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arXiv:2206.08711 · Physical review. E

Ballistic transport of interacting Bose particles in a tight-binding chain

Pavel S. Muraev, Дмитрий Н. Максимов, Andrey R. Kolovsky

Published Dec 6, 2022• 2 citations
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Abstract

It is known that the quantum transport of noninteracting Bose particles across a tight-binding chain is ballistic in the sense that the current does not depend on the chain length. We address the question whether the transport of strongly interacting bosons can be ballistic as well. We find such a regime and show that, classically, it corresponds to the synchronized motion of local nonlinear oscillators. It is also argued that, unlike the case of noninteracting bosons, the transporting state responsible for the ballistic transport of interacting bosons is metastable, i.e., the current decays in the course of time. An estimate for the decay time is obtained.

DOI
10.1103/physreve.106.064203

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It is known that the quantum transport of noninteracting Bose particles across a tight-binding chain is ballistic in the sense that the current does not depend on the chain length. We address the question whether the transport of strongly interacting bosons can be ballistic as well. We find such a regime and show that, classically, it corresponds to the synchronized motion of local nonlinear oscillators. It is also argued that, unlike the case of noninteracting bosons, the transporting state responsible for the ballistic transport of interacting bosons is metastable, i.e., the current decays in the course of time. An estimate for the decay time is obtained.
We analyze the stationary current of bosonic carriers in the Bose-Hubbard chain of length L where the first and the last sites of the chain are attached to reservoirs of Bose particles acting as a particle source and sink, respectively. The analysis is carried out by using the pseudoclassical approach which reduces the original quantum problem to the classical problem for L coupled nonlinear oscillators. It is shown that an increase of oscillator nonlinearity (which is determined by the strength of interparticle interactions) results in a transition from the ballistic transport regime, where the stationary current is independent of the chain length, to the diffusive regime, where the current is inversely proportional to L.
We analyze the current of Bose particles across a tight-binding chain connected at both ends to the particles' reservoirs. Unlike the standard open Bose-Hubbard model, where the presence of reservoirs is taken into account by the Lindbladians acting on the first and last sites of the chain, we use semimicroscopic models for the reservoirs. This allows us to address the case of arbitrary reservoir temperature. In particular, we discuss the phenomenon of the resonant transmission for nearly condensed bosons, where the current across the chain is significantly enhanced for certain values of the gate voltage.
We consider quantum transport of non-interacting particles in a tight-binding chain coupled to Markovian reservoirs at its boundaries and subject to uniform on-site dephasing. Using the masterequation approach, we derived the exact analytic solution for the mean current along the chain. This analytic solution is obtained in the framework of single-particle quantum mechanics and, thus, equally applies for transport of non-interacting bosons and fermions. In the absence of phase damping, the results are extended to the complete many-body solution for bosonic problem in the form of anti-normally ordered characteristic function. This function allows us to calculate the distribution function for the current at each bond in the chain as well as the inter-bond current correlation functions.
We investigate the propagation of two-point density correlations in the one-dimensional Bose-Hubbard Hamiltonian in the thermodynamic limit in terms of the correlation transport distance (CTD), an experimentally measurable magnitude that characterizes the spatial spreading of correlations in time. We confirm that the integrable limits of the model exhibit CTD ballistic growth, while the onset of the chaotic phase leads to the emergence of a pronounced sub-ballistic regime, in agreement with previous results for finite systems. By a meticulous analysis of the spatio-temporal correlation profiles, we show that the correlation front nonetheless propagates ballistically for all interaction strengths, and that the chaos-induced slowdown of the CTD originates from the emergence of long-time distance-dependent correlation tails, together with an enhanced decay of the correlation front amplitude. Our results thus provide a detailed characterization of correlation transport that goes beyond a simple light-cone picture.
In this work, we investigate the critical properties of the Bose-Einstein condensation transition in a model of non-interacting bosons whose one-particle hamiltonian in the tight-binding approximation includes long-range couplings in a linear chain with periodic boundary conditions. The couplings along the chain are described by a kinetic hopping term which is responsible by the quantum mobility of the particles and whose amplitude decays with the distance between the sites as a power-law with a characteristic exponent a. We show that the density of states in the vicinity of the lower band edge of the energy spectrum strongly depends on a. In the re- gime of 1 < α < 2, the density of states vanishes as a power-law, similar to the behavior found for bosons in hypercubic lattices with dimension d = 2/(α -1). We determine the critical properties of the Bose-Einstein condensation transition that takes place in this regime using a hypothesis of a single characteristic length scale and a finite-size scaling analysis. In the regime of 3/2 < α < 2, the critical exponents are quite similar to those that characterize the transition in the corresponding hypercubic lattice. On the other hand, in the regime of 1 < α < 3/2, the exponents obtained from the single length scale hypothesis are quite distinct form those on the hypercubic lattice. This result indicates that the single length scale hypothesis can not correctly capture the critical exponents in the regime where the effective dimensionality of the model is above the upper critical dimension above which the transition has a mean-field critical behavior.
In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.