Unveiling Physical Properties of Many-Body Systems around Dynamical Quantum Phase Transitions

Abstract

The study of phase transitions in quantum many-body systems out of equilibrium is known as the dynamical quantum phase transitions (DQPTs). This newly established theory opens a broad aspect of physics concerning the non-equilibrium properties of quantum systems, particularly in light of the successful real-time access to quantum systems in laboratories. For instance, the physical picture of what happens during the non-equilibrium phase transitions is in general yet to be fully addressed. This dissertation serves as a collection of works on providing insights and directions to eventually unveil the complete picture of DQPTs.

To begin with, we propose a simple yet fundamental approach to studying the critical dynamics during DQPTs. We name it the Loschmidt amplitude spectrum (LAS) which extends the concept of Loschmidt amplitude (LA) from overlapping of time-evolved state only onto the ground state of a system to all its eigenstates. We demonstrate our scheme on the 1D transverse-field Ising model (TFIM), the paradigmatic model in condensed matter physics, as well as its variation – the axial next-nearest-neighbour Ising (ANNNI) model. In particular, we resolve the dynamics in the momentum space for the former model, and show that the momentum eigenstates redistribute themselves in the critical situation. Our scheme also reveals the preferred structure of the eigenstates by comparing LAS and the time evolution of the magnetisation of the latter model.

The second work focuses on the spin dynamics of 1D XY model around DQPTs. Inspired by the fact that quantum phase transitions are triggered by quantum fluctuations, we observe the fluctuations in spin via the notion of spin squeezing. Namely, the time evolution of its quantifier, the spin-squeezing parameter (SSP), under quenches between different phases as well as on critical boundaries is analysed. We show the extremum of SSP near critical times unveils the evolution of spin correlations that follows the preferable spin direction of the post-quenched Hamiltonian phase. In addition to this, we also demonstrate the specific patterns of evolution of the SSP in different quench scenarios.

Topological models are also shown to have DQPTs when quenched between topologically trivial and nontrivial phases. In the third work, we investigate the quench dynamics of the Su-Schrieffer-Heeger (SSH) model with staggered next-nearest-neighbour (NNN) hoppings. The additional hoppings expand the original SSH model to in total three topological phases. In our works, we show there exists quench scenarios where the number of critical momenta exceeds the change in winding number. These extra dynamical regions are shown to have special features in the locations of the critical momenta on the complex plane as well as the dynamical vector emphasising the evolution of LA. At the same time, the DQPTs in quenching between these dynamical regions reveals a temporary extreme activity in the entanglement state around critical times. The evolutions of correlations inside the subsystems also help distinguishing dynamical phases and further explain the cause of extremal entanglement during DQPTs.

Date of Award	6 Feb 2024
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Wing Chi YU (Supervisor)