Thermodynamics of interacting many-body quantum systems

TL;DR

This thesis explores the thermodynamics of interacting many-body quantum systems, focusing on transport, thermalisation, and quantum thermal machines, with new tensor-network methods for finite-temperature analysis.

Contribution

It introduces a novel tensor-network approach to study thermodynamics of quantum machines and investigates effects of integrability-breaking on transport and thermalisation.

Findings

Local integrability-breaking affects transport properties.

Eigenstate thermalisation relates to entanglement and correlations.

Tensor-network methods enable finite-temperature analysis of quantum machines.

Abstract

Technological and scientific advances have given rise to an era in which coherent quantum-mechanical phenomena can be probed and experimentally-realised over unprecedented timescales in condensed matter physics. In turn, scientific interest in non-equilibrium dynamics and irreversibility signatures of thermodynamics has taken place in recent decades, particularly in relation to cold-atom platforms and thermoelectric devices. In this PhD thesis I summarise some of the most important results obtained over the duration of my PhD, on the topic of thermodynamics involving interacting many-body quantum systems. The topics of discussion encompass three main themes: spin/particle transport in non-integrable systems, explorations in eigenstate thermalisation and finite-temperature transport in autonomous thermal machines. By questioning the effect of local integrability-breaking perturbations, I describe the subtle effects that may rise from conservation laws and their connection to linear response transport using microscopic models. Then, I describe thermalisation in the context of the eigenstate thermalisation hypothesis and its consequence to multipartite entanglement and high-order correlation functions. Finally, motivated by the necessity of describing quantum thermal machines in the finite-temperature regime, I introduce a novel tensor-network based method to investigate thermodynamic properties of autonomous machines that employ interacting many-body systems as working media.