Thermodynamics of interacting many-body quantum systems

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, such as transport, has taken place in recent decades, particularly in relation to cold-atom platforms and thermoelectric devices. Furthermore, the role of non-linear interactions in quantum thermal machines, whether a hindrance or a resource, has yet to be fully understood particularly in the finite-temperature regime. Diverse numerical and analytical approaches have come to fruition recently, designed to target these problems in certain regimes regulated by microscopic parameters. This thesis is divided in two parts. Part I is devoted to the study of spin/particle transport in strongly correlated systems in the regime of linear response and to the topic of thermalisation. We begin by addressing the role of integrability and its consequences related to transport, which we then use in the context of the single impurity model, where an integrable model on a one-dimensional lattice is perturbed by an impurity around the centre of the chain. Exhibiting the signatures of quantum chaos, we motivate our work by questioning the nature of transport in this model. We find that despite its chaotic signatures, transport remains ballistic as in the unperturbed model. This result brings us to the question of thermalisation, a topic which is elegantly explained in the context of the eigenstate thermalisation hypothesis (ETH). The ETH postulates that an energy eigenstate encodes the equilibrium ensemble properties in sufficiently complex systems and that local observables in systems initially kept away from equilibrium will eventually thermalise under unitary evolution. Using this framework we find that thermalisation in the single impurity model is anomalous, and the statistical properties of the unperturbed model end up embedded in the perturbed model. We then proceed to investigate the consequences of eigenstate thermalisation in the multipartite entanglement structure of the eigenstates in chaotic Hamiltonians through the quantum Fisher information. We find that the quantum Fisher information can be used to discriminate a pure eigenstate ensemble from a true thermal state. Finally, we address the statistical correlations between matrix elements of local observables in the energy eigenbasis, and provide a connection between these correlations and the timescales of late-time chaos from the out-of-time-order correlators. In Part II we delve into the theory of open quantum systems, particularly in configurations whereby an interacting quantum system is kept out of equilibrium by the action of thermal reservoirs. We begin studying boundary-driven systems, in which a many-body quantum system is driven out of equilibrium be inducing and removing excitations from the boundaries. This treatment allows us to solidify our results in Part I. We criticise boundary-driven configurations from the thermodynamic perspective and argue that such a procedure can only be used to evaluate infinite-temperature properties. Motivated by this fact, we then propose a novel methodology to tractably address finite-temperature transport and thermodynamics in many-body quantum systems, in the context of autonomous thermal machines, overcoming the limitations of boundary-driven configurations.