Entanglement entropy of disordered quantum chains following a global quench

Abstract

We numerically investigate the growth of the entanglement entropy Sent(t) in time t-after a global quench from a product state-in quantum chains with various kinds of disorder. The main focus is, in particular, on fermionic chains with bond disorder. In the noninteracting case at criticality we numerically test recent predictions by the real space renormalization group for the entanglement growth in time, the maximal entanglement as a function of block size, and the decay of a density wave order parameter. We show that multiprecision calculations are required to reach the scaling regime and perform such calculations for specific cases. For interacting models with binary bond disorder we present data based on infinite size density matrix renormalization group calculations and exact diagonalizations. We obtain first numerical evidence for a many-body localized phase in bond disordered systems where Sent(t) ∼ ln t seems to hold. Our results for bond disorder are contrasted with the well studied case of potential disorder.

Signatures of many-body localization in the dynamics of two-site entanglement

“…[21][22][23][40][41][42][43][44]) have analysed the evolution of the entanglement entropy of large blocks in disordered spin chains. Its logarithmic growth [21][22][23] , intimately related to the existence of an extensive number of local integrals of motions, has been identified as a unique trait of MBL.…”

Non-equilibrium dynamics of one-dimensional isolated quantum systems

“…Azösszefonódási entrópia kvencs utáni dinamikájával kapcsolatban részletes vizsgálatokat olvashatunk az irodalomban [78][79][80][81]180].…”

“…Concerning the functional form of the relaxation process after a quench in random quantum systems, there have been detailed studies about the time-dependence of the entanglement entropy [78][79][80][81]180]. If the system consists of non-interacting fermions -such as the random XX-spin chain or the critical random transverse-field Ising chain -the dynamical entanglement entropy grows ultra slowly in time as S(t) ∼ a ln ln t ,…”

“…where denotes the size of a block in a bipartite system and can be chosen to be proportional to the size of the system L [79,180]. These scaling forms can be explained by a strong disorder renormalization-group (SDRG) approach [103].…”

“…To circumvent numerical instability as observed in previous calculations for large systems using eigenvalue solver routines [79,180], we use multiple precision arithmetic to study the timeevolution through direct matrix multiplications.…”