Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

Abstract

We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focusing on the behavior of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area and volume-law entanglement, being characteristic of the quantum disentangled liquid. This behavior appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.A. S. acknowledges EPSRC for studentship funding under Grant No. EP/M508007/1. J. K. is supported by the Marie Curie Programme under EC Grant agreement No. 703697. The work of D. L. K. was supported by EPSRC Grant No. EP/M007928/1. R. M. was in part supported by DFG under Grant No. SFB 1143