The emergent integrability of the many-body localized phase is naturally understood in terms of localized quasiparticles. As a result, the occupations of the one-particle density matrix in eigenstates show a Fermi-liquid-like discontinuity. Here we show that in the steady state reached at long times after a global quench from a perfect density-wave state, this occupation discontinuity is absent, reminiscent of a Fermi liquid at a finite temperature, while the full occupation function remains strongly nonthermal. We discuss how one can understand this as a consequence of the local structure of the density-wave state and the resulting partial occupation of quasiparticles. This partial occupation can be controlled by tuning the initial state and can be described by an effective temperature.
We numerically study the dynamics on the ergodic side of the many-body localization transition in a periodically driven Floquet model with no global conservation laws. We describe and employ a numerical technique based on the fast Walsh-Hadamard transform that allows us to perform an exact time evolution for large systems and long times. As in models with conserved quantities (e.g., energy and/or particle number) we observe a slowing down of the dynamics as the transition into the many-body localized phase is approached. More specifically, our data is consistent with a subballistic spread of entanglement and a stretched-exponential decay of an autocorrelation function, with their associated exponents reflecting slow dynamics near the transition for a fixed system size. However, with access to larger system sizes, we observe a clear flow of the exponents towards faster dynamics and can not rule out that the slow dynamics is a finite-size effect. Furthermore, we observe examples of non-monotonic dependence of the exponents with time, with dynamics initially slowing down but accelerating again at even larger times, consistent with the slow dynamics being a crossover phenomena with a localized critical point.
We study the dynamical behavior of the one-dimensional Anderson insulator
in the presence of a local noise. We show that the noise induces logarithmically
slow energy and entanglement growth, until the system reaches an infinite-temperature
state, where both quantities saturate to extensive values. The saturation
value of the entanglement entropy approaches the average entanglement
entropy over all possible product states. At infinite temperature,
we find that a density excitation spreads logarithmically with time,
without any signs of asymptotic diffusive behavior. In addition, we
provide a theoretical picture which qualitatively reproduces the phenomenology
of particle transport.
Generic quantum many-body systems typically show a linear growth of the entanglement entropy after a quench from a product state. While entanglement is a property of the wave function, it is generated by the unitary time evolution operator and is therefore reflected in its increasing complexity as quantified by the operator entanglement entropy.Using numerical simulations of a static and a periodically driven quantum spin chain, we show that there is a robust correspondence between the entanglement entropy growth of typical product states with the operator entanglement entropy of the unitary evolution operator, while special product states, e.g. σz basis states, can exhibit faster entanglement production.In the presence of a disordered magnetic field in our spin chains, we show that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorderdependent exponent, and clarify the apparent discrepancy in previous results. These systems, in the absence of conserved densities, provide further evidence for slow information spreading on the ergodic side of the many-body localization transition. arXiv:1908.07010v1 [cond-mat.dis-nn]
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