Extended slow dynamical regime close to the many-body localization transition

Abstract

5 pages, 3 figuresInternational audienceMany-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L=28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth $S(t)\propto t^{1/z}$ with a disorder-dependent exponent $z\ge1$, in contrast with the pure ballistic growth $z=1$ of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance $I(t) \propto t^{-\zeta}$ with a continuously varying disorder-dependent exponent $\zeta$, vanishing at the transition. This provides a clear experimental signature for detecting this non-conventional regime

Rare‐region effects and dynamics near the many‐body localization transition

“…[58], provided the interpretation of these results in terms of Griffiths physics. These numerical studies, as well as subsequent work using exact diagonalization [89,90], and approximate memory-matrix approaches [91] found anomalous diffusion at essentially all values of disorder. (In Ref.…”

Quantum Entanglement Growth under Random Unitary Dynamics

“…The additional single-site gates are the Hadamard and phase gates defined in Eqs. (29) and (30). respectively.…”

“…This irreversible growth of entanglementquantified by the growth of the von Neumman entropyis important for several reasons. It is an essential part of thermalization, and as a result has been addressed in diverse contexts ranging from conformal field theory [1][2][3][4] and holography [5][6][7][8][9][10][11][12] to integrable [13][14][15][16][17][18][19], nonintegrable [20][21][22][23], and strongly disordered spin chains [24][25][26][27][28][29][30]. Entanglement growth is also of practical importance as the crucial obstacle to simulating quantum dynamics numerically, for example, using matrix product states or the density matrix renormalization group [31].…”

Learning phase transitions from dynamics

“…where the ith component of m(t ) is the expectation value of σ z i at time t. This definition of the imbalance is the direct generalization of that typically used when the initial state is only taken to be one with a charge-density-wave ordering [64][65][66][67].…”

“…This Hamiltonian exhibits a transition between a delocalized and a many-body localized state at a critical disorder strength that depends on the energy density of the state under consideration [60][61][62][63]. The dynamics of initial product states of spin polarization differs substantially between the two phases: While spins in the many-body localized phase retain a long-term correlation with their initial configuration, in the delocalized phase this correlation is lost over time as expected from an ergodic system [64][65][66][67]. In what follows we will be considering the dynamics of initial states that evolve in time under the Hamiltonian of Eq.…”