Many body localized systems weakly coupled to baths

Abstract

We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bath. Using general arguments and dimensional analysis, we constrain the overall phase diagram of the coupled system and bath. Our analysis incorporates all the previously discussed regimes, and also uncovers a new intrinsically quantum regime that has not hitherto been discussed. We discuss baths that are themselves near a localization transition, or are strongly disordered but protected against localization by symmetry or topology. We also discuss situations where the system and bath have different dimensionality (the case of 'boundary MBL' and 'boundary baths').

Loschmidt echo in many-body localized phases

“…In other words, the energies of same local excitation for different eigenstates would be split by an exponentially small amount depending on the state of the distant spins. 31 This splitting, described in the main text via the operator spreading gives rise to oscillations at a sufficiently long times, and leads to the power-law decay of spin-echo fluctuations.…”

“…While measuring entanglement spreading experimentally is generally a very hard problem, the same dephasing dynamics could be detected in the relaxation of observables in a global quench, 24 modified spin-echo type setups, 25 quantum revivals, 29 and other dynamical experimental signatures of the MBL phase. [29][30][31][32] In this paper we propose fluctuations of Loschmidt echo as an alternative probe of dephasing dynamics, and demonstrate that they decay as a power-law in the MBL phase, saturating at the value that is exponentially small in the system size. We note that our setup should be experimentally accessible, as it relies on the interferometry performed on individual degrees of freedom and does not require the change of global sign of the Hamiltonian.…”

Characterizing the many-body localization transition using the entanglement spectrum

“…Many body localization (MBL) and the resulting breakdown of statistical mechanics in disordered interacting systems has been the subject of much recent research [1][2][3][4][5][6]. The intensive research has yielded a plethora of insights into the properties of this non-ergodic regime, including its connections of integrability [7][8][9][10][11][12], its response properties [13,14], and the circumstances under which the phenomenon may arise [15][16][17][18][19][20][21][22][23]. However, the quantum phase transition between a 'thermal' phase where statistical mechanics is obeyed and a 'many body localized' (MBL) phase where it is not continues to be an open problem.…”

Describing many-body localized systems in thermal environments

“…This difficulty is also reflected in the fact that previous studies are either limited to small system sizes [32,[35][36][37][38][39][40] or make rather specific assumptions regarding the properties of the environment, e.g. describing it by classical noise [33,41] or by dephasing processes corresponding to an infinite-temperature thermal environment [27][28][29][30][31]42].…”