On the possibility of many-body localization in a doped Mott insulator

Abstract

Many-body localization (MBL) is currently a hot issue of interacting systems, in which quantum mechanics overcomes thermalization of statistical mechanics. Like Anderson localization of non-interacting electrons, disorders are usually crucial in engineering the quantum interference in MBL. For translation invariant systems, however, the breakdown of eigenstate thermalization hypothesis due to a pure many-body quantum effect is still unclear. Here we demonstrate a possible MBL phenomenon without disorder, which emerges in a lightly doped Hubbard model with very strong interaction. By means of density matrix renormalization group numerical calculation on a two-leg ladder, we show that whereas a single hole can induce a very heavy Nagaoka polaron, two or more holes will form bound pair/droplets which are all localized excitations with flat bands at low energy densities. Consequently, MBL eigenstates of finite energy density can be constructed as composed of these localized droplets spatially separated. We further identify the underlying mechanism for this MBL as due to a novel ‘Berry phase’ of the doped Mott insulator, and show that by turning off this Berry phase either by increasing the anisotropy of the model or by hand, an eigenstate transition from the MBL to a conventional quasiparticle phase can be realized.

Charge-spin mutual entanglement: A case study by exact diagonalization of the one hole doped t-J loop

“…Recently, the signature of a possible MBL has been also found in the study of an extremely large U model of two-leg ladder by the density matrix renormalization group method. Interestingly, when the phase-string sign structure is turned off, all the signatures of the MBL disappear completely 28 .…”

Slow dynamics in translation-invariant quantum lattice models

“…The eigenstates of H 0 are classical product states of spins, while V introduces quantum dynamics. Such models have recently been in-vestigated as potential analogs of MBL in translationinvariant systems when λ is small [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] . Despite much effort, the understanding of models for small but finite λ remains less complete than that of strongly disordered systems, partly due to more pronounced finite size effects 32 .…”

Partial breakdown of quantum thermalization in a Hubbard-like model

“…This phase, the "quantum disentangled liquid" (QDL), is characterized by heavy particles which are fully thermalized, but light particles which have not thermalized independently of the heavy particles. Other work has also considered the possibility that thermalization can break down in translationally invariant systems [29][30][31][32][33][34][35][36][37][38][39][40][41][42] .…”