arXiv subjects

Vipin Kerala Varma

Publications and source records attributed to Vipin Kerala Varma.

At least 19 recordsLinked to original sources

arXiv2019

Diffusive transport in a quasiperiodic Fibonacci chain: absence of many-body localization at small interactions

We study high-temperature magnetization transport in a many-body spin-1/2 chain with on-site quasiperiodic potential governed by the Fibonacci rule. In the absence of interactions it is known that the system is critical with the transport described by a continuously varying dynamical exponent (from ballistic to localized) as a function of the on-site potential strength. Upon introducing weak interactions, we find that an anomalous noninteracting dynamical exponent becomes diffusive for any potential strength. This is borne out by a boundary-driven Lindblad dynamics as well as unitary dynamics, with agreeing diffusion constants. This must be contrasted to random potential where transport is subdiffusive at such small interactions. Mean-field treatment of the dynamics for small U always slows down the non-interacting dynamics to subdiffusion, and is therefore unable to describe diffusion in an interacting quasiperiodic system. Finally, briefly exploring larger interactions we find a regime of interaction-induced subdiffusive dynamics, despite the on-site potential itself having no "rare-regions".

cond-mat.str-el↗

arXiv2019

Length scales in the many-body localized phase and their spectral signatures

We compute and compare the decay lengths of several correlation functions and effective coupling constants in the many-body localized (MBL) phase. To this end, we consider the distribution of the logarithms of these couplings and correlators: in each case the log-coupling follows a normal distribution with mean and variance that grow linearly with separation. Thus, a localization length is asymptotically sharply defined for each of these quantities. These localization lengths differ numerically from one another, but all of them remain short up to the numerically observed MBL transition, indicating stability of the MBL phase against isolated ergodic inclusions. We also show how these broad distributions may be extracted using interferometric probes such as double electron-electron resonance (DEER) and the statistics of local spin precession frequencies.

cond-mat.str-el↗

arXiv2018

Asymmetry in energy versus spin transport in certain interacting, disordered systems

We study energy transport in XXZ spin chains driven to nonequilibrium configurations by thermal reservoirs of different temperatures at the boundaries. We discuss the transition between diffusive and subdiffusive transport regimes in sectors of zero and finite magnetization at high temperature. At large anisotropies we find that diffusive energy transport prevails over a large range of disorder strengths, which is in contrast to spin transport that is subdiffusive in the same regime for weak disorder strengths. However, when finite magnetization is induced, both energy and spin currents decay as a function of system size with the same exponent. Based on this, we conclude that diffusion of energy is much more pervasive than that of magnetization in these disordered spin-1/2 systems, and occurs across a significant range of the interaction-disorder parameter phase-space; we suggest this is due to conservation laws present in the clean XXZ limit.

cond-mat.dis-nn↗

arXiv2018

Anomalous and regular transport in spin 1/2 chains: AC conductivity

We study magnetization transport in anisotropic spin-$1/2$ chains governed by the integrable XXZ model with and without integrability-breaking perturbations at high temperatures ($T\to \infty$) using a hybrid approach that combines exact sum-rules with judiciously chosen Ansätze. In the integrable XXZ model we find (i) super-diffusion at the isotropic (Heisenberg) point, with frequency dependent conductivity $ σ'(ω\to 0) \sim |ω|^α$, where $α=-3/7$ in close numerical agreement with recent $t$-DMRG computations; (ii) a continuously drifting exponent from $α=-1^+$ in the XY limit of the model to $α>0$ within the Ising regime; and (iii) a diffusion constant saturating in the XY coupling deep in the Ising limit. We consider two kinds of integrability breaking perturbations --- a simple next-nearest-neighbor spin-flip term ($J_2$) and a three-spin assisted variant ($t_2$), natural in the fermion particle representation of the spin chain. In the first case we discover a remarkable sensitivity of $σ'(ω)$ to the sign of $J_2$, with enhanced low frequency spectral weight and a pronounced upward shift in the magnitude of $α$ for $J_2>0$. Perhaps even more surprising, we find sub-diffusion ($α>0$) over a range of $J_2<0$. By contrast, the effects of the \enquote{fermionic} three-spin perturbation are sign symmetric; this perturbation produces a clearly observable hydrodynamic relaxation. At large strength of the integrability breaking term $J_2\to \pm \infty$ the problem is effectively non-interacting (fermions hopping on odd and even sublattices) and we find $α\to -1$ behavior reminiscent of the XY limit of the XXZ chain. Exact diagonalization studies largely corroborate these findings at mid-frequencies.

cond-mat.str-el↗

arXiv2017

Finite-size anomalies of the Drude weight: role of symmetries and ensembles

We revisit the subtelties of computing the high temperature spin stiffness $D$ of the spin-$1/2$ XXZ chain using exact diagonalization to analyze its dependence on system symmetries and ensemble. Within the canonical ensemble and for states with zero magnetization, we find $D$ vanishes exactly due to spin-inversion symmetry for all but the anisotropies $\tilde Δ_{MN} = \cos(πM /N)$ with $N > M$ and coprime, provided system sizes $L \ge 2N$, for which states with different spin-inversion signature become degenerate due to the underlying $sl_2$ loop algebra symmetry. All these loop-algebra degenerate states carry finite currents which we conjecture [based on $L$ and anisotropies $\tilde Δ_{MN}$ (with $N<L/2$) available to us] to dominate the grand-canonical ensemble evaluation of $D$ in the thermodynamic limit. Including a magnetic flux not only breaks spin-inversion in the zero magnetization sector but also lifts the loop-algebra degeneracies in all symmetry sectors --- this effect is more pertinent at smaller $Δ$ due to the larger contributions to $D$ coming from the low-magnetization sectors which are more sensitive to the system's symmetries. Thus we generically find a finite $D$ for fluxed rings and arbitrary $0<Δ<1$ in both ensembles. In contrast, at the isotropic point and in the gapped phase ($Δ\ge 1$) $D$ is found to vanish in the thermodynamic limit, independent of symmetry or ensemble. Our analysis demonstrates how convergence to the thermodynamic limit within the gapless phase ($Δ< 1$) may be accelerated and the finite-size anomalies overcome: $D$ extrapolates nicely in the thermodynamic limit to either the recently computed lower-bound or the Thermodynamic Bethe Ansatz result provided both spin-inversion is broken and the additional degeneracies at the $\tilde Δ_{MN}$ anisotropies are lifted.

cond-mat.str-el↗

arXiv2017

Fractality in nonequilibrium steady states of quasiperiodic systems

We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular we focus on the Aubry-André-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a transparent and experimentally viable technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state. We also find that the dynamics in the nonequilibrium steady state depends on the length of the chain chosen: generic length chains harbour qualitatively slower transport (different scaling exponent) than Fibonacci length chains, which is in turn slower than in the closed system. We conjecture that such fractal nonequilibrium steady states should arise in generic driven critical systems that have fractal properties.

cond-mat.dis-nn↗

arXiv2017

Energy diffusion in the ergodic phase of a many body localizable spin chain

The phenomenon of many-body localization in disordered quantum many-body systems occurs when all transport is suppressed despite the fact that the excitations of the system interact. In this work we report on the numerical simulation of autonomous quantum dynamics for disordered Heisenberg chains when the system is prepared with an initial inhomogeneity in the energy density profile. Using exact diagonalisation and a dynamical code based on Krylov subspaces we are able to simulate dynamics for up to L = 26 spins. We find, surprisingly, the breakdown of energy diffusion even before the many-body localization transition whilst the system is still in the ergodic phase. Moreover, in the ergodic phase we also find a large region in parameter space where the energy dynamics remains diffusive but where spin transport has been previously evidenced to occur only subdiffusively: this is found to be true for initial states composed of infinitely many hydrodynamic modes (square-wave energy profile) or just the single longest mode (sinusoidal profile). This suggestive finding points towards a peculiar ergodic phase where particles are transported slower than energy, reminiscent of the situation in amorphous solids and of the gapped phase of the anisotropic Heisenberg model.

cond-mat.dis-nn↗

arXiv2017

Massively parallel implementation and approaches to simulate quantum dynamics using Krylov subspace techniques

We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel libraries such as PETSc/SLEPc combined with high-performance computing approaches in order to overcome the large memory requirements to be able to study systems whose Hilbert space dimension comprises over 9 billion independent quantum states. Moreover, we provide descriptions on the parallel approach used for the three most important stages of the simulation: handling the Hilbert subspace basis, constructing a matrix representation for a generic Hamiltonian operator and the time evolution of the system by means of the Krylov subspace methods. We employ our setup to study the evolution of quasidisordered and clean many-body systems, focussing on the return probability and related dynamical exponents: the large system sizes accessible provide novel insights into their thermalization properties.

physics.comp-ph↗

arXiv2016

Localization of interacting Fermi gases in quasiperiodic potentials

We investigate the zero-temperature metal-insulator transition in a one-dimensional two-component Fermi gas in the presence of a quasi-periodic potential resulting from the superposition of two optical lattices of equal intensity but incommensurate periods. A mobility edge separating (low energy) Anderson localized and (high energy) extended single-particle states appears in this continuous-space model beyond a critical intensity of the quasi-periodic potential. In order to discern the metallic phase from the insulating phase in the interacting many-fermion system, we employ unbiased quantum Monte Carlo (QMC) simulations combined with the many-particle localization length familiar from the modern theory of the insulating state. In the noninteracting limit, the critical optical-lattice intensity for the metal-insulator transition predicted by the QMC simulations coincides with the Anderson localization transition of the single-particle eigenstates. We show that weak repulsive interactions induce a shift of this critical point towards larger intensities, meaning that repulsion favors metallic behavior. This shift appears to be linear in the interaction parameter, suggesting that even infinitesimal interactions can affect the position of the critical point.

cond-mat.quant-gas↗

arXiv2016

Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system

We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems.

cond-mat.dis-nn↗

arXiv2016

Entanglement and Majorana edge states in the Kitaev model

We investigate the von Neumann entanglement entropy and Schmidt gap in the ground state of the Kitaev model on the honeycomb lattice for square and cylindrical subsystems. We find that, for both the subsystems, the free-fermionic contribution to the entanglement entropy $S_E$ exhibits signatures of the phase transitions between the gapless and gapped phases. However, we find that $S_E$ does not show an expected monotonic behaviour as a function of the coupling $J_z$ between the suitably defined one-dimensional chains within the gapless phase for either geometry; moreover the system generically reaches a point of minimum entanglement within the gapless phase before the entanglement saturates or increases again until the gapped phase is reached. This may be attributed to the competition between the nearest neighbour correlation functions of the $x-x$ and $z-z$ bonds, and to the onset of gapless $\vec{k}$-modes in the bulk spectrum. On the other hand $S_E$ always monotonically varies with $J_z$ in the gapped phase independent of the subregion size or shape. Finally, further confirming the Li-Haldane conjecture, we find that the Schmidt gap $Δ$ defined from the entanglement spectrum also signals the topological transitions but only if there are corresponding zero energy Majorana edge states that simultaneously appear or disappear across the transitions. We analytically corroborate some of our results on entanglement entropy, Schmidt gap and the bulk-edge correspondence using perturbation theory.

cond-mat.str-el↗

arXiv2016

Conduction in quasi-periodic and quasi-random lattices: Fibonacci, Riemann, and Anderson models

We study the ground state conduction properties of noninteracting electrons in aperiodic but non-random one-dimensional models with chiral symmetry, and make comparisons against Anderson models with non-deterministic disorder. The first model we consider is the Fibonacci lattice, which is a paradigmatic model of quasicrystals; the second is the Riemann lattice, which we define inspired by Dyson's proposal on the possible connection between the Riemann hypothesis and a suitably defined quasicrystal. Our analysis is based on Kohn's many-particle localization tensor defined within the modern theory of the insulating state. In the Fibonacci quasicrystal, where all single-particle eigenstates are critical (i.e., intermediate between ergodic and localized), the noninteracting electron gas is found to be a conductor at most electron densities, including the half-filled case; however, at various specific fillings $ρ$, including the values $ρ= 1/g^n$, where $g$ is the golden ratio and $n$ is any integer, the gas turns into an insulator due to spectral gaps. Metallic behaviour is found at half-filling in the Riemann lattice as well; however, in contrast to the Fibonacci quasicrystal, the Riemann lattice is generically an insulator due to single-particle eigenstate localization, likely at all other fillings. Its behaviour turns out to be alike that of the off-diagonal Anderson model, albeit with different system-size scaling of the band-centre anomalies. The advantages of analysing the Kohn's localization tensor instead of other measures of localization familiar from the theory of Anderson insulators (such as the participation ratio or the Lyapunov exponent) are highlighted.

cond-mat.dis-nn↗

arXiv2015

Kohn's localisation in disordered fermionic systems with and without interactions

Understanding the metal-insulator transition in disordered many-fermion systems, both with and without interactions, is one of the most challenging and consequential problems in condensed matter physics. In this paper we address this issue from the perspective of the modern theory of the insulating state (MTIS), which has already proven to be effective for band and Mott insulators in clean systems. First we consider noninteracting systems with different types of aperiodic external potentials: uncorrelated disorder (one-dimensional Anderson model), deterministic disorder (Aubry-André Hamiltonian and its modification including next-nearest neighbour hopping), and disorder with long-range correlations (self-affine potential). We show how the many-body localisation tensor defined within the MTIS may be used as a powerful probe to discriminate the insulating and the metallic phases, and to locate the transition point. Then we investigate the effect of weak repulsive interactions in the Aubry-André Hamiltonian, a model which describes a recent cold-atoms experiment. By treating the weak interactions within a mean-field approximation we obtain a linear shift of the transition point towards stronger disorder, providing evidence for delocalisation induced by interactions.

cond-mat.dis-nn↗

arXiv2015

Interaction-induced Drude weight enhancement in frustrated systems

We investigate the effect of next nearest-neighbour hopping on the zero temperature Drude weight or superfluidity in mesoscopic one-dimensional systems of (a) single particle with quasidisorder (Aubry-André model) and (b) hardcore bosons with nearest-neighbour interaction. We show that there is an interaction-induced enhancement of the Drude weight when the next nearest-neighbour hopping is frustrated for the many-body system. The observed non-monotonic behaviour of the Drude weight occurs because the repulsive interactions first suppress the frustration in the system, leading to a rise in the Drude weight, whereas at much larger interaction strengths the charge density wave fluctuations set in the insulator and the Drude weight drops. The present work reveals a novel scenario in which a persistent flow enhancement is plausible in the presence of kinetic frustration and repulsive interactions.

cond-mat.str-el↗

arXiv2014

Conformal map and harmonic measure of the Bunimovich stadium

We consider the conformal mapping of the Bunimovich stadium, a region enclosed by a Jordan curve with four smooth corners, primarily in the context of a particle undergoing Brownian motion within its closed geometry with Dirichlet boundary conditions. A Chebyshev weighting of the solutions of Symm's integral equation is employed to give a numerical conformal map of the region onto the canonical domain of the unit disk in the complex plane. As a measure of the accuracy of the transformation, the domes' harmonic measure evaluated at the centre of the stadium is thereby extracted and is compared with results obtained from Schwarz-Christoffel transformations and Monte Carlo simulations; the pros and cons of the method are reiterated.

math.NA↗

arXiv2014

Renormalization of two-body interactions due to higher-body interactions of lattice bosons

We calculate thermodynamic properties of soft-core lattice bosons with on-site $n$-body interactions using up to twelfth and tenth order strong coupling expansion in one and two dimensional cubic lattices at zero temperature. Using linked cluster techniques, we show that it is possible to exactly renormalize the two-body interactions for quasiparticle excitations and ground-state energy by resumming the three and four body terms in the system, which suggests that all higher-body on-site interactions may be exactly and perturbatively resummed into the two-body terms for similar system observables. The renormalization procedure that we develop is applicable to a broad range of systems analyzable by linked cluster expansions, ranging from perturbative quantum chromodynamics to spin models, giving either an exact or approximate resummation depending on the specific system and properties. Universality at various three-body interaction strengths for the two dimensional boson Hubbard model is checked numerically.

cond-mat.quant-gas↗

arXiv2013

Antiferromagnetic Ising model saturation field entropies: ladders and kagome lattice

Saturation field entropies of antiferromagnetic Ising models on quasi one-dimensional lattices (ladders) and the kagome lattice are calculated. The former is evaluated exactly by constructing the corresponding transfer matrices, while the latter calculation uses Binder's algorithm for efficiently and exactly computing the partition function of over 1300 spins to give, in Boltzmann's units, S = 0.393589(6). We comment on the relation of the kagome lattice to the experimental situation in the spin-ice compound dysprosium titanium oxide.

cond-mat.stat-mech↗

arXiv2012

Spin wave theory for interacting hardcore bosons on cubic lattices: a comparative study

Motivated by excellent comparisons of spin wave theory (SWT) with Quantum Monte Carlo (QMC) calculations of non-interacting hardore bosons (Bernardet et al.) and superlattices (Hen et al.), we develop an SWT for interacting hardcore bosons on a d-dimensional cubic lattice at zero temperature and compare thermodynamical properties with results of Stochastic Series Expansions (SSE): there is good comparison between SWT and SSE results for the simple cubic lattice at small repulsive strengths but differences arise between the results of the two approaches for the square lattice at strong repulsions. The boundaries of the three phases - Mott insulating (MI), superfluid (SF) and Néel solid (NS) - can be readily estimated from calculations of particle density, signalling either a first order (SF <--> NS) or second order transition (MI <--> SF). Comparison is made with results of the Bethe ansatz in one dimension and QMC in two dimensions.

cond-mat.str-el↗