Equilibration in the many-body localized phase
This event is part of the Condensed Matter Theory Seminar Series.
We study the dynamics after a sudden quench of quantum states evolving under an isotropic Heisenberg spin-1/2 Hamiltonian with disordered couplings. This system exhibits a ETH-MBL transition for strong enough disorder. We show that the slow dynamics of MBL has profound consequences on its equilibration behaviour and properties. Namely, that one cannot describe the long time behaviour of such states using a diagonal ensemble of eigenstates. We investigate the behaviour away from equilibrium using fidelity, Loschmidt Echo, purity and inverse participation ratio and notions like scrambling time. Moreover, we show that the dynamical exponents governing these phenomena are different in the ETH and MBL phase and that the scaling behaviour detects the transition. Since ground states of ETH and MBL phases are not easily distinguishable, we argue that the ETH-MBL transition is indeed a dynamical phase transition.