arXiv subjects

Masudul Haque

Publications and source records attributed to Masudul Haque.

At least 55 records · Page 3Linked to original sources

arXiv2018

Eigenstate Thermalization, Random Matrix Theory and Behemoths

The eigenstate thermalization hypothesis (ETH) is one of the cornerstones in our understanding of quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this paper. We report on the construction of highly nonlocal operators, Behemoths, that are building blocks for various kinds of local and non-local operators. The Behemoths have a singular distribution and width $w\sim \mathcal{D}^{-1}$ ($\mathcal{D}$ being the Hilbert space dimension). From them, one may construct local operators with the ordinary Gaussian distribution and $w\sim \mathcal{D}^{-1/2}$ in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with $w\sim \mathcal{D}^{-δ}$, $0<δ<1/2$. This operator construction is based on a deep analogy with random matrix theory and shows striking agreement with numerical simulations of non-integrable many-body systems.

cond-mat.stat-mech↗

arXiv2018

Dynamics and level statistics of interacting fermions in the Lowest Landau Level

We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated pair hopping terms in addition to static repulsion. This setting and this type of Hamiltonian has a significant history in numerical studies of fractional quantum Hall (FQH) physics, but the many-body quantum dynamics generated by such correlated hopping has not been explored in detail. We focus on initial states containing all the fermions in one block of orbitals. We characterize in detail how the fermionic liquid spreads out starting from such a state. We identify and explain differences with regular (single-particle) hopping Hamiltonians. Such differences are seen, e.g. in the entanglement dynamics, in that some initial block states are frozen or near-frozen, and in density gradients persisting in long-time equilibrated states. Examining the level spacing statistics, we show that the most common Hamiltonians used in FQH physics are not integrable, and explain that GOE statistics (level statistics corresponding to the Gaussian Orthogonal Ensemble) can appear in many cases despite the lack of time-reversal symmetry.

cond-mat.str-el↗

arXiv2017

Classical Dynamics of Harmonically Trapped Interacting Particles

Motivated by current interest in the dynamics of trapped quantum gases, we study the microcanonical dynamics of a trapped one-dimensional gas of classical particles interacting via a finite-range repulsive force of tunable strength. We examine two questions which have been of interest in quantum dynamics: (1) the breathing mode (size oscillation) dynamics of the trapped gas and the dependence of the breathing frequency on the interaction strength, and (2) the long-time relaxation and possible thermalization of the finite isolated gas. We show that the breathing mode frequency has non-monotonic dependence on the magnitude of the mutual repulsion, decreasing for small interactions and increasing for larger interactions. We explain these dependences in terms of slowing-down or speeding-up effects of two-body collision processes. We find that the gas thermalizes within a reasonable finite timescale in the sense of single-particle energies acquiring a Boltzmann distribution, only when the interaction strength is large compared to the energy per particle.

cond-mat.stat-mech↗

arXiv2017

Eigenstate Thermalization Scaling in Majorana Clusters: from Chaotic to Integrable Sachdev-Ye-Kitaev Models

The eigenstate thermalization hypothesis (ETH) is a conjecture on the nature of isolated quantum systems that guarantees the thermal behavior of subsystems when it is satisfied. ETH has been tested in various forms on a number of local many-body interacting systems. Here we examine the validity of ETH in a class of nonlocal disordered many-body interacting systems --- the Sachdev-Ye-Kitaev Majorana (SYK) models --- that may be tuned from chaotic behavior to integrability. Our analysis shows that SYK$_4$ (with quartic couplings), which is maximally chaotic in the large system size limit, satisfies the standard ETH scaling while SYK$_2$ (with quadratic couplings), which is integrable, does not. We show that the low-energy and high-energy properties are affected drastically differently when the two Hamiltonians are mixed.

cond-mat.stat-mech↗

arXiv2017

Propagation and jamming dynamics in Heisenberg spin ladders

We investigate the propagation dynamics of initially localized excitations in spin-1/2 Heisenberg ladders. We consider initial states with two overturned spins, either on neighboring sites on the same leg or on the two sites of a single rung, in an otherwise polarized (ferromagnetic) background. Compared to the corresponding dynamics in a chain (single leg), we observe several additional modes of propagation. We connect these propagation modes to features of the spectrum of the ladder system, and to different effective models corresponding to different segments of the spectrum. In addition to the regular propagation modes, we observe for one mode a peculiar `jamming' dynamics where components of the excitations remain localized in an unusual manner. A comparison with the spin-1 bilinear-biquadratic chain is developed and explored, where a similar phenomenon is shown to occur.

cond-mat.quant-gas↗

arXiv2016

Response of fermions in Chern bands to spatially local quenches

We study the dynamical evolution of Chern-band systems after subjecting them to local quenches. For open-boundary systems, we show for half-filling that the chiral nature of edge states is manifested in the time-dependent chiral response to local density quenches on the edge. In the presence of power-law traps, we show how to mimic the half-filling situation by choosing the appropriate number of fermions depending on the trap size, and explore chiral responses of edges to local quenches in such a configuration. We find that perturbations resulting from the quenches propagate at different group velocities depending on the bulk band gap. Our results provide different routes to check dynamically the non-trivial nature of Chern bands.

cond-mat.quant-gas↗

arXiv2016

Wavepacket dynamics on Chern band lattices in a trap

The experimental realization of lattices with Chern bands in ultracold-atom and photonic systems has motivated the study of time-dependent phenomena, such as spatial propagation, in lattices with nontrivial topology. We study the dynamics of gaussian wavepackets on the Haldane honeycomb Chern-band lattice model, in the presence of a harmonic trap. We focus on the transverse response to a force, which is due partly to the Berry curvature and partly to the transverse component of the energy band curvature. We evaluate the accuracy of a semiclassical description, which treats the wavepacket as a point particle in both real and momentum space, in reproducing the motion of a realistic wavepacket with finite extent. We find that, in order to accurately capture the wavepacket dynamics, the extent of the wavepacket in momentum space needs to be taken into account. The dynamics is sensitive to the interplay of band dispersion and Berry curvature over the finite region of momentum (reciprocal) space where the wavepacket has support. Moreover, if the wavepacket is prepared with a finite initial momentum, the semiclassical analysis reproduces its motion as long as it has a large overlap with the eigenstates of a single band. The semiclassical description generally improves with increasing real-space size of the wavepacket, as long as the external conditions (e.g., external force) remain uniform throughout the spatial extent of the wavepacket.

cond-mat.quant-gas↗

arXiv2015

Nonsmooth and level-resolved dynamics illustrated with the tight binding model

We point out that in the first order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas. Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function $\sinc x \equiv \sin x / x$. These physical effects appear in many systems with approximately equally spaced spectra, and is also robust for larger-amplitude coupling beyond the domain of perturbation theory. We use a one-dimensional periodically driven tight-binding model to illustrate these effects, both within and outside the perturbative regime.

cond-mat.quant-gas↗

arXiv2015

Quantum quench in 2D using the variational Baeriswyl wavefunction

By combining the Baeriswyl wavefunction with equilibrium and time-dependent variational principles, we develop a non-equilibrium formalism to study quantum quenches for two dimensional spinless fermions with nearest-neighbour hopping and repulsion. The variational ground state energy and the short time dynamics agree convincingly with the results of numerically exact simulations. We find that depending on the initial and final interaction strength, the quenched system either exhibits undamped oscillations or relaxes to a time independent steady state. The time averaged expectation value of the CDW order parameter rises sharply when crossing from the steady state regime to the oscillating regime, indicating that the system, being non-integrable, shows signs of thermalization with an effective temperature above or below the equilibrium critical temperature, respectively.

cond-mat.str-el↗

arXiv2015

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

cond-mat.str-el↗

arXiv2015

Quasi-soliton scattering in quantum spin chains

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The time evolved block decimation (TEBD) algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.

cond-mat.str-el↗

arXiv2015

Inhomogeneous quenches in a fermionic chain: exact results

We consider the non-equilibrium physics induced by joining together two tight binding fermionic chains to form a single chain. Before being joined, each chain is in a many-fermion ground state. The fillings (densities) in the two chains might be the same or different. We present a number of exact results for the correlation functions in the non-interacting case. We present a short-time expansion, which can sometimes be fully resummed, and which reproduces the so-called `light cone' effect or wavefront behavior of the correlators. For large times, we show how all interesting physical regimes may be obtained by stationary phase approximation techniques. In particular, we derive semiclassical formulas in the case when both time and positions are large, and show that these are exact in the thermodynamic limit. We present subleading corrections to the large-time behavior, including the corrections near the edges of the wavefront. We also provide results for the return probability or Loschmidt echo. In the maximally inhomogeneous limit, we prove that it is exactly gaussian at all times. The effects of interactions on the Loschmidt echo are also discussed.

cond-mat.stat-mech↗

arXiv2015

Bose-Hubbard ladder subject to effective magnetic field: quench dynamics in a harmonic trap

Motivated by a recent experiment with optical lattices that has realized a ladder geometry with an effective magnetic field (Atala et al., Nature Physics \textbf{10}, 588 (2014)), we study the dynamics of bosons on a tight-binding two-leg ladder with complex hopping amplitudes. This system displays a quantum phase transition even without interactions. We study the non-equilibrium dynamics without and with interactions, in the presence of a harmonic trapping potential. In particular we consider dynamics induced by quenches of the trapping potential and of the magnitude of the rung hopping. We present a striking "slowing down" effect in the collective mode dynamics near the phase transition. This manifestation of a slowing down phenomenon near a quantum phase transition can be visualized unusually directly: the collective mode dynamics can be followed experimentally in real time and real space by imaging the atomic cloud.

cond-mat.quant-gas↗

arXiv2015

Dynamics of the impurity screening cloud following quantum quenches of the Resonant Level Model

We present a detailed analysis of the evolution of impurity screening cloud in the Resonant Level Model (RLM) followed by quenches of system parameters. The considered quenches are either local or found to be effectively local. The screening cloud is characterized by impurity-bath correlators and by the entanglement of a block centered around the impurity with the rest of the system. We consider several local quench protocols, such as, quenches from initially decoupled to coupled impurity, quenches between different finite couplings of the impurity, and `detuning quenches' involving changing the onsite impurity potential away from or to the chemical potential of the bath. The relevant correlators and the entanglement display versions of the `light-cone' effect, since the information about the quench travels through the bath at finite speed. At long times (`inside' the light cone), the impurity screening cloud relaxes exponentially to the final equilibrium structure, with the relaxation rate given by the emergent energy scale of impurity screening. Also, snaphots of the time-evolving spatial profile of impurity-bath correlators show exponential dependences on space, with the length scale given by the screening length.

cond-mat.str-el↗

arXiv2015

Off-diagonal matrix elements of local operators in many-body quantum systems

In the time evolution of isolated quantum systems out of equilibrium, local observables generally relax to a long-time asymptotic value, governed by the expectation values (diagonal matrix elements) of the corresponding operator in the eigenstates of the system. The temporal fluctuations around this value, response to further perturbations, and the relaxation toward this asymptotic value, are all determined by the off-diagonal matrix elements. Motivated by this non-equilibrium role, we present generic statistical properties of off-diagonal matrix elements of local observables in two families of interacting many-body systems with local interactions. Since integrability (or lack thereof) is an important ingredient in the relaxation process, we analyze models that can be continuously tuned to integrability. We show that, for generic non-integrable systems, the distribution of off-diagonal matrix elements is a gaussian centered at zero. As one approaches integrability, the peak around zero becomes sharper, so that the distribution is approximately a combination of two gaussians. We characterize the proximity to integrability through the deviation of this distribution from a gaussian shape. We also determine the scaling dependence on system size of the average magnitude of off-diagonal matrix elements.

cond-mat.stat-mech↗

arXiv2014

Repulsive to attractive interaction quenches of 1D Bose gas in a harmonic trap

We consider quantum quenches of harmonically trapped one-dimensional bosons from repulsive to attractive interactions, and the resulting breathing dynamics of the so-called `super-Tonks-Girardeau' (sTG) state. This state is highly excited compared to the ground state of the attractive gas, and is the lowest eigenstate where the particles are not bound or clustered. We analyze the dynamics from a spectral point of view, identifying the relevant eigenstates of the interacting trapped many-body system, and analyzing the nature of these quantum eigenstates. To obtain explicit eigenspectra, we use Hamiltonians with finite-dimensional Hilbert spaces to approximate the Lieb-Liniger system. We employ two very different approximate approaches: an expansion in a truncated single-particle harmonic-trap basis and a lattice (Bose-Hubbard) model. We show how the breathing frequency, identified with the energy difference between the sTG state and another particular eigenstate, varies with interaction.

cond-mat.quant-gas↗

arXiv2014

Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy

In the spectrum of many-body quantum systems, the low-energy eigenstates were the traditional focus of research. The interest in the statistical properties of the full eigenspectrum has grown more recently, in particular in the context of non-equilibrium questions. Wave functions of interacting lattice quantum systems can be characterized either by local observables, or by global properties such as the participation ratio (PR) in a many-body basis or the entanglement between various partitions. We present a study of the PR and of the entanglement entropy (EE) between two roughly equal spatial partitions of the system, in all the eigenfunctions of local Hamiltonians. Motivated by the similarity of the PR and EE - both are generically larger in the bulk and smaller near the edges of the spectrum - we quantitatively analyze the correlation between them. We elucidate the effect of (proximity to) integrability, showing how low-entanglement and low-PR states appear also in the middle of the spectrum as one approaches integrable points. We also determine the precise scaling behavior of the eigenstate-to-eigenstate fluctuations of the PR and EE with respect to system size, and characterize the statistical distribution of these quantities near the middle of the spectrum.

cond-mat.stat-mech↗

arXiv2014

Modulated trapping of interacting bosons in one dimension

We investigate the response of harmonically confined bosons with contact interactions (trapped Lieb-Liniger gas) to modulations of the trapping strength. We explain the structure of resonances at a series of driving frequencies, where size oscillations and energy grow exponentially. For strong interactions (Tonks-Girardeau gas), we show the effect of resonant driving on the bosonic momentum distribution. The treatment is `exact' for zero and infinite interactions, where the dynamics is captured by a single-variable ordinary differential equation. For finite interactions the system is no longer exactly solvable. For weak interactions, we show how interactions modify the resonant behavior for weak and strong driving, using a variational approximation which adds interactions to the single-variable description in a controlled way.

cond-mat.quant-gas↗