Many-body localization of 1D disordered impenetrable two-component fermions

Abstract

We study effects of disorder on eigenstates of 1D two-component fermions with infinitely strong Hubbard repulsion. We demonstrate that the spin-independent (potential) disorder reduces the problem to the one-particle Anderson localization taking place at arbitrarily weak disorder. In contrast, a random magnetic field can cause reentrant many-body localization-delocalization transitions. Surprisingly weak magnetic field destroys one-particle localization caused by not too strong potential disorder, whereas at much stronger fields the states are many-body localized. We present numerical support of these conclusions.

Disordered impenetrable two-component fermions in one dimension

“…We explicitly showed that it strongly couples the charge and spin degrees of freedom and this leads to the many-body localization-delocalization transition. This provides an extended picture of recent numerical results for the Hubbard model with infinitely strong on-site repulsion by means of exact diagonalization [19]. Our findings are relevant for ongoing experiments with ultracold gases in optical lattices, where the type of disorder can be controlled.…”

“…( 48) to the Hamiltonian H ′ (45) one can no longer reduce the problem to a single-particle one and genuinely manybody effects start to play a crucial role. In particular, the random magnetic field leads to the hybridization of the localized single particle eigenstates of the Hamiltonian (45), leading to the many-body localizationdelocalization transition [19].…”

“…[12][13][14] and references therein). Traditional setups for analyzing MBL transition are one-dimensional (1D) models, such as the Heisenberg XXZ spin chain and the Fermi-Hubbard model [15][16][17][18][19]. On the one hand, these systems are paradigmatically important for condensed matter.…”

“…It was also reported that in the symmetric situation of a sufficiently strong random magnetic field spin excitations are localised whereas states in the charge sector remain extended [40]. Recently, the disordered Fermi-Hubbard model for two-component fermions with infinitely strong on-site repulsion (the t−0 model) was investigated numerically [19]. It was demonstrated that in the spin-independent (potential) disorder the states exhibit Anderson localization (AL).…”