arXiv subjects

Soumi Ghosh

Publications and source records attributed to Soumi Ghosh.

9 recordsLinked to original sources

arXiv2025

Witnessing Short- and Long-Range Nonstabilizerness via the Information Lattice

We study nonstabilizerness on the information lattice, and demonstrate that noninteger local information directly indicates nonstabilizerness. For states with a clear separation of short- and large-scale information, noninteger total information at large scales $\Gamma$ serves as a witness of long-range nonstabilizerness. We propose a folding procedure to separate the global and edge-to-edge contributions to $\Gamma$. As an example we show that the ferromagnetic ground state of the spin-1/2 three-state Potts model has long-range nonstabilizerness originating from global correlations, while the paramagnetic ground state has at most short-range nonstabilizerness.

quant-ph↗

arXiv2024

Scaling of Fock space propagator in quasiperiodic many-body localizing systems

Recently many body localized systems have been treated as a hopping problem on a Fock space lattice with correlated disorder, where the many-body eigenstates exhibit multi-fractal character. The many-body propagator in Fock space has been shown to be useful for capturing this multifractality and extracting a Fock-space localization length for systems with random disorder in real space. Here we study a one-dimensional interacting system of spinless Fermions in the presence of a deterministic quasiperiodic potential using the Fock-space propagator. From the system-size scaling of the self-energy associated with the diagonal elements and the scaling of the off-diagonal elements of the propagator, we extract fractal characteristics and FS localization lengths, respectively, which behave similarly to that in the random system. We compute the sample-to-sample fluctuations of the typical self-energy and the off-diagonal propagator over different realizations of the potential and show that the fluctuations in the self-energy distinguish quasiperiodic and random systems, whereas the fluctuations of the off-diagonal elements cannot demarcate the two types of potential.

cond-mat.dis-nn↗

arXiv2023

Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices

The dynamics of non-Hermitian quantum systems have taken on an increasing relevance in light of quantum devices which are not perfectly isolated from their environment. The interest in them also stems from their fundamental differences from their Hermitian counterparts, particularly with regard to their spectral and eigenvector correlations. These correlations form the fundamental building block for understanding the dynamics of quantum systems as all other correlations can be reconstructed from it. In this work, we study such correlations across a localisation transition in non-Hermitian quantum systems. As a concrete setting, we consider non-Hermitian power-law banded random matrices which have emerged as a promising platform for studying localisation in disordered, non-Hermitian systems. We show that eigenvector correlations show marked differences between the delocalised and localised phases. In the delocalised phase, the eigenvectors are strongly correlated as evinced by divergent correlations in the limit of vanishingly small complex eigenvalue spacings. On the contrary, in the localised phase, the correlations are independent of the eigenvalue spacings. We explain our results in the delocalised phase by appealing to the Ginibre random matrix ensemble. On the other hand, in the localised phase, an analytical treatment sheds light on the suppressed correlations, relative to the delocalised phase. Given that eigenvector correlations are fundamental ingredients towards understanding real- and imaginary-time dynamics with non-Hermitian generators, our results open a new avenue for characterising dynamical phases in non-Hermitian quantum many-body systems.

cond-mat.dis-nn↗

arXiv2022

Scaling of Fock-space propagator and multifractality across the many-body localization transition

We implement a recursive Green function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random onsite potential. We show that the typical value of the imaginary part of the local FS self-energy, Δ_t, related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition; and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength W. In particular, we show that a fractal dimension D_s extracted from Δ_t jumps discontinuously across the transition, from D_s<1 in the MBL phase to D_s= 1 in the thermal phase. Moreover, Δ_t follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a non-ergodic volume in the thermal phase diverges with a Kosterlitz-Thouless like essential singularity at the critical point W_c, and controls the continuous vanishing of Δ_t as W_c is approached. In contrast, a correlation length (ξ) extracted from Δ_t exhibits a power-law divergence on approaching W_c from the MBL phase.

cond-mat.dis-nn↗

arXiv2022

Spectral Properties of Disordered Interacting Non-Hermitian Systems

Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian interacting disordered Hamiltonians and attempt to analyze their chaotic behavior or lack of it through the lens of the recently introduced non-hermitian analog of the spectral form factor and the complex spacing ratio. We consider three widely relevant non-hermitian models which are unique in their ways and serve as excellent platforms for such investigations. Two of the models considered are short-ranged and have different symmetries. The third model is long-ranged, whose hermitian counterpart has itself become a subject of growing interest. All these models exhibit a deep connection with the non-hermitian Random Matrix Theory of corresponding symmetry classes at relatively weak disorder. At relatively strong disorder, the models show the absence of complex eigenvalue correlation, thereby, corresponding to Poisson statistics. Our thorough analysis is expected to play a crucial role in understanding disordered open quantum systems in general.

cond-mat.dis-nn↗

arXiv2020

Transport in the non-ergodic extended phase of interacting quasiperiodic systems

We study the transport properties and the spectral statistics of a one-dimensional closed quantum system of interacting spinless fermions in a quasiperiodic potential which produces a single particle mobility edge in the absence of interaction. For such systems, it has been shown that the many body eigenstates can be of three different kinds: extended and ETH (eigenstate thermalization hypothesis) obeying (thermal), localized and ETH violating (many body localized) and extended and ETH violating (non-ergodic extended). Here we investigate the non-ergodic extended phase from the point of view of level spacing statistics and charge transport. We calculate the dc conductivity and the low frequency conductivity $σ(ω)$ and show that both are consistent with sub-diffusive transport. This is contrasted with diffusive transport in the thermal phase and blocked transport in the MBL phase.

cond-mat.dis-nn↗

arXiv2019

Many Body Localization Due to Correlated Disorder in Fock Space

In presence of strong enough disorder one dimensional systems of interacting spinless fermions at non-zero filling factor are known to be in a many body localized phase. When represented in Fock space, the Hamiltonian of such a system looks like that of a single particle hopping on a Fock lattice in the presence of a random disordered potential. The coordination number of the Fock lattice increases linearly with the system size L in 1D. Thus in the thermodynamic limit, the disordered interacting problem in 1D maps on to an Anderson model with infinite coordination number. Despite this, this system displays localization which appears counterintuitive. A close observation of the on-site disorders on the Fock lattice reveals a large degree of correlation among them as they are derived from an exponentially smaller number of on-site disorders in real space. This indicates that the correlations between the on-site disorders on a Fock lattice has a strong effect on the localization properties of the corresponding many-body system. In this work we perform a systematic quantitative exploration of the nature of correlations of the Fock space potential required for localization. Without changing the typical strength of the on-site disorders in Fock lattice we show that changing the correlation strength can induce thermalization or localization in systems. From among the various functional forms of correlations we study through exact diagonalization, we find that only the linear variation of correlations with Hamming distance in Fock space is able to drive a thermal-MBL phase transition where the transition is driven by the correlation strength. Systems with the other forms of correlations we study are found to be ergodic.

cond-mat.dis-nn↗

arXiv2018

Criterion for the occurrence of many body localization in the presence of a single particle mobility edge

Non-interacting fermions in one dimension can undergo a localization-delocalization transition in the presence of a quasi-periodic potential as a function of that potential. In the presence of interactions, this transition transforms into a Many-Body Localization (MBL) transition. Recent studies have suggested that this type of transition can also occur in models with quasi-periodic potentials that possess single particle mobility edges. Two such models were studied in PRL 115,230401(2015) but only one was found to exhibit an MBL transition in the presence of interactions while the other one did not. In this work we investigate the occurrence of MBL in the presence of weak interactions in five different models with single particle mobility edges in one dimension with a view to obtaining a criterion for the same. We find that not all such models undergo a thermal-MBL phase transition in presence of weak interactions. We propose a criterion to determine whether MBL is likely to occur in presence of interaction based only on the properties of the non-interacting models. The relevant quantity $ε$ is a measure of how localized the localized states are relative to how delocalized the delocalized states are in the non-interacting model. We also study various other features of the non-interacting models such as the divergence of the localization length at the mobility edge and the presence or absence of `ergodicity' and localization in their many-body eigenstates. However, we find that these features cannot be used to predict the occurrence of MBL upon the introduction of weak interactions.

cond-mat.dis-nn↗

arXiv2016

Unusual Dirac fermions on the surface of noncentrosymmetric $α$ - BiPd superconductor

Combining multiple emergent correlated properties such as superconductivity and magnetism within the topological matrix can have exceptional consequences in garnering new and exotic physics. Here, we study the topological surface states from a noncentrosymmetric $α$-BiPd superconductor by employing angle-resolved photoemission spectroscopy (ARPES) and first principle calculations. We observe that the Dirac surface states of this system have several interesting and unusual properties, compared to other topological surface states. The surface state is strongly anisotropic and the in-plane Fermi velocity varies rigorously on rotating the crystal about the $y$-axis. Moreover, it acquires an unusual band gap as a function of $k_y$, possibly due to hybridization with bulk bands, detected upon varying the excitation energy. Coexistence of all the functional properties, in addition to the unusual surface state characteristics make this an interesting material.

cond-mat.supr-con↗