Thermalization and Many-body Localization

Abstract

This dissertation examines two topics in the area of quantum thermalization: thermalization

of entanglement and many-body localization phase transition. We first explore the dynamics of the entanglement entropy near equilibrium in two quantumchaotic spin chains undergoing unitary time evolution. It is found that entanglement entropy relaxes slower near equilibration for a time-independent Hamiltonian with an extensive conserved energy, while such slow relaxation is absent in a Floquet spin chain with no local conservation law. We thus argue that slow diffusive energy transport is responsible for the slow relaxation of the entanglement entropy in the Hamiltonian system, and also attempt to make the relation more quantitative. We next turn to the many-body localization (MBL) transition, which is the quantum phase transition between the MBL phase, where localized conserved quantities emerge, and the

thermal phase. We introduce and explore a Floquet spin chain model for numerical studies of this transition in finite-size systems. With no local conservation laws and rapid thermalization in the thermal phase, we argue that choosing a Floquet model can maximize contrast between the MBL phase and the thermal phase in such finite-size systems. Lastly, we present a simplified strong-randomness renormalization group (RG) that captures some aspects of the MBL phase transition in generic disordered one-dimensional systems and might serve as a “zeroth-order” approximation for future RG studies. This RG can be formulated analytically and is mathematically equivalent to a domain coarsening model that has been previously solved, which thus enables us to obtain the critical fixed point distribution and critical exponents analytically or to numerical precision. One interesting feature is that the rare Griffiths regions are fractal, which might be qualitatively correct beyond our approximation and suggest stronger Griffiths effects than previously assumed.