arXiv subjects

S. A. Parameswaran

Publications and source records attributed to S. A. Parameswaran.

At least 55 records · Page 3Linked to original sources

arXiv2021

Hydrodynamic non-linear response of interacting integrable systems

We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.

cond-mat.str-el↗

arXiv2021

Domain wall competition in the Chern insulating regime of twisted bilayer graphene

We consider magic-angle twisted bilayer graphene (TBG) at filling $ν=+3$, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a valley- and spin-polarized Chern insulating ground state that spontaneously breaks time-reversal symmetry, and is stabilized by a hexagonal boron nitride (hBN) substrate. We identify three different types of domain wall, and study their properties and energetic selection mechanisms via theoretical arguments and Hartree-Fock calculations adapted to deal with inhomogeneous moiré systems. We comment on the implications of these results for transport and scanning probe experiments.

cond-mat.str-el↗

arXiv2021

Theory of competing excitonic orders in insulating WTe$_2$ monolayers

We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-excitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the WTe$_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link the competition between the excitonic phases to the orbital structure of electronic wavefunctions at the Fermi surface and hence its proximity to the underlying gapped Dirac point in WTe$_2$. We briefly discuss collective modes of the two excitonic states, and comment on implications for experiments.

cond-mat.str-el↗

arXiv2021

Beyond the Freshman's Dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models

We construct models hosting classical fractal spin liquids on two realistic three-dimensional (3D) lattices of corner-sharing triangles: trillium and hyperhyperkagome (HHK). Both models involve the same form of three-spin Ising interactions on triangular plaquettes as the Newman-Moore (NM) model on the 2D triangular lattice. However, in contrast to the NM model and its 3D generalizations, their degenerate ground states and low-lying excitations cannot be described in terms of scalar cellular automata (CA), because the corresponding fractal structures lack a simplifying algebraic property, often termed the 'Freshman's dream'. By identifying a link to matrix CAs -- that makes essential use of the crystallographic structure -- we show that both models exhibit fractal symmetries of a distinct class to the NM-type models. We devise a procedure to explicitly construct low-energy excitations consisting of finite sets of immobile defects or "fractons", by flipping arbitrarily large self-similar subsets of spins, whose fractal dimensions we compute analytically. We show that these excitations are associated with energetic barriers which increase logarithmically with system size, leading to "fragile" glassy dynamics, whose existence we confirm via classical Monte Carlo simulations. We also discuss consequences for spontaneous fractal symmetry breaking when quantum fluctuations are introduced by a transverse magnetic field, and propose multi-spin correlation function diagnostics for such transitions. Our findings suggest that matrix CAs may provide a fruitful route to identifying fractal symmetries and fracton-like behaviour in lattice models, with possible implications for the study of fracton topological order.

cond-mat.stat-mech↗

arXiv2021

Quantum oscillations in the zeroth Landau Level and the serpentine Landau fan

We identify an unusual mechanism for quantum oscillations in nodal semimetals, driven by a single pair of Landau levels periodically closing their gap at the Fermi energy as a magnetic field is varied. These `zero Landau level' quantum oscillations (ZQOs) appear in the nodal limit where the zero-field Fermi volume vanishes, and have distinctive periodicity and temperature dependence. We link the Landau spectrum of a two-dimensional (2D) nodal semimetal to the Rabi model, and show by exact solution that across the entire Landau fan, pairs of opposite-parity Landau levels are intertwined in a `serpentine' manner. We propose 2D surfaces of topological crystalline insulators as natural settings for ZQOs, and comment on implications for anomaly physics in 3D nodal semimetals.

cond-mat.mes-hall↗

arXiv2021

Exciton band topology in spontaneous quantum anomalous Hall insulators: applications to twisted bilayer graphene

We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite non-zero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently-reported broken-symmetry spontaneous QAH insulators in substrate aligned magic-angle twisted bilayer graphene.

cond-mat.str-el↗

arXiv2021

Superuniversality from disorder at two-dimensional topological phase transitions

We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons') identified with `electric charge' excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal' across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.

cond-mat.str-el↗

arXiv2020

Asymptotically exact theory for nonlinear spectroscopy of random quantum magnets

We study nonlinear response in quantum spin systems {near infinite-randomness critical points}. Nonlinear dynamical probes, such as two-dimensional (2D) coherent spectroscopy, can diagnose the nearly localized character of excitations in such systems. {We present exact results for nonlinear response in the 1D random transverse-field Ising model, from which we extract information about critical behavior that is absent in linear response. Our analysis yields exact scaling forms for the distribution functions of relaxation times that result from realistic channels for dissipation in random magnets}. We argue that our results capture the scaling of relaxation times and nonlinear response in generic random quantum magnets in any spatial dimension.

cond-mat.dis-nn↗

arXiv2020

Glide symmetry breaking and Ising criticality in the quasi-1D magnet CoNb$_2$O$_6$

We construct a microscopic spin-exchange Hamiltonian for the quasi-1D Ising magnet CoNb$_2$O$_6$ that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field-tuned quantum critical point in CoNb$_2$O$_6$ corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and `quasiparticle breakdown' in the polarized phase at high transverse field.

cond-mat.str-el↗

arXiv2020

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, that are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles. We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is sub-ballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via $x\sim t^{2/3}$) along both lines and at the $SO(4)$-symmetric point where they intersect. Our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.

cond-mat.stat-mech↗

arXiv2020

Odd Fracton Theories, Proximate Orders, and Parton Constructions

The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy non-trivial conditions on their low-energy properties when a combination of lattice translation and $U(1)$ symmetry are imposed. We describe a framework to characterize the action of symmetry on fractons and other sub-dimensional fractional excitations, and use this together with the LSM theorem to establish that X-cube fracton order can occur only at integer or half-odd-integer filling. Using explicit parton constructions, we demonstrate that "odd" versions of X-cube fracton order can occur in systems at half-odd-integer filling, generalizing the notion of odd $Z_2$ gauge theory to the fracton setting. At half-odd-integer filling, exiting the X-cube phase by condensing fractional quasiparticles leads to symmetry-breaking, thereby allowing us to identify a class of conventional ordered phases proximate to phases with fracton order. We leverage a dual description of one of these ordered phases to show that its topological defects naturally have restricted mobility. Condensing pairs of these defects then leads to a fracton phase, whose excitations inherit these mobility restrictions.

cond-mat.str-el↗

arXiv2020

Excitonic fractional quantum Hall hierarchy in Moiré heterostructures

We consider fractional quantum Hall states in systems where two flat Chern number $C=\pm 1$ bands are labeled by an approximately conserved 'valley' index and interchanged by time reversal symmetry. At filling factor $ν=1$ this setting admits an unusual hierarchy of correlated phases of excitons, neutral particle-hole pair excitations of a fully valley-polarized `orbital ferromagnet' parent state where all electrons occupy a single valley. Excitons experience an effective magnetic field due to the Chern numbers of the underlying bands. This obstructs their condensation in favor of a variety of crystalline orders and gapped and gapless liquid states. All these have the same quantized charge Hall response and are electrically incompressible, but differ in their edge structure, orbital magnetization, and hence valley and thermal responses. We explore the relevance of this scenario for Moiré heterostructures of bilayer graphene on a hexagonal boron nitride substrate.

cond-mat.str-el↗

arXiv2020

`Unhinging' the surfaces of higher-order topological insulators and superconductors

We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting $\mathsf{C}_{2n}\mathcal T$ symmetry upon the introduction of non-Abelian surface topological order. In both cases, the topological order on a single side surface breaks time reversal symmetry, but appears with its time-reversal conjugate on alternating sides in a $\mathsf{C}_{2n}\mathcal T$ preserving pattern. In the absence of the HOTI/HOTSC bulk, such a pattern necessarily involves gapless chiral modes on hinges between $\mathsf{C}_{2n}\mathcal T$-conjugate domains. However, using a combination of $K$-matrix and anyon condensation arguments, we show that on the boundary of a 3D HOTI/HOTSC these topological orders are fully gapped and hence `anomalous'. Our results suggest that new patterns of surface and hinge states can be engineered by selectively introducing topological order only on specific surfaces.

cond-mat.str-el↗

arXiv2020

Quantum oscillations probe the Fermi surface topology of the nodal-line semimetal CaAgAs

Nodal semimetals are a unique platform to explore topological signatures of the unusual band structure that can manifest by accumulating a nontrivial phase in quantum oscillations. Here we report a study of the de Haasvan Alphen oscillations of the candidate topological nodal line semimetal CaAgAs using torque measurements in magnetic fields up to 45 T. Our results are compared with calculations for a toroidal Fermi surface originating from the nodal ring. We find evidence of a nontrivial Berry phase shift only in one of the oscillatory frequencies. We interpret this as a Berry phase arising from the semi-classical electronic Landau orbit which links with the nodal ring when the magnetic field lies in the mirror (ab) plane. Furthermore, additional Berry phase accumulates while rotating the magnetic field for the second orbit in the same orientation which does not link with the nodal ring. These effects are expected in CaAgAs due to the lack of inversion symmetry. Our study experimentally demonstrates that CaAgAs is an ideal platform for exploring the physics of nodal line semimetals and our approach can be extended to other materials in which trivial and nontrivial oscillations are present.

cond-mat.str-el↗

arXiv2019

Distinguishing localization from chaos: challenges in finite-size systems

We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we argue that a recent study [Šuntajs et al., arXiv:1905.06345] of the behavior of the Thouless energy and level repulsion in disordered spin chains likely reaches misleading conclusions, in particular as to the absence of MBL as a true phase of matter.

cond-mat.str-el↗

arXiv2019

Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunnelling microscopy experiments on Bi(111) surfaces. We show that the domain wall properties depend sensitively on the filling factor $ν$ of the underlying (integer) quantum Hall states. For $ν=1$ and in the absence of impurity scattering we argue that the wall hosts a single-channel Luttinger liquid whose gaplessness is a consequence of valley and charge conservation. For $ν=2$, it supports a two-channel Luttinger liquid, which for sufficiently strong interactions enters a symmetry-preserving thermal metal phase with a charge gap coexisting with gapless neutral intervalley modes. The domain wall physics in this state is identical to that of a bosonic topological insulator protected by $U(1)\times U(1)$ symmetry, and we provide a formal mapping between these problems. We discuss other unusual properties and experimental signatures of these `anomalous' one-dimensional systems.

cond-mat.str-el↗

arXiv2019

Twisted bilayer graphene in a parallel magnetic field

We study the effect of an in-plane magnetic field on the non-interacting dispersion of twisted bilayer graphene. Our analysis is rooted in the chirally symmetric continuum model, whose zero-field band structure hosts exactly flat bands and large energy gaps at the magic angles. At the first magic angle, the central bands respond to a parallel field by forming a quadratic band crossing point (QBCP) at the Moire Brillouin zone center. Over a large range of fields, the dispersion is invariant with an overall scale set by the magnetic field strength. For deviations from the magic angle and for realistic interlayer couplings, the motion and merging of the Dirac points lying near charge neutrality are discussed in the context of the symmetries, and we show that small magnetic fields are able to induce a qualitative change in the energy spectrum. We conclude with a discussion on the possible ramifications of our study to the interacting ground states of twisted bilayer graphene systems.

cond-mat.str-el↗

arXiv2019

Classical Dimers on Penrose Tilings

We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings). Instead, their maximum matchings have a monomer density of $81-50φ\approx 0.098$ in the thermodynamic limit, with $φ=\left(1+\sqrt{5}\right)/2$ the golden ratio. Maximum matchings divide the tiling into a fractal of nested closed regions bounded by loops that cannot be crossed by monomers. These loops connect second-nearest neighbour even-valence vertices, each of which lies on such a loop. Assigning a charge to each monomer with a sign fixed by its bipartite sublattice, we find that each bounded region has an excess of one charge, and a corresponding set of monomers, with adjacent regions having opposite net charge. The infinite tiling is charge neutral. We devise a simple algorithm for generating maximum matchings, and demonstrate that maximum matchings form a connected manifold under local monomer-dimer rearrangements. We show that dart-kite Penrose tilings feature an imbalance of charge between bipartite sub-lattices, leading to a minimum monomer density of $\left(7-4φ\right)/5\approx 0.106$ all of one charge.

cond-mat.str-el↗