arXiv subjects

Sourav Nandy

Publications and source records attributed to Sourav Nandy.

17 recordsLinked to original sources

arXiv2025

Fate of diffusion under integrability breaking of classical integrable magnets

Diffusive transport is a ubiquitous phenomenon, yet the microscopic origin of diffusion in interacting physical systems remains a challenging question, irrespective of whether quantum effects are dominant or not. In this work, we study infinite temperature spin diffusion in a classical integrable, space-time discrete version of anisotropic Landau-Lifshitz magnet in the easy-axis regime, subjected to integrability-breaking perturbations. Our numerical results based on large-scale simulations reveal i) a sharp change in the spin diffusion constant as a function of perturbation strength in the thermodynamic limit and ii) a crossover from non-Gaussian to Gaussian statistics of magnetization transfer reflected in higher order cumulants under integrability breaking. Both our observations hint to the presence of non-trivial diffusion mechanism inherent to integrable systems.

cond-mat.stat-mech↗

arXiv2025

Boundary-driven magnetization transport in the spin-$1/2$ XXZ chain: Role of the system-bath coupling strength and timescales

Understanding the transport properties of quantum many-body systems is a central challenge in condensed matter and statistical physics. Theoretical studies usually rely on two main approaches: Dynamics of linear-response functions in closed systems and boundary-driven dynamics governed by Markovian master equations for open systems. While the equivalence of their dynamical behavior has been explored in recent studies, a systematic comparison of the transport coefficients obtained from these two classes of approaches remains a largely open question. Here, we address this gap by comparing and contrasting the dc diffusion constant $\mathcal{D}_{\text{dc}}$ according to the two approaches, focusing on the specific example of magnetization transport in the spin-$1/2$ XXZ chain. Using exact numerical simulations for finite system sizes, we find (i) a clear mismatch between the two $\mathcal{D}_{\text{dc}}$ and (ii) a strong dependence of $\mathcal{D}_{\text{dc}}$ on the system-bath coupling strength for the open system, where neither (i) nor (ii) tend to vanish in the thermodynamic limit. These findings suggest limitations of the open-system approach to transport coefficients. To gain insight into the origin of (i) and (ii), we go beyond $\mathcal{D}_{\text{dc}}$ and analyze the full time dependence of the diffusion coefficient $D(t)$ in the open system. In this way, we find that both (i) and (ii) vanish up to a finite time scale. While this time scale gradually increases with system size and tends to be macroscopic in the thermodynamic limit, this increase is still slow compared to the increase of the time to reach the steady state, where (i) and (ii) do not vanish. This observation can be seen as a wrong, yet unavoidable order of limits of long times first and large system sizes afterwards.

cond-mat.stat-mech↗

arXiv2024

Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains

Understanding the physics of the integrable spin-1/2 XXZ chain has witnessed substantial progress, due to the development and application of sophisticated analytical and numerical techniques. In particular, infinite-temperature magnetization transport has turned out to range from ballistic, over superdiffusive, to diffusive behavior in different parameter regimes of the anisotropy. Since integrability is rather the exception than the rule, a crucial question is the change of transport under integrability-breaking perturbations. This question includes the stability of superdiffusion at the isotropic point and the change of diffusion constants in the easy-axis regime. In our work, we study this change of diffusion constants by a variety of methods and cover both, linear response theory in the closed system and the Lindblad equation in the open system, where we throughout focus on periodic boundary conditions. In the closed system, we compare results from the recursion method to calculations for finite systems and find evidence for a continuous change of diffusion constants over the full range of perturbation strengths. In the open system weakly coupled to baths, we find diffusion constants in quantitative agreement with the ones in the closed system in a range of nonweak perturbations, but disagreement in the limit of weak perturbations. Using a simple model in this limit, we point out the possibility of a diverging diffusion constant in such an open system.

cond-mat.stat-mech↗

arXiv2024

Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions

We investigate the Lindblad equation in the context of boundary-driven magnetization transport in spin-$1/2$ chains. Our central question is whether the nonequilibrium steady state of the open system, including its buildup in time, can be described on the basis of the dynamics in the closed system. To this end, we rely on a previous work [Phys. Rev. B 108, L201119 (2023)], where a description in terms of spatio-temporal correlation functions has been suggested in the case of weak driving and small system-bath coupling. Because this work has focused on integrable systems and periodic boundary conditions, we here extend the analysis in three directions: We (i) consider nonintegrable systems, (ii) take into account open boundary conditions and other bath-coupling geometries, and (iii) provide a comparison to time-evolving block decimation. While we find that nonintegrability plays a minor role, the choice of the specific boundary conditions can be crucial, due to potentially nondecaying edge modes. Our large-scale numerical simulations suggest that a description based on closed-system correlation functions is an useful alternative to already existing state-of-the-art approaches.

cond-mat.stat-mech↗

arXiv2024

Einstein relation for subdiffusive relaxation in Stark chains

We investigate chains of interacting spinless fermions subject to a finite external field $F$ (also called Stark chains) and focus on the regime where the charge thermalization follows the subdiffusive hydrodynamics. First, we study reduced models conserving the dipole moment and derive an explicit Einstein relation which links the subdiffusive transport coefficient with the correlations of the dipolar current. This relation explains why the decay rate, $\Gamma_q$, of the density modulation with wave-vector $q$ shows $q^4$-dependence. In the case of the Stark model, a similar Einstein relation is also derived and tested using various numerical methods. They confirm an exponential reduction of the transport coefficient with increasing $F$. On the other hand, our study of the Stark model indicates that upon increasing $q$ there is a crossover from subdiffusive behavior, $\Gamma_q \propto q^4$, to the normal diffusive relaxation, $\Gamma_q \propto q^2$, at the wave vector $q^*$ which vanishes for $F \to 0$.

cond-mat.str-el↗

arXiv2024

Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2 \times Z_2$ symmetry, and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical point with a continuous phase transition. We compute the critical exponents $z$, $β$, $γ$ and $ν$, and the central charge $c$ numerically using exact diagonalization (ED) for systems with periodic boundary conditions. We find that both $z$ and $c$ are equal to $1$, implying that the critical point is governed by a conformal field theory. The values obtained for $β/ν$, $γ/ν$, and $ν$ from ED suggest that the model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between the four-state Potts model and two decoupled transverse field Ising models. An analysis on larger systems but with open boundaries using density-matrix renormalization group calculations, however, shows that the self-dual point may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates. A subset of these eigenstates have wave functions which are independent of $h$ and have unusual entanglement structure, suggesting that they are quantum many-body scars. The number of such states scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if $h \gg 1$ or $h \ll 1$. If $h$ is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

cond-mat.stat-mech↗

arXiv2023

Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions

State-of-the-art approaches to extract transport coefficients of many-body quantum systems broadly fall into two categories: (i) they target the linear-response regime in terms of equilibrium correlation functions of the closed system; or (ii) they consider an open-system situation typically modeled by a Lindblad equation, where a nonequilibrium steady state emerges from driving the system at its boundaries. While quantitative agreement between (i) and (ii) has been found for selected model and parameter choices, also disagreement has been pointed out in the literature. Studying magnetization transport in the spin-1/2 XXZ chain, we here demonstrate that at weak driving, the nonequilibrium steady state in an open system, including its buildup in time, can remarkably be constructed just on the basis of correlation functions in the closed system. We numerically illustrate this direct correspondence of closed-system and open-system dynamics, and show that it allows the treatment of comparatively large open systems, usually only accessible to matrix product state simulations. We also point out potential pitfalls when extracting transport coefficients from nonequilibrium steady states in finite systems.

cond-mat.stat-mech↗

arXiv2023

Reconstructing effective Hamiltonians from nonequilibrium (pre-)thermal steady states

Reconstructing Hamiltonians from local measurements is key to enabling reliable quantum simulation: both validating the implemented model, and identifying any left-over terms with sufficient precision is a problem of increasing importance. Here we propose a deep-learning-assisted variational algorithm for Hamiltonian reconstruction by pre-processing a dataset that is diagnosed to contain thermal measurements of local operators. We demonstrate the efficient and precise reconstruction of local Hamiltonians, while long-range interacting Hamiltonians are reconstructed approximately. Away from equilibrium, for periodically and random multipolar driven systems, we reconstruct the effective Hamiltonian widely used for Floquet engineering of metastable steady states. Moreover, our approach allows us to reconstruct an effective quasilocal Hamiltonian even in the heating regime beyond the validity of the prethermal plateau, where perturbative expansions fail.

quant-ph↗

arXiv2023

Quantum state complexity meets many-body scars

Scar eigenstates in a many-body system refers to a small subset of non-thermal finite energy density eigenstates embedded into an otherwise thermal spectrum. This novel non-thermal behaviour has been seen in recent experiments simulating a one-dimensional PXP model with a kinetically-constrained local Hilbert space realized by a chain of Rydberg atoms. We probe these small sets of special eigenstates starting from particular initial states by computing the spread complexity associated to time evolution of the PXP hamiltonian. Since the scar subspace in this model is embedded only loosely, the scar states form a weakly broken representation of the Lie Algebra. We demonstrate why a careful usage of the Forward Scattering Approximation (or similar strategies thereof) is required to extract an appropriate set of Lanczos coefficients in this case as the consequence of this approximate symmetry. This leads to a well defined notion of a closed Krylov subspace and consequently, that of spread complexity. We show how the spread complexity shows approximate revivals starting from both $|\mathbb{Z}_2\rangle$ and $|\mathbb{Z}_3\rangle$ states and how these revivals can be made more accurate by adding optimal perturbations to the bare Hamiltonian. We also investigate the case of the vacuum as the initial state, where revivals can be stabilized using an iterative process of adding few-body terms.

quant-ph↗

arXiv2020

Dephasing in strongly disordered interacting quantum wires

Many-body localization is a fascinating theoretical concept describing the intricate interplay of quantum interference, i.e. localization, with many-body interaction induced dephasing. Numerous computational tests and also several experiments have been put forward to support the basic concept. Typically, averages of time-dependent global observables have been considered, such as the charge imbalance. We here investigate within the disordered spin-less Hubbard ($t-V$) model how dephasing manifests in time dependent variances of observables. We find that after quenching a Néel state the local charge density exhibits strong temporal fluctuations with a damping that is sensitive to disorder $W$: variances decay in a power law manner, $t^{-ζ}$, with an exponent $ζ(W)$ strongly varying with $W$. A heuristic argument suggests the form, $ζ\approxα(W)ξ_\text{sp}$, where $ξ_\text{sp}(W)$ denotes the noninteracting localization length and $α(W)$ characterizes the multifractal structure of the dynamically active volume fraction of the many-body Hilbert space. In order to elucidate correlations underlying the damping mechanism, exact computations are compared with results from the time-dependent Hartree-Fock approximation. Implications for experimentally relevant observables, such as the imbalance, will be discussed.

cond-mat.dis-nn↗

arXiv2019

Collapse and revival of quantum many-body scars via Floquet engineering

The presence of quantum scars, athermal eigenstates of a many-body Hamiltonian with finite energy density, leads to absence of ergodicity and long-time coherent dynamics in closed quantum systems starting from simple initial states. Such non-ergodic coherent dynamics, where the system does not explore its entire phase space, has been experimentally observed in a chain of ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg chain, that the drive frequency acts as a tuning parameter for several reentrant transitions between ergodic and non-ergodic regimes. The former regime shows rapid thermalization of correlation functions and absence of scars in the spectrum of the system's Floquet Hamiltonian. The latter regime, in contrast, has scars in its Floquet spectrum which control the long-time coherent dynamics of correlation functions. Our results open a new possibility of drive frequency-induced tuning between ergodic and non-ergodic dynamics in experimentally realizable disorder-free quantum many-body systems.

quant-ph↗

arXiv2019

Transport across junctions of pseudospin-one fermions

We study transport across ballistic junctions of materials which host pseudospin-one fermions as emergent low-energy quasiparticles. The effective low-energy Hamiltonians of such fermions are described by integer spin Weyl models. We show that current conservation in such integer spin-$s$ Weyl systems requires continuity across a boundary of only $2s$ (out of $2s+1$) components of the wave function. Using the current conservation conditions, we study the transport between normal metal-barrier-normal metal (NBN) and normal metal-barrier-superconductor (NBS) junctions of such systems in the presence of an applied voltage $eV$. We show that for a specific value of the barrier potential $U_0$, such NBN junctions act as perfect collimators; any quasiparticle which is incident on the barrier with a non-zero angle of incidence is reflected back with unit probability for any barrier width $d$. We discover an interesting symmetry of this system, namely, the conductance is invariant under $U_0 \to 2(μ_L \pm eV)-U_0$, where $μ_L$ is the chemical potential and the +(-) sign corresponds to particle (hole) mediated transport. For NBS junctions with a proximity-induced $s$-wave pairing potential, which also display such a collimation, we chart out the properties of the subgap tunneling conductance $G$ as a function of the barrier strength and applied voltage. We point out the effect of the collimation on the subgap tunneling conductance of these NBS junctions and discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2018

Steady states of a quasiperiodically driven integrable system

Driven many-body quantum systems where some parameter in the Hamiltonian is varied quasiperiodically in time may exhibit nonequilibrium steady states that are qualitatively different from their periodically driven counterparts. Here we consider a prototypical integrable spin system, the spin-$1/2$ transverse field Ising model in one dimension, in a pulsed magnetic field. The time dependence of the field is taken to be quasiperiodic by choosing the pulses to be of two types that alternate according to a Fibonacci sequence. We show that a novel steady state emerges after an exponentially long time when local properties (or equivalently, reduced density matrices of subsystems with size much smaller than the full system) are considered. We use the temporal evolution of certain coarse-grained quantities in momentum space to understand this nonequilibrium steady state in more detail and show that unlike the previously known cases, this steady state is neither described by a periodic generalized Gibbs ensemble nor by an infinite temperature ensemble. Finally, we study a toy problem with a single two-level system driven by a Fibonacci sequence; this problem shows how sensitive the nature of the final steady state is to the different parameters.

cond-mat.str-el↗

arXiv2017

Periodically driven integrable systems with long-range pair potentials

We study periodically driven closed systems with a long-ranged Hamiltonian by considering a generalized Kitaev chain with pairing terms which decay with distance as a power law characterized by exponent $α$. Starting from an initial unentangled state, we show that all local quantities relax to well-defined steady state values in the thermodynamic limit and after $n \gg 1$ drive cycles for any $α$ and driving frequency $ω$. We introduce a distance measure, $\mathcal{D}_l(n)$, that characterizes the approach of the reduced density matrix of a subsystem of $l$ sites to its final steady state. We chart out the $n$ dependence of ${\mathcal D}_l(n)$ and identify a critical value $α=α_c$ below which they generically decay to zero as $(ω/n)^{1/2}$. For $α> α_c$, in contrast, ${\mathcal D}_l(n) \sim (ω/n)^{3/2}[(ω/n)^{1/2}]$ for $ω\to \infty [0]$ with at least one intermediate dynamical transition. We also study the mutual information propagation to understand the nature of the entanglement spreading in space with increasing $n$ for such systems. We point out existence of qualitatively new features in the space-time dependence of mutual information for $ω< ω^{(1)}_c$, where $ω^{(1)}_c$ is the largest critical frequency for the dynamical transition for a given $α$. One such feature is the presence of {\it multiple} light cone-like structures which persists even when $α$ is large. We also show that the nature of space-time dependence of the mutual information of long-ranged Hamiltonians with $α\le 2$ differs qualitatively from their short-ranged counterparts with $α> 2$ for any drive frequency and relate this difference to the behavior of the Floquet group velocity of such driven system.

cond-mat.str-el↗

arXiv2017

Aperiodically driven integrable systems and their emergent steady states

Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long time behavior of the local properties synchronize with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in at least two cases. While any typical realization of random noise causes eventual heating to an infinite temperature ensemble for all local properties in spite of the system being integrable, noise which is self-similar in time leads to an entirely different steady state, which we dub as "geometric generalized Gibbs ensemble", that emerges only after an astronomically large time scale. To understand the approach to steady state, we study the temporal behavior of certain coarse-grained quantities in momentum space that fully determine the reduced density matrix for a subsystem with size much smaller than the total system. Such quantities provide a concise description for any drive protocol in integrable systems that are reducible to a free fermion representation.

cond-mat.str-el↗

arXiv2016

Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state

We study a class of periodically driven $d-$dimensional integrable models and show that after $n$ drive cycles with frequency $ω$, pure states with non-area-law entanglement entropy $S_n(l) \sim l^{α(n,ω)}$ are generated, where $l$ is the linear dimension of the subsystem, and $d-1 \le α(n,ω) \le d$. We identify and analyze the crossover phenomenon from an area ($S \sim l^{ d-1}$ for $d\geq1$) to a volume ($S \sim l^{d}$) law and provide a criterion for their occurrence which constitutes a generalization of Hastings' theorem to driven integrable systems in one dimension. We also find that $S_n$ generically decays to $S_{\infty}$ as $(ω/n)^{(d+2)/2}$ for fast and $(ω/n)^{d/2}$ for slow periodic drives; these two dynamical phases are separated by a topological transition in the eigensprectrum of the Floquet Hamiltonian. This dynamical transition manifests itself in the temporal behavior of all local correlation functions and does not require a critical point crossing during the drive. We find that these dynamical phases show a rich re-entrant behavior as a function of $ω$ for $d=1$ models, and also discuss the dynamical transition for $d>1$ models. Finally, we study entanglement properties of the steady state and show that singular features (cusps and kinks in $d=1$) appear in $S_{\infty}$ as a function of $ω$ whenever there is a crossing of the Floquet bands. We discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2016

Eigenstate Gibbs Ensemble in Integrable Quantum Systems

The Eigenstate Thermalization Hypothesis implies that for a thermodynamically large system in one of its eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of {\it relevant} conserved quantities. In a generic system, only the energy plays that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and hence the reduced density matrix requires specification of an infinite number of parameters (Generalized Gibbs Ensemble). However, here we show by unbiased statistical sampling of the individual eigenstates with a given finite energy density, that the local description of an overwhelming majority of these states of even such an integrable system is actually Gibbs-like, i.e. requires only the energy density of the eigenstate. Rare eigenstates that cannot be represented by the Gibbs ensemble can also be sampled efficiently by our method and their local properties are then shown to be described by appropriately {\it truncated} Generalized Gibbs Ensembles. We further show that the presence of these rare eigenstates differentiates the model from the generic (non-integrable) case and leads to the system being described by a Generalized Gibbs Ensemble at long time under a unitary dynamics following a sudden quench, even when the initial state is a Gibbs-like eigenstate of the pre-quench Hamiltonian.

cond-mat.stat-mech↗