weak TIs maintain surface conductivity at any disorder if symmetry is preserved on-average, at least when electron interactions on the surface are weak. However the interplay of strong interactions and disorder with the boundary anomaly has not yet been theoretically addressed. Here we study this combination for the edge of a 2D TI and the surface of a 3D weak TI, showing how it can lead to an "Anomalous Many Body Localized" (AMBL) phase that preserves the anomaly. We discuss how the anomalous Kramers parity switching with pi flux arises in the bosonized theory of the localized helical state. The anomaly can be probed in localized boundaries by electrostatically sensing nonlinear hopping transport with e/2 shot noise. Our AMBL construction in 3D weak TIs fails for 3D strong TIs, suggesting that their anomaly restrictions are distinguished by strong interactions.

cond-mat.str-el↗

arXiv2019

Quantum entropic self-localization with ultracold fermions

We study a driven, spin-orbit coupled fermionic system in a lattice at the resonant regime where the drive frequency equals the Hubbard repulsion, for which non-trivial constrained dynamics emerge at fast timescales. An effective density-dependent tunneling model is derived, and examined in the sparse filling regime in 1D. The system exhibits entropic self-localization, where while even numbers of atoms propagate ballistically, odd numbers form localized bound states induced by an effective attraction from a higher configurational entropy. These phenomena occur in the strong coupling limit where interactions only impose a constraint with no explicit Hamiltonian term. We show how the constrained dynamics lead to quantum few-body scars and map to an Anderson impurity model with an additional intriguing feature of non-reciprocal scattering. Connections to many-body scars and localization are also discussed.

quant-ph↗

arXiv2019

A chiral twist on the high-$T_c$ phase diagram in Moiré heterostructures

We show that the large orbital degeneracy inherent in Moiré heterostructures naturally gives rise to a `high-$T_c$' like phase diagram with a chiral twist - wherein an exotic $\textit{quantum anomalous Hall}$ insulator phase is flanked by chiral $d+id$ superconducting domes. Specifically, we analyze repulsively interacting fermions on hexagonal (triangular or honeycomb) lattices near Van Hove filling, with an ${\rm SU}(N_f)$ flavor degeneracy. This model is inspired by recent experiments on graphene Moiré heterostructures. At this point, a nested Fermi surface and divergent density of states give rise to strong ($\ln^2$) instabilities to correlated phases, the competition between which can be controllably addressed through a combination of weak coupling parquet renormalization group and Landau-Ginzburg analysis. For $N_f=2$ (i.e. spin degeneracy only) it is known that chiral $d+id$ superconductivity is the unambiguously leading weak coupling instability. Here we show that $N_f\geq4$ leads to a richer (but still unambiguous and fully controllable) behavior, wherein at weak coupling the leading instability is to a fully gapped and chiral $\textit{Chern insulator}$, characterized by a spontaneous breaking of time reversal symmetry and a quantized Hall response. Upon doping this phase gives way to a chiral $d+id$ superconductor. We further consider deforming this minimal model by introducing an orbital splitting of the Van Hove singularities, and discuss the resulting RG flow and phase diagram. Our analysis thus bridges the minimal model and the practical Moiré band structures, thereby providing a transparent picture of how the correlated phases arise under various circumstances. Meanwhile, a similar analysis on the square lattice predicts a phase diagram where (for $N_f>2$) a nodal staggered flux phase with `loop current' order gives way upon doping to a nodal $d$-wave superconductor.

cond-mat.str-el↗

arXiv2019

Localization in fractonic random circuits

We study the spreading of initially-local operators under unitary time evolution in a 1d random quantum circuit model which is constrained to conserve a $U(1)$ charge and its dipole moment, motivated by the quantum dynamics of fracton phases. We discover that charge remains localized at its initial position, providing a crisp example of a non-ergodic dynamical phase of random circuit dynamics. This localization can be understood as a consequence of the return properties of low dimensional random walks, through a mechanism reminiscent of weak localization, but insensitive to dephasing. The charge dynamics is well-described by a system of coupled hydrodynamic equations, which makes several nontrivial predictions in good agreement with numerics. Importantly, these equations also predict localization in 2d fractonic circuits. Immobile fractonic charge emits non-conserved operators, whose spreading is governed by exponents distinct to non-fractonic circuits. Fractonic operators exhibit a short time linear growth of observable entanglement with saturation to an area law, as well as a subthermal volume law for operator entanglement. The entanglement spectrum follows semi-Poisson statistics, similar to eigenstates of MBL systems. The non-ergodic phenomenology persists to initial conditions containing non-zero density of dipolar or fractonic charge. Our work implies that low-dimensional fracton systems preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories. It also implies that 1d and 2d fracton systems should realize true MBL under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translation invariant systems and in d>1 being evaded by the nature of the mechanism responsible for localization. We also suggest a possible route to new non-ergodic phases in high dimensions.

cond-mat.stat-mech↗

arXiv2019

Localized surfaces of three dimensional topological insulators

We study the surface of a three-dimensional spin chiral $\mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of interaction and statistically-symmetric disorder, that confines the gapless fermionic degrees of freedom to a network of one-dimensional helical domain-walls that can be localized. We identify two distinct regimes of this gapless insulating phase, a `clogged' regime wherein the network localization is induced by its junctions between otherwise metallic helical domain-walls, and a `fully localized' regime of localized domain-walls. The experimental signatures of these regimes are also discussed.

cond-mat.str-el↗