arXiv subjects

Ranjan Modak

Publications and source records attributed to Ranjan Modak.

At least 37 records · Page 2Linked to original sources

arXiv2023

Uncertainty Relation for Non-Hermitian Systems

We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of operators. We show that the cumulative gain in the quantum Fisher information when measuring two good observables for such non-Hermitian systems is way better than their Hermitian counterpart. Minimum uncertainty states being the best candidates for this gain near the exceptional point supports the intelligent or simultaneous non-Hermitian quantum sensors.

quant-ph↗

arXiv2023

Non-Hermitian description of sharp quantum resetting

We study a non-interacting quantum particle, moving on a one-dimensional lattice, which is subjected to repetitive measurements. We investigate the consequence when such motion is interrupted and restarted from the same initial configuration, known as the quantum resetting problem. We show that such systems can be described by the time evolution under certain time-dependent non-Hermitian Hamiltonians. We construct two such Hamiltonians and compare the results with the exact dynamics. Using this effective non-Hermitian description we evaluate the timescale of the survival probability as well as the optimal resetting time for the system.

quant-ph↗

arXiv2023

Observational entropic study of Anderson localization

The notion of the thermodynamic entropy in the context of quantum mechanics is a controversial topic. While there were proposals to refer von Neumann entropy as the thermodynamic entropy, it has it's own limitations. The observational entropy has been developed as a generalization of Boltzmann entropy, and it is presently one of the most promising candidates to provide a clear and well-defined understanding of the thermodynamic entropy in quantum mechanics. In this work, we study the behaviour of the observational entropy in the context of localization-delocalization transition for one-dimensional Aubrey-André (AA) model. We find that for the typical mid-spectrum states, in the delocalized phase the observation entropy grows rapidly with coarse-grain size and saturates to the maximal value, while in the localized phase the growth is logarithmic. Moreover, for a given coarse-graining, it increases logarithmically with system size in the delocalized phase, and obeys area law in the localized phase. We also find the increase of the observational entropy followed by the quantum quench, is logarithmic in time in the delocalized phase as well as at the transition point, while in the localized phase it oscillates. Finally, we also venture the self-dual property of the AA model using momentum space coarse-graining.

quant-ph↗

arXiv2022

Geometric quenches in quasi-disordered lattice system

While global quantum quench has been extensively used in the literature to understand the localization-delocalization transition for the one-dimensional quantum spin chain, the effect of geometric quench (which corresponds to a sudden change of the geometry of the chain) in the context of such transitions is yet to be well understood. In this work, we investigate the effect of geometric quench in the Aubry-Andre model, which supports localization-delocalization transition even in one dimension. We study the spreading of the entanglement and the site-occupation with time and find many interesting features that can be used to characterize localization-delocalization transition. We observe that geometric quench causes a power-law type growth of the entanglement entropy in the delocalized phase in contrast to the linear growth which is found in the global quench studies. Remarkably, we also find that the saturation values in the Many-body localized (MBL) phase obey Area law in contrast to the usual volume law which is a signature feature of the MBL phase in the context of global quench.

cond-mat.dis-nn↗

arXiv2021

Finite-size scalings in measurement-induced dynamical phase transition

Repetitive measurements can cause freezing of dynamics of a quantum state, which is known as quantum Zeno effect. We consider an interacting one-dimensional fermionic system and study the fate of the many-body quantum Zeno transition if the system is allowed to evolve repetitively under the unitary dynamics, followed by a measurement process. Measurement induced phase transitions can be accessed by tuning a suitably defined parameter representing measurement strength (frequency). We use different diagnostics, such as long-time evolved entanglement entropy, purity and their fluctuations in order to characterize the transition. We further perform a finite size scaling analysis in order to detect the transition points and evaluate associated scaling exponents via an unbiased numerical strategy of cost function minimization, which provides a platform to compare finite-size scaling ansatze proposed previously in context of many-body Zeno transition.

quant-ph↗

arXiv2021

Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system

Much has been learned about universal properties of the eigenstate entanglement entropy for one-dimensional lattice models, which is described by a Hermitian Hamiltonian. While very less of it has been understood for non-Hermitian systems. In the present work we study a non-Hermitian, non-interacting model of fermions which is invariant under combined $PT$ transformation. Our models show a phase transition from $PT$ unbroken phase to broken phase as we tune the hermiticity breaking parameter. Entanglement entropy of such systems can be defined in two different ways, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates which form a complete set of bi-orthonormal eigenstates. We demonstrate that the entanglement entropy of the ground state and also of the typical excited states show some unique features in both of these phases of the system. Most strikingly, entanglement entropy obtained taking a combination of both left and right eigenstates shows an exponential divergence with system size at the transition point. While in the $PT$-unbroken phase, the entanglement entropy obtained from only the right (or equivalently left) eigenstates shows identical behavior as of an equivalent Hermitian system which is connected to the non-Hermitian system by a similarity transformation.

cond-mat.stat-mech↗

arXiv2021

Many-body dynamical phase transition in quasi-periodic potential

Much has been learned regarding dynamical quantum phase transition (DQPT) due to sudden quenches across quantum critical points in traditional quantum systems. However, not much has been explored when a system undergoes a localization-delocalization transition. Here, we study one dimensional fermionic systems in presence of a quasi-periodic potential, which induces delocalization-localization transition even in 1D. We show signatures of DQPT in the many-body dynamics, when quenching is performed between phases belonging to different universality classes. We investigate how the non-analyticity in the dynamical free energy gets affected with filling fractions in the bare system and, further, study the fate of DQPT under interaction. Strikingly, whenever quenching is performed from the low-entangled localized phase to the high-entangled delocalized phase, our studies suggest an intimate relationship between DQPT and the rate of the entanglement growth -- Faster growths of entanglement entropy ensures quicker manifestation of the non-analiticties in the many-body dynamical free energy.

cond-mat.quant-gas↗

arXiv2020

Entanglement revivals as a probe of scrambling in finite quantum systems

The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppressed. We show that while for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling. Our results are checked by exact numerical techniques in free-fermion and free-boson theories, and by time-dependent density matrix renormalisation group in interacting integrable and chaotic models.

cond-mat.stat-mech↗

arXiv2020

Many-body localization in long range model: Real space renormalization group study

We develop a real space renormalization group (RSRG) scheme by appropriately inserting the long range hopping $t\sim r^{-α}$ with nearest neighbour interaction to study the entanglement entropy and maximum block size for many-body localization (MBL) transition. We show that for $α<2$ there exists a localization transition with renormalized disorder that depends logarithmically on the finite size of the system. The transition observed for $α>2$ does not need a rescaling in disorder strength. Most importantly, we find that even though the MBL transition for $α>2$ falls in the same universality class as that of the short-range models, while transition for $α<2$ belongs to a different universality class. {Due to the intrinsic nature of the RSRG flow towards delocalization, MBL phase for $α>2$ might suffer an instability in the thermodynamic limit while the underlying systems support algebraic localization. Moreover, we verify these findings by inserting microscopic details to the RSRG scheme where we additionally find a more appropriate rescaling function for disorder strength; we indeed uncover a power law scaling with a logarithmic correction and a distinctly different stretched exponential scaling for $α<2$ and $α>2$, respectively, by analyzing system with finite size. This finding further suggests that microscopic RSRG scheme is able to give a hint of instability of the MBL phase for $α>2$ even considering systems of finite size.

cond-mat.dis-nn↗

arXiv2020

Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder

Much have been learned about universal properties of entanglement entropy (EE) and participation ration (PR) for Anderson localization. We find a new sub-extensive scaling with system size of the above measures for algebraic localization as noticed in one-dimensional long-range hopping models in the presence of uncorrelated disorder. While the scaling exponent of EE seems to vary universally with the long distance localization exponent of single particle states (SPSs), PR does not show such university as it also depends on the short range correlations of SPSs. On the other hand, in presence of correlated disorder, an admixture of two species of SPSs (ergodic delocalized and non-ergodic multifractal or localized) are observed, which leads to extensive (sub-extensive) scaling of EE (PR). Considering typical many-body eigenstates, we obtain above results that are further corroborated with the asymptotic dynamics. Additionally, a finite time secondary slow growth in EE is witnessed only for correlated case while for uncorrelated case there exists only primary growth followed by the saturation. We believe that our findings from typical many-body eigenstate would remain unaltered even in the weakly interacting limit.

cond-mat.dis-nn↗

arXiv2019

Correlation and entanglement spreading in nested spin chains

The past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. While most of the work initially focused on the study of prototypical models such as the well-known Heisenberg chain, many theoretical results have been recently extended to a class of more complicated $\it{nested}$ integrable systems, displaying different species of quasiparticles. Still, in the simplest context of quantum quenches, the vast majority of theoretical predictions have been numerically verified only in systems with an elementary Bethe ansatz description. In this work, we fill this gap and present a direct numerical test of some results presented in the recent literature for nested systems, focusing in particular on the Lai-Sutherland model. Using time-dependent density matrix renormalization group and exact diagonalization methods, we compute the spreading of both correlation functions and entanglement entropy after a quench from a simple class of product initial states. This allows us to test the validity of the nested version of a conjectured formula, based on the quasiparticle picture, for the growth of the entanglement entropy, and the Bethe ansatz predictions for the "light-cone" velocity of correlation functions.

cond-mat.stat-mech↗

arXiv2018

Entanglement production in bosonic systems: Linear and logarithmic growth

We study the time evolution of the entanglement entropy in bosonic systems with time-independent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian initial states. We show that all quadratic Hamiltonians can be decomposed into three parts: (a) unstable, (b) stable, and (c) metastable. If present, each part contributes in a characteristic way to the time-dependence of the entanglement entropy: (a) linear production, (b) bounded oscillations, and (c) logarithmic production. In the second part, we use numerical calculations to go beyond Gaussian states and quadratic Hamiltonians. We provide numerical evidence for the conjecture that entanglement production through quadratic Hamiltonians has the same asymptotic behavior for non-Gaussian initial states as for Gaussian ones. Moreover, even for non-quadratic Hamiltonians, we find a similar behavior at intermediate times. Our results are of relevance to understanding entanglement production for quantum fields in dynamical backgrounds and ultracold atoms in optical lattices.

hep-th↗

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↗

arXiv2017

Quantum adiabatic protocols using emergent local Hamiltonians

We present two applications of emergent local Hamiltonians to speed up quantum adiabatic protocols for isolated noninteracting and weakly interacting fermionic systems in one-dimensional lattices. We demonstrate how to extract maximal work from initial band-insulating states, and how to adiabatically transfer systems from linear and harmonic traps into box traps. Our protocols consist of two stages. The first one involves a free expansion followed by a quench to an emergent local Hamiltonian. In the second stage, the emergent local Hamiltonian is "turned off" quasistatically. For the adiabatic transfer from a harmonic trap, we consider both zero- and nonzero-temperature initial states.

cond-mat.stat-mech↗

arXiv2017

Work extraction in an isolated quantum lattice system: Grand canonical and generalized Gibbs ensemble predictions

We study work extraction (defined as the difference between the initial and the final energy) in noninteracting and (effectively) weakly interacting isolated fermionic quantum lattice systems in one dimension, which undergo a sequence of quenches and equilibration. The systems are divided in two parts, which we identify as the subsystem of interest and the bath. We extract work by quenching the on-site potentials in the subsystem, letting the entire system equilibrate, and returning to the initial parameters in the subsystem using a quasi-static process (the bath is never acted upon). We select initial states that are direct products of thermal states of the subsystem and the bath, and consider equilibration to the generalized Gibbs ensemble (GGE, noninteracting case) and to the Gibbs ensemble (GE, weakly interacting case). We identify the class of quenches that, in the thermodynamic limit, results in GE and GGE entropies after the quench that are identical to the one in the initial state (quenches that do not produce entropy). Those quenches guarantee maximal work extraction when thermalization occurs. We show that the same remains true in the presence of integrable dynamics that results in equilibration to the GGE.

cond-mat.stat-mech↗

arXiv2016

Many-body localization in incommensurate models with a mobility edge

We review the physics of many-body localization in models with incommensurate potentials. In particular, we consider one-dimensional quasiperiodic models with single-particle mobility edges. Although a conventional perspective suggests that delocalized states act as a thermalizing bath for the localized states in the presence of of interactions, there is evidence that such systems can display non-ergodicity. This is in part due to the fact that the delocalized states do not have any kind of protection due to symmetry or topology and are thus susceptible to localization. A study of non-interacting incommensurate models shows that they admit extended, partially extended, and fully localized many-body states. These models cannot thermalize dynamically and remain localized upon the introduction of interactions. In particular, for a certain range of energy, the system can host a non-ergodic extended (i.e. metallic) phase in which the energy eigenstates violate the eigenstate thermalization hypothesis (ETH) but the entanglement entropy obeys volume-law scaling. The level statistics and entanglement growth also indicate the lack of ergodicity in these models. The phenomenon of localization and non-ergodicity in a system with interactions despite the presence of single-particle delocalized states is closely related to the so-called "many-body proximity effect" and can also be observed in models with disorder coupled to systems with delocalized degrees of freedom. Many-body localization in systems with incommensurate potentials (without single-particle mobility edges) have been realized experimentally, and we show how this can be modified to study the the effects of such mobility edges. Demonstrating the failure of thermalization in the presence of a single-particle mobility edge in the thermodynamic limit would indicate a more robust violation of the ETH.

cond-mat.str-el↗

arXiv2016

Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess "additional" integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

cond-mat.dis-nn↗

arXiv2015

Many body localization in the presence of a single particle mobility edge

In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon the introduction of interactions. It has also been shown that mobility edges can appear in the single particle spectrum for certain types of quasiperiodic potentials. Here, we investigate the effect of interactions in two models with such mobility edges. Employing the technique of exact diagonalization for finite-sized systems, we calculate the level spacing distribution, time evolution of entanglement entropy, optical conductivity, and return probability to detect MBL. We find that MBL does indeed occur in one of the two models we study, but the entanglement appears to grow faster than logarithmically with time unlike in other MBL systems.

cond-mat.dis-nn↗