arXiv subjects

Adway Kumar Das

Publications and source records attributed to Adway Kumar Das.

16 recordsLinked to original sources

arXiv2026

Identifying mobility edge from finite temperature spectral form factor

The spectral form factor (SFF) is a measure of energy correlations and has been widely used to identify the transition from the ergodic to the localized phase in interacting many-body quantum systems. In this work, we show that in a disordered Heisenberg spin-$\frac{1}{2}$ model, the finite temperature SFF can be used to generate a canonical phase diagram exhibiting a critical temperature $T_\mathrm{MBL}$. Using simple ideas of statistical mechanics, we obtain the critical energy density $\epsilon_\mathrm{MBL}$ dual to $T_\mathrm{MBL}$. We show that the mobility edge, numerically estimated from the spread of local perturbations and the optical conductivity, indeed coincides with $\epsilon_\mathrm{MBL}$.

cond-mat.dis-nn↗

arXiv2026

Signatures of Nonergodicity in Sparse Random Matrices

The prevalence of sparsity in interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically demonstrate that the Anderson transition can be identified through the statistical properties of the ground state. By analytically deriving the energy moments and calculating the shifted kurtosis, we estimate the critical sparsity threshold for this localization-delocalization transition. The short-range energy correlation in the bulk indicates that the Anderson transition at infinite temperature coincides with the quantum phase transition. Furthermore, long-range energy correlations in the bulk spectrum reveal a Thouless energy scale, suggesting a broad nonergodic regime within the delocalized phase.

cond-mat.dis-nn↗

arXiv2026

Ground state and persistent oscillations in the quantum East model

For the 1D quantum East model with open boundaries, we show that in the limit $s \to -\infty$, the ground state is accurately captured by a simple spin-coherent product state. We further identify a low-entanglement excited eigenstate that differs from the ground state only by a $π$-rotation of the boundary spin, remaining well approximated by a spin-coherent state. For a range of $-\infty<s<0$, the edge-coherent product state overlaps with two eigenstates separated by a size-independent energy gap, leading to persistent coherent oscillations of both global and local observables in the thermodynamic limit. These oscillations originate from boundary physics and are distinct from quantum many-body scars or hypercube-like Fock-space mechanisms.

quant-ph↗

arXiv2025

Spectral statistics, non-equilibrium dynamics and thermalization in random matrices with global $\mathbb{Z}_2$-symmetry

$\mathbb{Z}_2$ symmetry is ubiquitous in quantum mechanics where it drives various phase transitions and emergent physics. The role of $\mathbb{Z}_2$ symmetry in the thermalization of a local observable in a disordered system can be understood using random matrix theory. To do so, we consider random symmetric centrosymmetric (SC) matrix as a toy model where a $\mathbb{Z}_2$ symmetry, namely, the exchange symmetry is conserved. Such a conservation law splits the Hilbert space into decoupled subspaces such that the energy spectrum of a SC matrix is a superposition of two pure spectra. After discussing the known results on the correlations of such mixed spectrum, we consider different initial states and analytically compute the time evolution of their survival probability and associated timescales. We show that there exist certain low-energy initial states which do not decay over a very long timescales such that a measure zero fraction of random SC matrices exhibit spontaneous symmetry breaking. Later, we look at the equilibrium values of local observables like the density-density correlation, kinetic energy operator and compare them against the average values from the microcanonical and canonical ensembles. We find that when the observable violates (respects) the global symmetry of the Hamiltonian, the equilibrium value is independent (dependent) of the symmetry of the initial state. However, irrespective of such symmetry constraints, the fluctuations of the diagonal terms of the observables within microcanonical shells decay with system size such that the ansatz of eigenstate thermalization hypothesis remains valid. We show that the equilibrium value converges to the canonical average for all the observables and initial states, indicating that thermalization occurs despite the presence of a global symmetry.

cond-mat.stat-mech↗

arXiv2025

Anomalous energy correlations and spectral form factor in the nonergodic phase of the $β$-ensemble

The $β$-ensemble is a prototypical model of a single particle system on a one-dimensional disordered lattice with inhomogeneous nearest neighbor hopping. Corresponding nonergodic phase has an anomalous critical energy scale, $E_c$: correlations are present above and absent below $E_c$ as reflected in the number variance. We study the dynamical properties of the $β$-ensemble where the critical energy controls the characteristic timescales. In particular, the spectral form factor equilibrates at a relaxation time, $t_\mathrm{R} \equiv E_c^{-1}$, which is parametrically smaller than the Heisenberg time, $t_\mathrm{H}$, given by the inverse of the mean level spacing. Incidentally, the dimensionless relaxation time, $τ_\mathrm{R} \equiv t_\mathrm{R}/t_\mathrm{H} \ll 1$ is equal to the Dyson index, $β$. We show that the energy correlations are absent within a temporal window $t_\mathrm{R} < t < t_\mathrm{H}$, which we term as the correlation void. This is in contrast to the mechanism of equilibration in a typical many-body system. We analytically explain the qualitative behavior of the number variance and the spectral form factor of the $β$-ensemble by a spatially local mapping to the Anderson model.

cond-mat.dis-nn↗

arXiv2025

Spectral form factor and energy correlations in banded random matrices

Banded random matrices were introduced as a more realistic alternative to full random matrices for describing the spectral statistics of heavy nuclei. Initially considered by Wigner, they have since become a paradigmatic model for investigating level statistics and the localization-delocalization transition in disordered quantum systems. In this work, we demonstrate that, despite the absence of short-range energy correlations, weak long-range energy correlations persist in the nonergodic phase of banded random matrices. This result is supported by our numerical and analytical studies of quantities that probe both short- and long-range energy correlations, namely, the spectral form factor, level number variance, and power spectrum. We derive the timescales for the onset of spectral correlations (ramp) and for the saturation (plateau) of the spectral form factor. Unexpectedly, we find that in the nonergodic phase, these timescales decrease as the bandwidth of the matrices is reduced. We also show that the high-frequency behavior of the power spectrum of energy fluctuations can distinguish between the nonergodic and ergodic phases of the banded random matrices.

cond-mat.dis-nn↗

arXiv2025

Proposal for many-body quantum chaos detection with single-site measurements

We demonstrate that the long-time dynamics of an observable associated with a single lattice site is sufficient to determine whether a many-body quantum system exhibits level statistics characteristic of random matrix theory, a widely used diagnostic of quantum chaos. In particular, we focus on the partial survival probability and spin autocorrelation function at a single site, both evolved under a disordered spin-1/2 chain, which is a setup realizable in current experimental platforms. Given the precision and timescales currently achievable, our results indicate that the detection of many-body quantum chaos is feasible, but constrained to small system sizes.

cond-mat.stat-mech↗

arXiv2025

Proposal for many-body quantum chaos detection

In this work, the term ``quantum chaos'' refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using e.g.~the spectral form factor, which detects both short- and long-range level correlations. The spectral form factor corresponds to the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole) when the system is chaotic. We discuss how this structure could be detected through the quench dynamics of two physical quantities accessible to experimental many-body quantum systems: the survival probability and the spin autocorrelation function. The survival probability is equivalent to the spectral form factor with an additional filter. When the system is small, the dip of the correlation hole reaches sufficiently large values at times which are short enough to be detected with current experimental platforms. As the system is pushed away from chaos, the correlation hole disappears, signaling integrability or localization. We also provide a relatively shallow circuit with which the correlation hole could be detected with commercially available quantum computers.

cond-mat.stat-mech↗

arXiv2025

Emergent multifractality in power-law decaying eigenstates

Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates which allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1d tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions which are in agreement with numerical simulations.

cond-mat.dis-nn↗

arXiv2023

Robust non-ergodicity of ground state in the $β$ ensemble

In various chaotic quantum many-body systems, the ground states show non-trivial athermal behavior despite the bulk states exhibiting thermalization. Such athermal states play a crucial role in quantum information theory and its applications. Moreover, any generic quantum many-body system in the Krylov basis is represented by a tridiagonal Lanczos Hamiltonian, which is analogous to the matrices from the $β$ ensemble, a well-studied random matrix model with level repulsion tunable via the parameter $β$. Motivated by this, here we focus on the localization properties of the ground and anti-ground states of the $β$ ensemble. Both analytically and numerically, we show that both the edge states demonstrate non-ergodic (fractal) properties for $β\sim\mathcal{O}(1)$ while the typical bulk states are ergodic. Surprisingly, the fractal dimension of the edge states remain three time smaller than that of the bulk states irrespective of the global phase of the $β$ ensemble. In addition to the fractal dimensions, we also consider the distribution of the localization centers of the spectral edge states, their mutual separation, as well as the spatial and correlation properties of the first excited states.

cond-mat.dis-nn↗

arXiv2023

Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles

We introduce a two-parameter ensemble of generalized $2\times 2$ real symmetric random matrices called the $β$-Rosenzweig-Porter ensemble (\brpe), parameterized by $β$, a fictitious inverse temperature of the analogous Coulomb gas model, and $γ$, controlling the relative strength of disorder. \brpe\ encompasses RPE from all of the Dyson's threefold symmetry classes: orthogonal, unitary and symplectic for $β=1,2,4$. Firstly, we study the energy correlations by calculating the density and 2nd moment of the Nearest Neighbor Spacing (NNS) and robustly quantify the crossover among various degrees of level repulsions. Secondly, the dynamical properties are determined from an exact calculation of the temporal evolution of the fidelity enabling an identification of the characteristic Thouless and the equilibration timescales. The relative depth of the correlation hole in the average fidelity serves as a dynamical signature of the crossover from chaos to integrability and enables us to construct the phase diagram of \brpe\ in the $γ$-$β$ plane. Our results are in qualitative agreement with numerically computed fidelity for $N\gg2$ matrix ensembles. Furthermore, we observe that for large $N$ the 2nd moment of NNS and the relative depth of the correlation hole exhibit a second order phase transition at $γ=2$.

cond-mat.dis-nn↗

arXiv2023

Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States

Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we provide an example of a nearest-neighbor tight-binding disordered model which carries both localized and extended states without forming the mobility edge (ME). Unexpectedly, this example appears to be given by a well-studied $β$-ensemble with independently distributed random diagonal potential and inhomogeneous kinetic hopping terms. In order to analytically tackle the problem, we locally map the above model to the 1D Anderson model with matrix-size- and position-dependent hopping and confirm the coexistence of localized and extended states, which is shown to be robust to the perturbations of both potential and kinetic terms due to the separation of the above states in space. In addition, the mapping shows that the extended states are non-ergodic and allows to analytically estimate their fractal dimensions.

cond-mat.dis-nn↗

arXiv2022

Transport in deformed centrosymmetric networks

Centrosymmetry often mediates Perfect State Transfer (PST) in various complex systems ranging from quantum wires to photosynthetic networks. We introduce the Deformed Centrosymmetric Ensemble (DCE) of random matrices, $H(λ) \equiv H_+ + λH_-$, where $H_+$ is centrosymmetric while $H_-$ is skew-centrosymmetric. The relative strength of the $H_\pm$ prompts the system size scaling of the control parameter as $λ= N^{-\fracγ{2}}$. We propose two quantities, $\mathcal{P}$ and $\mathcal{C}$, quantifying centro- and skewcentro-symmetry, respectively, exhibiting second order phase transitions at $γ_\text{P}\equiv 1$ and $γ_\text{C}\equiv -1$. In addition, DCE posses an ergodic transition at $γ_\text{E} \equiv 0$. Thus equipped with a precise control of the extent of centrosymmetry in DCE, we study the manifestation of $γ$ on the transport properties of complex networks. We propose that such random networks can be constructed using the eigenvectors of $H(λ)$ and establish that the maximum transfer fidelity, $F_T$, is equivalent to the degree of centrosymmetry, $\mathcal{P}$.

cond-mat.dis-nn↗

arXiv2022

Chaos due to symmetry-breaking in deformed Poisson ensemble

The competition between strength and correlation of coupling terms in a Hamiltonian defines numerous phenomenological models exhibiting spectral properties interpolating between those of Poisson (integrable) and Wigner-Dyson (chaotic) ensembles. It is important to understand how the off-diagonal terms of a Hamiltonian evolve as one or more symmetries of an integrable system are explicitly broken. We introduce a deformed Poisson ensemble to demonstrate an exact mapping of the coupling terms to the underlying symmetries of a Hamiltonian. From the maximum entropy principle we predict a chaotic limit which is numerically verified from the spectral properties and the survival probability calculations.

nlin.CD↗

arXiv2022

Non-ergodic extended states in $β$-ensemble

Matrix models showing chaotic-integrable transition in the spectral statistics are important for understanding Many Body Localization (MBL) in physical systems. One such example is the $β$-ensemble, known for its structural simplicity. However, eigenvector properties of $β$-ensemble remain largely unexplored, despite energy level correlations being thoroughly studied. In this work we numerically study the eigenvector properties of $β$-ensemble and find that the Anderson transition occurs at $γ= 1$ and ergodicity breaks down at $γ= 0$ if we express the repulsion parameter as $β= N^{-γ}$. Thus other than Rosenzweig-Porter ensemble (RPE), $β$-ensemble is another example where Non-Ergodic Extended (NEE) states are observed over a finite interval of parameter values ($0 < γ< 1$). We find that the chaotic-integrable transition coincides with the breaking of ergodicity in $β$-ensemble but with the localization transition in the RPE or the 1-D disordered spin-1/2 Heisenberg model where this coincidence occurs at the localization transition. As a result, the dynamical time-scales in the NEE regime of $β$-ensemble behave differently than the later models.

cond-mat.dis-nn↗

arXiv2019

Eigenvalue Statistics for Generalized Symmetric and Hermitian Matrices

The Nearest Neighbour Spacing (NNS) distribution can be computed for generalized symmetric 2x2 matrices having different variances in the diagonal and in the off-diagonal elements. Tuning the relative value of the variances we show that the distributions of the level spacings exhibit a crossover from clustering to repulsion as in GOE. The analysis is extended to 3x3 matrices where distributions of NNS as well as Ratio of Nearest Neighbour Spacing (RNNS) show similar crossovers. We show that it is possible to calculate NNS distributions for Hermitian matrices (N=2, 3) where also crossovers take place between clustering and repulsion as in GUE. For large symmetric and Hermitian matrices we use interpolation between clustered and repulsive regimes and identify phase diagrams with respect to the variances.

nlin.CD↗