arXiv subjects

Masudul Haque

Publications and source records attributed to Masudul Haque.

At least 73 records · Page 4Linked to original sources

arXiv2014

Real-space structure of the impurity screening cloud in the Resonant Level Model

We present a detailed investigation of the impurity screening cloud in the Resonant Level Model. The screening is visible in the structure of impurity-bath correlators as a function of distance from the impurity. We characterize the screening cloud through scaling analyses of impurity-bath correlators and entanglement entropies. We devise and study several situations where the screening cloud is destroyed or modified: finite temperatures, energetic detuning of the impurity from the chemical potential, and the situation of an unconventional bath with diverging density of states.

cond-mat.str-el↗

arXiv2014

Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries

We study the entanglement spectrum of a Chern insulator on a cylinder geometry, with the cut separating the two partitions taken parallel to the cylinder edge, at varying distances from the edge. In contrast to similar studies on a torus, there is only one cut, and hence only one virtual edge mode in the entanglement spectrum. The entanglement spectrum has a gap when the cut is close enough to the physical edge of the cylinder such that the edge mode spatially extends over the cut. This effect is suppressed for parameter choices where the edge mode is sharply localized at the edge. In the extreme case of a perfectly localized edge mode, the entanglement spectrum is gapless even if the smaller partition consists of a single edge row. For the single-row cut, we construct the corresponding entanglement Hamiltonian, which is a one-dimensional tight-binding Hamiltonian with complex long-range hopping and interesting properties. We also study and explain the effect of two different schemes of flux insertion through a ring described by such an entanglement Hamiltonian.

cond-mat.str-el↗

arXiv2014

Finite-size scaling of eigenstate thermalization

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite, and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic non-integrable systems these fluctuations scale with a universal power law $D^{-1/2}$ with the dimension $D$ of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models, and several observables for each model. Each family includes integrable members, and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

cond-mat.stat-mech↗

arXiv2013

Bethe ansatz description of edge-localization in the open-boundary XXZ spin chain

At large values of the anisotropy Δ, the open-boundary Heisenberg spin-1/2 chain has eigenstates displaying localization at the edges. We present a Bethe ansatz description of this `edge-locking' phenomenon in the entire Δ>1 region. We focus on the simplest spin sectors, namely the highly polarized sectors with only one or two overturned spins, i.e., one-particle and two-particle sectors. Edge-locking is associated with pure imaginary solutions of the Bethe equations, which are not commonly encountered in periodic chains. In the one-particle case, at large anisotropies there are two eigenstates with imaginary Bethe momenta, related to localization at the two edges. For any finite chain size, one of the two solutions become real as the anisotropy is lowered below a certain value. For two particles, a richer scenario is observed, with eigenstates having the possibility of both particles locked on the same or different edge, one locked and the other free, and both free either as single magnons or as bound composites corresponding to `string' solutions. For finite chains, some of the edge-locked spins get delocalized at certain values of the anisotropy (`exceptional points'), corresponding to imaginary solutions becoming real. We characterize these phenomena thoroughly by providing analytic expansions of the Bethe momenta for large chains, large anisotropy, and near the exceptional points. In the large-chain limit all the exceptional points coalesce at the isotropic point (Δ=1) and edge-locking becomes stable in the whole Δ>1 region.

cond-mat.str-el↗

arXiv2013

Single-impurity Kondo physics at extreme particle-hole asymmetry

We study the fate of the Kondo effect with one-dimensional conduction baths at very low densities, such that the system explores the bottom of the conduction band. This can involve either finite low densities, or a small number of fixed conduction electrons in a large system, i.e., the limit of large bath sizes can be taken with either fixed small density or with fixed number. We characterize the Kondo physics for such systems through the energy gain due to Kondo coupling, which is a general analog of the Kondo temperature scale, and through real-space profiles of densities and spin-spin correlation functions.

cond-mat.mes-hall↗

arXiv2013

Fine structures in the spectrum of the open-boundary Heisenberg chain at large anisotropies

At large anisotropies, the spectrum of the Heisenberg XXZ spin chain separates into `bands' with energies largely determined by the number of domain walls. The band structure is richer with open boundary conditions: there are more bands and the bands develop intricate fine structures. We characterize and explain these structures and substructures in the open-boundary chain. The fine structures are explained using degenerate perturbation theory. We also present some dynamical consequences of these sub-band structures, through explicit time evolution of the wavefunction from initial states motivated by the fine structure analysis.

cond-mat.str-el↗

arXiv2013

Breathing mode in the Bose-Hubbard chain with a harmonic trapping potential

We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low energy eigenspectrum of the trapped many-boson system, and study overlaps of the initial state with eigenstates of the quenched Hamiltonian. There is an intermediate interaction regime, between a "free-boson" limit and a "free-fermion" limit, in which the Bose-Hubbard breathing mode frequency approaches the Gross-Pitaevskii prediction. In addition, we present a striking failure of the time-dependent Gutzwiller approximation for describing breathing modes.

cond-mat.quant-gas↗

arXiv2013

Entanglement spectrum of the two dimensional Bose-Hubbard model

We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two dimensional square lattice at unit filling, both in the Mott insulating and in the superfluid phase. In the Mott phase, we demonstrate that the ES is dominated by the physics at the boundary between the two subsystems. On top of the boundary-local (perturbative) structure, the ES exhibits substructures arising from one-dimensional dispersions along the boundary. In the superfluid phase, the structure of the ES is qualitatively different, and reflects the spontaneously broken U(1) symmetry of the phase. We attribute the basic low-lying structure to a so-called "tower of states" (TOS) Hamiltonian of the model. We then discuss how these characteristic structures evolve across the superfluid to Mott insulator transition and their influence on the behavior of the entanglement entropies. Finally, we briefly outline the implications of the ES structure on the efficiency of matrix-product-state based algorithms in two dimensions.

cond-mat.str-el↗

arXiv2013

Viewpoint: Toward Fractional Quantum Hall physics with cold atoms

Viewpoint on Nigel R. Cooper and Jean Dalibard, "Reaching Fractional Quantum Hall States with Optical Flux Lattices", Phys. Rev. Lett. 110, 185301 (2013), and N. Y. Yao, A. V. Gorshkov, C. R. Laumann, A. M. Läuchli, J. Ye, and M. D. Lukin, "Realizing Fractional Chern Insulators in Dipolar Spin Systems", Phys. Rev. Lett. 110, 185302 (2013). Researchers propose new ways to recreate fractional quantum Hall physics using ultracold atoms and molecules.

cond-mat.str-el↗

arXiv2013

Quantum quenches and work distributions in ultra-low-density systems

We present results on quantum quenches in systems with a fixed number of particles in a large region. We show that the typical differences between local and global quenches present in systems with regular thermodynamic limit are lacking in this low-density limit. In particular, we show that in this limit local quenches may not lead to equilibration to the new ground state, and that global quenches can have power-law work distributions ("edge singularities") typically associated with local quenches for finite-density systems. We also show that this regime allows for large edge singularity exponents beyond that allowed by the constraints of the usual thermodynamic limit. This large-exponent singularity has observable consequences in the time evolution, leading to a distinct intermediate power-law regime in time. We demonstrate these results first using local quantum quenches in a low-density Kondo-like system, and additionally through global and local quenches in Bose-Hubbard, Aubry-Andre, and hard-core boson systems in the low-density regime.

cond-mat.stat-mech↗

arXiv2012

Strongly interacting bosons in multi-chromatic potentials supporting mobility edges: localization, quasi-condensation and expansion dynamics

We provide an account of the static and dynamic properties of hard-core bosons in a one-dimensional lattice subject to a multi-chromatic quasiperiodic potential for which the single-particle spectrum has mobility edges. We use the mapping from strongly interacting bosons to weakly interacting fermions, and provide exact numerical results for hard-core bosons in and out of equilibrium. In equilibrium, we find that the system behaves like a quasi-condensate (insulator) depending on whether the Fermi surface of the corresponding fermionic system lies in a spectral region where the single-particle states are delocalized (localized). We also study non-equilibrium expansion dynamics of initially trapped bosons, and demonstrate that the extent of partial localization is determined by the single-particle spectrum.

cond-mat.quant-gas↗

arXiv2012

Linear quantum quench in the Heisenberg XXZ chain: time dependent Luttinger model description of a lattice system

We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to switching on a nearest neighbour interaction for hard-core bosons or an interaction quench for free fermions. The physical observables we investigate are: the energy pumped into the system during the quench, the spin-flip correlation function, and the bipartite fluctuations of the z component of the spin in a box. We find excellent agreement between exact numerics (infinite system time-evolving block decimation, iTEBD) and analytical results from bosonization, as a function of the quench time, spatial coordinate and interaction strength. This provides a stringent and much-needed test of Luttinger liquid theory in a non-equilibrium situation.

cond-mat.str-el↗

arXiv2012

Spin modulation instabilities and phase separation dynamics in trapped two-component Bose condensates

In the study of trapped two-component Bose gases, a widely used dynamical protocol is to start from the ground state of a one-component condensate and then switch half the atoms into another hyperfine state. The slightly different intra-component and inter-component interactions can then lead to highly nontrivial dynamics. We study and classify the possible subsequent dynamics, over a wide variety of parameters spanned by the trap strength and by the inter- to intra-component interaction ratio. A stability analysis suited to the trapped situation provides us with a framework to explain the various types of dynamics in different regimes.

cond-mat.quant-gas↗

arXiv2012

Non-equilibrium dynamics in Bose-Hubbard ladders

Motivated by a recent experiment on the non-equilibrium dynamics of interacting bosons in ladder-shaped optical lattices, we report exact calculations on the sweep dynamics of Bose-Hubbard systems in finite two-leg ladders. The sweep changes the energy bias between the legs linearly over a finite time. As in the experiment, we study the cases of [a] the bosons initially all in the lower-energy leg (ground state sweep) and [b] the bosons initially all in the higher-energy leg (inverse sweep). The approach to adiabaticity in the inverse sweep is intricate, as the transfer of bosons is non-monotonic as a function of both sweep time and intra-leg tunnel coupling. Our exact study provides explanations for these non-monotonicities based on features of the full spectrum, without appealing to concepts (e.g., gapless excitation spectrum) that are more appropriate for the thermodynamic limit. We also demonstrate and study Stueckelberg oscillations in the finite-size ladders.

cond-mat.quant-gas↗

arXiv2012

Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point

We study the entanglement spectrum (ES) of a finite XXZ spin 1/2 chain in the limit Δ-> -1^+ for both open and periodic boundary conditions. At Δ=-1 (ferromagnetic point) the model is equivalent to the Heisenberg ferromagnet and its degenerate ground state manifold is the SU(2) multiplet with maximal total spin. Any state in this so-called "symmetric sector" is an equal weight superposition of all possible spin configurations. In the gapless phase at Δ>-1 this property is progressively lost as one moves away from the Δ=-1 point. We investigate how the ES obtained from the states in this manifold reflects this change, using exact diagonalization and Bethe ansatz calculations. We find that in the limit Δ->-1^+ most of the ES levels show divergent behavior. Moreover, while at Δ=-1 the ES contains no information about the boundaries, for Δ>-1 it depends dramatically on the choice of boundary conditions. For both open and periodic boundary conditions the ES exhibits an elegant multiplicity structure for which we conjecture a combinatorial formula. We also study the entanglement eigenfunctions, i.e. the eigenfunctions of the reduced density matrix. We find that the eigenfunctions corresponding to the non diverging levels mimic the behavior of the state wavefunction, whereas the others show intriguing polynomial structures. Finally we analyze the distribution of the ES levels as the system is detuned away from Δ=-1.

cond-mat.str-el↗

arXiv2012

Boundary-locality and perturbative structure of entanglement spectra in gapped systems

The entanglement between two parts of a many-body system can be characterized in detail by the entanglement spectrum. Focusing on gapped phases of one-dimensional systems, we show how this spectrum is dominated by contributions from the boundary between the parts. This contradicts the view of an "entanglement Hamiltonian" as a bulk entity. The boundary-local nature of the entanglement spectrum is clarified through its hierarchical level structure, through the combination of two single-boundary spectra to form a two-boundary spectrum, and finally through consideration of dominant eigenfunctions of the entanglement Hamiltonian. We use the boundary-locality to formulate a perturbative scheme for calculating entanglement spectra.

cond-mat.str-el↗

arXiv2012

Strongly interacting one-dimensional bosons in arbitrary-strength optical lattices: from Bose-Hubbard to sine-Gordon and beyond

We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the sine-Gordon regime of weak lattices, to the complete absence of a lattice. Using the Bose-Fermi mapping between strongly interacting bosons and weakly interacting fermions, we derive the phase diagram in the parameter space of lattice depth and chemical potential. This extends previous knowledge from tight-binding (Bose-Hubbard) studies in a new direction which is important because the lattice depth is a readily adjustable experimental parameter. Several other results (equations of state, energy gaps, profiles in harmonic trap) are presented as corollaries to the physics contained in this phase diagram. Generically, both incompressible (gapped) and compressible phases coexist in a trap; this has implications for experimental measurements.

cond-mat.quant-gas↗

arXiv2012

Itinerant electrons in the Coulomb phase

We study the interplay between magnetic frustration and itinerant electrons. For example, how does the coupling to mobile charges modify the properties of a spin liquid, and does the underlying frustration favor insulating or conducting states? Supported by Monte Carlo simulations, our goal is in particular to provide an analytical picture of the mechanisms involved. The models under considerations exhibit Coulomb phases in two and three dimensions, where the itinerant electrons are coupled to the localized spins via double exchange interactions. Because of the Hund coupling, magnetic loops naturally emerge from the Coulomb phase and serve as conducting channels for the mobile electrons, leading to doping-dependent rearrangements of the loop ensemble in order to minimize the electronic kinetic energy. At low electron density ρ, the double exchange coupling mainly tends to segment the very long loops winding around the system into smaller ones while it gradually lifts the extensive degeneracy of the Coulomb phase with increasing ρ. For higher doping, the results are strongly lattice dependent, displaying loop crystals with a given loop length for some specific values of ρ, which can melt into another loop crystal by varying ρ. Finally, we contrast this to the qualitatively different behavior of analogous models on kagome or triangular lattices.

cond-mat.stat-mech↗