Logarithmically Slow Relaxation in Quasiperiodically Driven Random Spin Chains

Philipp T. Dumitrescu, Romain Vasseur, and Andrew C. Potter

Phys. Rev. Lett. 120, 070602 – Published 16 February 2018

Abstract

We simulate the dynamics of a disordered interacting spin chain subject to a quasiperiodic time-dependent drive, corresponding to a stroboscopic Fibonacci sequence of two distinct Hamiltonians. Exploiting the recursive drive structure, we can efficiently simulate exponentially long times. After an initial transient, the system exhibits a long-lived glassy regime characterized by a logarithmically slow growth of entanglement and decay of correlations analogous to the dynamics at the many-body delocalization transition. Ultimately, at long time scales, which diverge exponentially for weak or rapid drives, the system thermalizes to infinite temperature. The slow relaxation enables metastable dynamical phases, exemplified by a “time quasicrystal” in which spins exhibit persistent oscillations with a distinct quasiperiodic pattern from that of the drive. We show that in contrast with Floquet systems, a high-frequency expansion strictly breaks down above fourth order, and fails to produce an effective static Hamiltonian that would capture the prethermal glassy relaxation.

Received 11 August 2017
Revised 20 November 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.070602

Physics Subject Headings (PhySH)

Nonequilibrium statistical mechanics Spontaneous symmetry breaking

1-dimensional spin chains Disordered systems

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & TechnologyAtomic, Molecular & OpticalStatistical Physics & Thermodynamics

Authors & Affiliations

Philipp T. Dumitrescu^1,*, Romain Vasseur^2,3,4, and Andrew C. Potter¹

¹Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
²Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
³Materials Science Division, Lawrence Berkeley National Laboratories, Berkeley, California 94720, USA
⁴Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA