Signatures of Quantum Chaos and fermionization in the incoherent transport of bosonic carriers in the Bose-Hubbard chain

TL;DR

This paper investigates how inter-particle interactions influence the stationary current in a Bose-Hubbard chain, revealing a transition to quantum chaos and fermionization reflected in spectral statistics and current behavior.

Contribution

It demonstrates the link between quantum chaos, fermionization, and transport properties in the Bose-Hubbard model, highlighting spectral changes and current suppression.

Findings

Current decreases sharply beyond the chaos transition point.

Spectral statistics shift from Poisson to Wigner-Dyson and back to Poisson.

Fermionization leads to counter-intuitive current dependence on particle number.

Abstract

We analyse the stationary current of Bose particles across the Bose-Hubbard chain connected to a battery, focusing on the effect of inter-particle interactions. It is shown that the current magnitude drastically decreases as the strength of inter-particle interactions exceeds the critical value which marks the transition to quantum chaos in the Bose-Hubbard Hamiltonian. We found that this transition is well reflected in the non-equilibrium many-body density matrix of the system. Namely, the level-spacing distribution for eigenvalues of the density matrix changes from Poisson to Wigner-Dyson distributions. With the further increase of the interaction strength, the Wigner-Dyson spectrum statistics changes back to the Poisson statistics which now marks fermionization of the bosonic particles. With respect to the stationary current, this leads to the counter-intuitive dependence of the current magnitude on the particle number.