Bridging Quantum Thermodynamics, Gauge Theories, and Quantum Simulations

Abstract

This thesis concerns the thermodynamic laws that strongly coupled, open quantum systems obey, the application of these laws to problems in high-energy physics, and their potential verification on quantum simulators. A system of interest is strongly coupled to a reservoir when the system-reservoir interactions account for a non-negligible portion of the total energy. In this situation, it is unclear how to divide the interaction energy into system and reservoir contributions. I identify prescriptions for defining thermodynamic quantities that are consistent with the first law of thermodynamics. Instantaneous-quench processes are simple nonequilibrium processes realized in quantum simulation experiments. For these quench processes, I establish analytically and illustrate numerically which of these prescriptions are consistent with the second law. I then extend the framework to thermodynamic processes with arbitrary time-dependence. I show that the second law holds under physically motivated assumptions about the evolution of strongly coupled systems.

Gauge theories underpin our best models of nature's fundamental interactions. Lattice Hamiltonian formulations of these theories are most naturally suited to quantum simulations. However, calculations with such formulations must be restricted to a particular subspace of the total Hilbert space. This restriction complicates the separation of the system and the reservoir of a bipartite system. This corresponds to the situation encountered in strong coupling thermodynamics. Hence, the framework of strong-coupling quantum thermodynamics naturally applies to lattice gauge theories. The results demonstrate that thermodynamic quantities signal phase transitions during quench processes of lattice gauge theories.

Finally, this thesis connects quantum thermodynamics and quantum information science by uncovering a relationship between thermodynamic quantities and the entanglement Hamiltonian of a system coupled strongly to a reservoir. This connection enables a route to measuring thermodynamic quantities in quantum simulations of instantaneous, nonequilibrium quenches. As a first step towards experimental realization, a quasi-local operator \textit{ans\"atz} inspired by the Bisognano-Wichmann theorem is proposed for the entanglement Hamiltonian of thermal states of spin systems. I find that a quasi-local \textit{ans\"atz} effectively approximates the entanglement Hamiltonian of thermal states of lattice systems with short-range and long-range interactions. I also investigate the sensitivity of the \textit{ans\"atz} to phase transitions.

This thesis connects quantum thermodynamics, lattice gauge theories, and quantum simulations by demonstrating how to compute thermodynamic quantities in a lattice gauge theory undergoing nonequilibrium processes and by proposing an experimental route for testing the thermodynamic framework on a quantum simulator.