The full text of this item is not available at this time because the student has placed this item under an embargo for a period of time. The Libraries are not authorized to provide a copy of this work during the embargo period, even for Texas A&M users with NetID.
Non-Equilibrium Dynamics and the Absence of Thermalization in Quantum Many-Body Systems
Abstract
Statistical mechanics relies on relaxation towards the maximally entropic state in thermal equilibrium. The emergence of statistical mechanics in such systems, known as quantum thermalization, proceeds by the relaxation of local sub-regions to a thermal state via the exchange of quantum correlations with the remainder of the system. A sufficient condition for the thermalization of initial states in an isolated quantum system is the Eigenstate Thermalization Hypothesis (ETH). Recently, new mechanisms of ETH violation have emerged: quantum many-body scars and Hilbert space fragmentation. Here ETH-violating states coexist with thermal states in the man-body spectrum, where the time evolution of an initial state depends on the properties of the eigenstates it weighs on.
We obtain one of the first examples of a quantum many-body system with a fragmenting Hilbert space where a quantum many-body scar is analytically constructed. These exact states include an entanglement phase transition from area to log. When quenched from an initial state, a wide range of non-equilibrium dynamics are realized, such as superdiffusive domain wall melting. This work ultimately illustrated that a spectrum could hold exponentially many quantum many-body scars, whereas the traditional belief was that there could be, at most, polynomial many. Similarly, we introduced the first example of a quantum many-body scar with volume law entanglement scaling, rainbow scars. This work demonstrated that a highly excited state with an extensive entanglement entropy could retain a simple entanglement structure.
Another critical aspect of non-equilibrium dynamics is transport. We constructed a tunable time-dependent free fermion model that displays various universal behaviors. When time translation is violated, the subsequent late-time hydrodynamic behavior is always diffusive.
We conclude this dissertation by studying dissipative dynamics in a quantum circuit. By replacing classical logic with quantum logic, we eliminate the need for mid-circuit measurements, realizing an autonomous error-correcting model. The model we consider, Toom’s model, is a cellular automaton that is a known decoder for the Toric code. Thus this work is a stepping stone to higher dimensional models that are quantum error correcting codes and provides a proof of principle example of stabilizing quantum matter in 2D.
Subject
Quantum many-body physicsthermalization
quantum many-body scars
quantum circuit
transport
fragmentation
entanglement
area law
volume law
Tooms model
integrability
localization
disorder-free localization
quantum error correction
Citation
Langlett, Christopher Michael (2023). Non-Equilibrium Dynamics and the Absence of Thermalization in Quantum Many-Body Systems. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /198926.
Related items
Showing items related by title, author, creator and subject.
-
Asiri, Saeed Mater M (2018-08-06)The ability to perform mechanical states reconstruction is an essential task in quantum optomechanics to understand different quantum aspects of mechanical states of motion. Many interesting phenomena appear when the light ...
-
Fan, Longfei (2018-08-03)Quantum measurement is the cornerstone of quantum computing and quantum information. It has many exciting applications. Various quantum optical systems are key to experimental physics because of their high precision and ...
-
Wang, Qian (Texas A&M University, 2005-02-17)In this dissertation, I have studied four theoretical problems in quantum tunneling, quantum computing, and high-temperature superconductivity. I have developed a generally-useful numerical tool for analyzing impurity-induced ...