Realising complex quantum states of matter via symmetries and heating

• Main Author: Tindall, Joseph
• Format: Dissertation
• Language: English
• Published: University of Oxford 2021
• Subjects: Condensed matter; Quantum theory; Superconductivity

Identifying mechanisms which can guide many-body quantum systems into regimes where properties such as entanglement and long-range coherence are manifest is a fundamental goal for those working in the field of strongly correlated systems. With this comes the potential to realise and exploit states of matter such as superconductors and superfluids, where quantum behaviour is observable at the macroscopic level. In this thesis we study how symmetries and heating can, counterintuively, be used to realise phases of matter with such desirable properties. We prove how heating a many-body system whilst preserving certain symmetries - such as those of the special unitary group - result in the formation of maximum entropy states which are confined to a subspace of the total Hilbert space and are capable of possessing finite, completely uniform off-diagonal correlations. This mechanism is termed heating-induced order and is independent of any microscopic details. We use the Hubbard model as a central example where this mechanism can be observed. Heating is introduced to the system via periodic driving or local dissipation and we study the various ordered steady states which emerge in this setup. We discuss the applicability of this mechanism to the thermodynamic limit and its relevance to recent solid-state experiments observing photo-induced superconductivity in irradiated compounds. We then show how, in an open quantum system, the satisfaction of a set of simple symmetry-based conditions guarantees an absence of stationarity and the formation of coherent oscillations in the long-time limit. We prove how this result subsumes and goes beyond the established notion of a Decoherence Free Subspace. When these conditions are satisfied in the presence of heating-induced order we observe the formation of an entangled, correlated state undergoing identical limit cycles at all positions in space. This leads us to formulate a novel process for quantum synchronisation which is based on the combination of these symmetry-based conditions and the mechanism of heating-induced order.