Quantum quenches in the many-body localized phase
By Maksym Serbyn, Z. Papi'c, D. Abanin. 2014
156 citations recorded by the source corpus.
Many-body localized (MBL) systems are characterized by the absence of transport and thermalization, and therefore cannot be described by conventional statistical mechanics. In this paper, using analytic arguments and numerical simulations, we study the behaviour of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, we find that the local observables reach stationary, highly non-thermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behaviour distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached), and from the ergodic phase (where relaxation is expected to be exponential). For the case of a local quench, we also find a power-law approach of local observables to their stationary values when the system is prepared in a mixed state. Quench protocols considered in this paper can be naturally implemented in systems of ultra cold atoms in disordered optical lattices, and the behaviour of local observables provides a direct experimental signature of many-body localization.
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Citations in the corpus
- Local integrals of motion in many‐body localized systems (2016, background): “The same mechanism is at the root of other distinguishing dynamical features of MBL systems, such as the power-law decay in time of the response to a (properly designed) spin-echo protocol [92], the power-law relaxation (towards non-thermal values) of the expectation value of local observables [95] ”
- Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “(56) has zero bipartite entanglement; in the thermal phase, h < hc, the half-chain entanglement entropy grows rapidly (red curve) towards a value which is extensive in system size; the growth on the MBL side, h > hc, in contrast is much slower, first achieving a sub-extensive level similar to that o”
- Many-body localization: An introduction and selected topics (2017, unknown): “Such observable will generically decay to its long-time value in a power-law fashion characteristic of the MBL phase (related to the lengthscale on which lioms interact), whereas it will not decay in an Anderson insulator [40].”
- Observation of many-body localization of interacting fermions in a quasirandom optical lattice (2015, background): “Additional insight can also be gained by analyzing the full relaxation dynamics of local observables [19, 20, 21], in an experimental setup featuring single site resolution [47, 48].”
- Avalanches and many-body resonances in many-body localized systems (2021, background): “The MBL phase and, more generally, Anderson localized phases, are gapless critical phases with slow dynamics due to resonances and near-resonances, as emphasized early on by Mott [13,14,45,46].”