Quantum entanglement and dynamics of low-dimensional quantum many-body systems

Abstract

Entanglement as a fundamental aspect of quantum mechanics plays a crucial role in many-body systems. Quantum dynamics, due to the intricate interplay between the locality of the interaction and the non-local nature of entanglement, greatly enriches the phenomena and brings the subject to the next complexity. In this dissertation, I will investigate entanglement and dynamics in low-dimensional systems from various perspectives. Chapter 1 examines the relationship between entanglement and topology in gapped quantum systems. We introduce a new framework called entanglement response, which offers a new perspective on the previously conjectured modular commutator formula that extracts the chiral central charge. Moreover, by incorporating global symmetries, we derive a new formula for the quantum Hall conductance. Chapter 2 extends our analysis of entanglement to mixed states. In particular, we inquire how entanglement can be used to define topological order in mixed states that are obtained by applying local decoherence to gapped ground states. This problem is naturally related to the active error correction, as we will address. Chapter 3 focuses on the dynamics of one-dimensional conformal field theories under specially engineered Floquet driving. We show that the Floquet dynamics support a heating phase that exhibits robust superuniversal features that rely only on conformal invariance. This heating phase is also shown to be useful in efficiently cooling. Chapter 4 delves into the entanglement dynamics of one-dimensional random unitary circuit doped with projective measurement. We focus on the limit where the measurement happens with a small probability. We will offer an explanation of the stability of the steady state by invoking the idea of quantum error correction.