arXiv subjects

Soumya Bera

Publications and source records attributed to Soumya Bera.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2020

Anomalous diffusion in particle-hole symmetric many-body localized systems

In this work we probe the dynamics of the particle-hole symmetric many-body localized (MBL) phase. We provide numerical evidence that it can be characterized by an algebraic propagation of both entanglement and charge, unlike in the conventional MBL case. We explain the mechanism of this anomalous diffusion through a formation of bound states, which coherently propagate via long-range resonances. By projecting onto the two-particle sector of the particle-hole symmetric model, we show that the formation and observed subdiffusive dynamics is a consequence of an interplay between symmetry and interactions.

cond-mat.dis-nn↗

arXiv2020

High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging KPZ-scaling in the zero-magnetization limit

The large-scale dynamics of quantum integrable systems is often dominated by ballistic modes due to the existence of stable quasi-particles. We here consider as an archetypical example for such a system the spin-$\frac{1}{2}$ XXX Heisenberg chain that features magnons and their bound states. An interesting question, which we here investigate numerically, arises with respect to the fate of ballistic modes at finite temperatures in the limit of zero magnetization $m{=}0$. At a finite magnetization density $m$, the spin autocorrelation function $Π(x,t)$ (at high temperatures) typically exhibits a trimodal behavior with left- and right-moving quasi-particle modes and a broad center peak with slower dynamics. The broadening of the fastest propagating modes exhibits a sub-diffusive $t^{1/3}$ scaling at large magnetization densities, $m {\rightarrow} \frac{1}{2}$, familiar from non-interacting models; it crosses over into a diffusive scaling $t^{1/2}$ upon decreasing the magnetization to smaller values. The behavior of the center peak appears to exhibit a crossover from transient super-diffusion to ballistic relaxation at long times. In the limit $m{\to}0$, the weight carried by the propagating peaks tends to zero; the residual dynamics is carried only by the central peak; it is sub-ballistic and characterized by a dynamical exponent $z$ close to the value $\frac{3}{2}$ familiar from Kardar-Parisi-Zhang (KPZ) scaling. We confirm, employing elaborate finite-time extrapolations, that the spatial scaling of the correlator $Π$ is in excellent agreement with KPZ-type behavior and analyze the corresponding corrections.

cond-mat.stat-mech↗

arXiv2019

Sub-diffusion in the Anderson model on random regular graph

We study the finite-time dynamics of an initially localized wave-packet in the Anderson model on the random regular graph (RRG). Considering the full probability distribution $Π(x,t)$ of a particle to be at some distance $x$ from the initial state at time $t$, we give evidence that $Π(x,t)$ spreads sub-diffusively over a range of disorder strengths, wider than a putative non-ergodic phase. We provide a detailed analysis of the propagation of $Π(x,t)$ in space-time $(x,t)$ domain, identifying four different regimes. These regimes in $(x,t)$ are determined by the position of a wave-front $X_{\text{front}}(t)$, which moves sub-diffusively to the most distant sites $X_{\text{front}}(t) \sim t^β$ with an exponent $β< 1$. We support our numerical results by a self-consistent semiclassical picture of wavepacket propagation relating the exponent $β$ with the relaxation rate of the return probability $Π(0,t) \sim e^{-Γt^β}$. Importantly, the Anderson model on the RRG can be considered as proxy of the many-body localization transition (MBL) on the Fock space of a generic interacting system. In the final discussion, we outline possible implications of our findings for MBL.

cond-mat.dis-nn↗

arXiv2019

Return probability for the Anderson model on the random regular graph

We study the return probability for the Anderson model on the random regular graph and give evidence of the existence of two distinct phases: a fully ergodic and nonergodic one. In the ergodic phase, the return probability decays polynomially with time with oscillations, being the attribute of the Wigner-Dyson-like behavior, while in the nonergodic phase the decay follows a stretched exponential decay.We give a phenomenological interpretation of the stretched exponential decay in terms of a classical random walker. Furthermore, comparing typical and mean values of the return probability, we show how to differentiate an ergodic phase from a nonergodic one. We benchmark this method first in two random matrix models, the power-law random banded matrices, and the Rosenzweig-Porter matrices, which host both phases. Second, we apply this method to the Anderson model on the random regular graph to give further evidence of the existence of the two phases.

cond-mat.dis-nn↗

arXiv2019

Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential

We investigate charge relaxation in disordered and quasi-periodic quantum-wires of spin-less fermions ($t{-}V$-model) at different inhomogeneity strength $W$ in the localized and nearly-localized regime. Our observable is the time-dependent density correlation function, $Φ(x,t)$, at infinite temperature. We find that disordered and quasi-periodic models behave qualitatively similar: Although even at longest observation times the width $Δx(t)$ of $Φ(x,t)$ does not exceed significantly the non-interacting localization length, $ξ_0$, strong finite-size effects are encountered. Our findings appear difficult to reconcile with the rare-region physics (Griffiths effects) that often is invoked as an explanation for the slow dynamics observed by us and earlier computational studies. As a relatively reliable indicator for the boundary towards the many-body localized (MBL) regime even under these conditions, we consider the exponent function $β(t) {=} d\ln Δx(t) / d\ln t$. Motivated by our numerical data for $β$, we discuss a scenario in which the MBL-phase splits into two subphases: in MBL$_\text{A}$ $Δx(t)$ diverges slower than any power, while it converges towards a finite value in MBL$_\text{B}$. Within the scenario the transition between MBL$_\text{A}$ and the ergodic phase is characterized by a length scale, $ξ$, that exhibits an essential singularity $\ln ξ\sim 1/|W-W_\text{c}|$. Relations to earlier numerics and proposals of two-phase scenarios will be discussed.

cond-mat.str-el↗

arXiv2019

Insights on heterogeneity in blinking mechanisms and non-ergodicity using sub-ensemble statistical analysis of single quantum-dots

Photo-luminescence intermittency (blinking) in semiconductor nanocrystals (NCs), a phenomenon ubiquitous to single-emitters, is generally considered to be temporally random intensity fluctuations between bright (On) and dark (Off) states. However, individual quantum-dots (QDs) rarely exhibit such telegraphic signal, and yet, the vast majority of single-NC blinking data are analyzed using a single fixed threshold, which generates binary trajectories. Further, blinking dynamics can vary dramatically over NCs in the ensemble, and it is unclear whether the exponents (m) of single-particle On-/Off-time distributions (P(t)-On/Off), which are used to validate mechanistic models of blinking, are narrowly distributed or not. Here, we sub-classify an ensemble based on the emissivity of QDs, and subsequently compare the (sub)ensemble behaviors. To achieve this, we analyzed a large number (>1000) of intensity trajectories for a model system, Mn+2 doped ZnCdS QDs, which exhibits diverse blinking dynamics. An intensity histogram dependent thresholding method allowed us to construct distributions of relevant blinking parameters (such as m). Interestingly, we find that single QD P(t)-On/Off s follow either truncated power law or power law, and their relative proportion vary over sub-populations. Our results reveal a remarkable variation in m(On/Off) amongst as well as within sub-ensembles, which implies multiple blinking mechanisms being operational among various QDs. We further show that the m(On/Off) obtained via cumulative single-particle P(t)-On/Off is clearly distinct from the weighted mean value of all single-particle m(On/Off), an evidence for the lack of ergodicity. Thus, investigation and analyses of a large number of QDs, albeit for a limited time-span of few decades, is crucial to characterize possible blinking mechanisms and heterogeneity therein

cond-mat.mes-hall↗

arXiv2019

Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities

We numerically study the dynamics on the ergodic side of the many-body localization transition in a periodically driven Floquet model with no global conservation laws. We describe and employ a numerical technique based on the fast Walsh-Hadamard transform that allows us to perform an exact time evolution for large systems and long times. As in models with conserved quantities (e.g., energy and/or particle number) we observe a slowing down of the dynamics as the transition into the many-body localized phase is approached. More specifically, our data is consistent with a subballistic spread of entanglement and a stretched-exponential decay of an autocorrelation function, with their associated exponents reflecting slow dynamics near the transition for a fixed system size. However, with access to larger system sizes, we observe a clear flow of the exponents towards faster dynamics and can not rule out that the slow dynamics is a finite-size effect. Furthermore, we observe examples of non-monotonic dependence of the exponents with time, with dynamics initially slowing down but accelerating again at even larger times, consistent with the slow dynamics being a crossover phenomena with a localized critical point.

cond-mat.dis-nn↗

arXiv2018

Dynamical quantum phase transitions in Weyl semimetals

The quench dynamics in type-I inversion symmetric Weyl semimetals (WSM) are explored in this work which, due to the form of the Hamiltonian, may be readily extended to two-dimensional Chern insulators. We analyze the role of equilibrium topological properties characterized by the Chern number of the pre-quench ground state in dictating the non-equilibrium dynamics of the system, specifically, the emergence of dynamical quantum phase transitions (DQPT). By investigating the ground state fidelity, it is found that a change in the signed Chern number constitutes a sufficient but not necessary condition for the occurrence of DQPTs. Depending on the ratio of the transverse and longitudinal hopping parameters, DQPTs may also be observed for quenches lying entirely within the initial Chern phase. Additionally, we analyze the zeros of the boundary partition function discovering that while the zeros generally form two-dimensional structures resulting in one-dimensional critical times, infinitesimal quenches may lead to one-dimensional zeros with zero-dimensional critical times provided the quench distance scales appropriately with the system size. This is strikingly manifested in the nature of non-analyticies of the dynamical free energy, revealing a logarithmic singularity. In addition, following recent experimental advances in observing the dynamical Fisher zeros of the Loschmidt overlap amplitude through azimuthal Bloch phase vortices by Bloch-state tomography, we rigorously investigate the same in WSMs. Finally, we establish the relationship between the dimension of the critical times and the presence of dynamical vortices, demonstrating that only one-dimensional critical times arising from two-dimensional manifolds of zeros of the boundary partition function lead to dynamical vortices.

cond-mat.stat-mech↗

arXiv2018

Multiscale entanglement clusters at the many-body localization phase transition

We study numerically the formation of entanglement clusters across the many-body localization phase transition. We observe a crossover from strong many-body entanglement in the ergodic phase to weak local correlations in the localized phase, with contiguous clusters throughout the phase diagram. Critical states close to the transition have a structure compatible with fractal or multiscale-entangled states, characterized by entanglement at multiple levels: small strongly entangled clusters are weakly entangled together to form larger clusters. The critical point therefore features subthermal entanglement and a power-law distributed cluster size, while the localized phase presents an exponentially decreasing cluster distribution. These results are consistent with some of the recently proposed phenomenological renormalization-group schemes characterizing the many-body localized critical point, and may serve to constrain other such schemes.

cond-mat.dis-nn↗

arXiv2018

Particle Production in Ultra-Strong Coupling Waveguide QED

Understanding large-scale interacting quantum matter requires dealing with the huge number of quanta that are produced by scattering even a few particles against a complex quantum object. Prominent examples are found from high energy cosmic ray showers to the optical or electrical driving of degenerate Fermi gases. We tackle this challenge in the context of many-body quantum optics, as motivated by the recent developments of circuit quantum electrodynamics at ultrastrong coupling. The issue of particle production is addressed quantitatively with a simple yet powerful concept rooted in the quantum superposition principle. This key idea is illustrated by the study of multi-photon emission from a single two-level artificial atom coupled to a high impedance waveguide. We find surprisingly that the off-resonant inelastic emission lineshape is dominated by broadband particle production, due to the large phase space associated with contributions that do not conserve the number of excitations. Such frequency conversion processes produce striking signatures in time correlation measurements, which can be tested experimentally in quantum waveguides. These ideas open new directions for the simulation of a variety of physical systems, from polaron dynamics in solids to complex superconducting quantum architectures.

cond-mat.mes-hall↗

arXiv2018

Accessing eigenstate spin-glass order from reduced density matrices

Many-body localized phases may not only be characterized by their ergodicity breaking, but can also host ordered phases such as the many-body localized spin-glass (MBL-SG). The MBL-SG is challenging to access in a dynamical measurement and therefore experimentally since the conventionally used Edwards-Anderson order parameter is a two-point correlation function in time. In this work, we show that many-body localized spin-glass order can also be detected from two-site reduced density matrices, which we use to construct an eigenstate spin-glass order parameter. We find that this eigenstate spin-glass order parameter captures spin-glass phases in random Ising chains both in many-body eigenstates as well as in the nonequilibrium dynamics from a local in time measurement. We discuss how our results can be used to observe MBL-SG order within current experiments in Rydberg atoms and trapped ion systems.

cond-mat.str-el↗

arXiv2018

Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain

Entanglement has developed into an essential concept for the characterization of phases and phase transitions in ground states of quantum many-body systems. In this work, we use the logarithmic negativity to study the spatial entanglement structure in the transverse-field Ising chain both in the ground state and at nonzero temperatures. Specifically, we investigate the entanglement between two disjoint blocks as a function of their separation, which can be viewed as the entanglement analog of a spatial correlation function. We find sharp entanglement thresholds at a critical distance beyond which the logarithmic negativity vanishes exactly and thus the two blocks become unentangled, which holds even in the presence of long-ranged quantum correlations, i.e., at the system's quantum critical point. Using Time-Evolving Block Decimation (TEBD), we explore this feature as a function of temperature and size of the two blocks and present a simple model to describe our numerical observations.

cond-mat.str-el↗

arXiv2017

One-particle-density-matrix occupation spectrum of many-body localized states after a global quench

The emergent integrability of the many-body localized phase is naturally understood in terms of localized quasiparticles. As a result, the occupations of the one-particle density matrix in eigenstates show a Fermi-liquid-like discontinuity. Here we show that in the steady state reached at long times after a global quench from a perfect density-wave state, this occupation discontinuity is absent, reminiscent of a Fermi liquid at a finite temperature, while the full occupation function remains strongly nonthermal. We discuss how one can understand this as a consequence of the local structure of the density-wave state and the resulting partial occupation of quasiparticles. This partial occupation can be controlled by tuning the initial state and can be described by an effective temperature.

cond-mat.dis-nn↗

arXiv2017

Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay

We investigate charge relaxation in quantum-wires of spin-less disordered fermions ($t{-}V$-model). Our observable is the time-dependent density propagator, $Π_{\varepsilon}(x,t)$, calculated in windows of different energy density, $\varepsilon$, of the many-body Hamiltonian and at different disorder strengths, $W$, not exceeding the critical value $W_\text{c}$. The width $Δx_\varepsilon(t)$ of $Π_\varepsilon(x,t)$ exhibits a behavior $d\ln Δx_\varepsilon(t) / d\ln t {=} β_\varepsilon(t)$, where the exponent function $β_\varepsilon(t){\lesssim}1/2$ is seen to depend strongly on $L$ at all investigated parameter combinations. (i) We confirm the existence of a region in phase space that exhibits subdiffusive dynamics in the sense that $β_\varepsilon{<}1/2$ in large window of times. However, subdiffusion might possibly be transient, only, finally giving way to a conventional diffusive behavior with $β_{\varepsilon}{=}1/2$. (ii) We cannot confirm the existence of many-body mobility edges even in regions of the phase-diagram that have been reported to be deep in the delocalized phase. (iii) (Transient) subdiffusion $0<β_\varepsilon(t)\lesssim 1/2$, coexists with an enhanced probability for returning to the origin, $Π_\varepsilon(0,t)$, decaying much slower than $1/Δx_\varepsilon (t)$. Correspondingly, the spatial decay of $Π_\varepsilon(x,t)$ is far from Gaussian being exponential or even slower. On a phenomenological level, our findings are broadly consistent with effects of strong disorder and (fractal) Griffiths regions.

cond-mat.str-el↗

arXiv2017

Spontaneous emission of Schrödinger cats in a waveguide at ultrastrong coupling

Josephson circuits provide a realistic physical setup where the light-matter fine structure constant can become of order one, allowing to reach a regime dominated by non-perturbative effects beyond standard quantum optics. Simple processes, such as spontaneous emission, thus acquire a many-body character, that can be tackled using a new description of the time-dependent state vector in terms of quantum-superposed coherent states. We find that spontaneous atomic decay at ultrastrong coupling leads to the emission of spectrally broad Schrödinger cats rather than of monochromatic single photons. These cats states remain partially entangled with the emitter at intermediate stages of the dynamics, even after emission, due to a large separation in time scales between fast energy relaxation and exponentially slow decoherence. Once decoherence of the qubit is finally established, quantum information is completely transfered to the state of the emitted cat.

cond-mat.mes-hall↗

arXiv2017

Anatomy of quantum critical wave functions in dissipative impurity problems

Quantum phase transitions reflect singular changes taking place in a many-body ground state, however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. New physical insights into the sub-Ohmic spin-boson model are provided by the coherent state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking, while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix product states (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.

cond-mat.str-el↗

arXiv2016

One-particle density matrix characterization of many-body localization

We study a model of interacting fermions in one dimension subject to random, uncorrelated onsite disorder. The model realizes an interaction-driven quantum phase transition between an ergodic and a many-body localized phase (MBL). We propose a single-particle framework to characterize these phases by the eigenstates (the natural orbitals) and the eigenvalues (the occupation spectrum) of the one-particle density matrix (OPDM) in many-body eigenstates. As a main result, we find that the natural orbitals are localized in the MBL phase, but delocalized in the ergodic phase. This qualitative change in these single-particle states is a many-body effect, since without interactions the single-particle energy eigenstates are all localized. The occupation spectrum in the ergodic phase is thermal in agreement with the eigenstate thermalization hypothesis, while in the MBL phase the occupations preserve a discontinuity at an emergent Fermi edge. This suggests that the MBL eigenstates are weakly dressed Slater determinants, with the eigenstates of the underlying Anderson problem as reference states. We discuss the statistical properties of the natural orbitals and of the occupation spectrum in the two phases and as the transition is approached. Our results are consistent with the existing picture of emergent integrability and localized integrals of motion, or quasiparticles, in the MBL phase. We emphasize the close analogy of the MBL phase to a zero-temperature Fermi liquid: in the studied model, the MBL phase is adiabatically connected to the Anderson insulator and the occupation-spectrum discontinuity directly indicates the presence of quasiparticles localized in real space. Finally, we show that the same picture emerges for interacting fermions in the presence of an experimentally-relevant bichromatic lattice and thereby demonstrate that our findings are not limited to a specific model.

cond-mat.dis-nn↗