Nonequilibrium and dissipative dynamics of 2D quantum spin systems

Driven-dissipative many-body systems remain a key unsolved problem in quantum mechanics that cuts across atomic-molecular-optical (AMO) physics, quantum information science (QIS) and condensed matter physics (CMP). A ubiquitous class of many-body systems are locally interacting quantum spins (QSs), whose many realisations include magnetic quantum matter in CMP; cold atoms in optical lattices in AMO physics; and qubit arrays in QIS.

Because QS systems tend to establish time-dependent correlations with their large environment, archetypal driven-dissipative systems are even harder to simulate than closed many-body systems. Simulations of open QS systems are out of reach of current quantum hardware, and thus development of numerical approaches on classical computers is an attractive alternative solution.

This PhD project seeks to apply state-of-the-art spectral algorithms to simulate non-equilibrium QS systems in two spatial dimensions. Our vision is to explore and understand the behaviour of interacting QSs embedded in realistic environments, with a particular focus on the role played by disorder which is ubiquitous in solid-state realisations. This ambitious goal will require extending our recently developed many-body Chebyshev method [F.

Brito & A. Ferreira, SciPost Phys. Core 7, 006 (2024)] to systems subject to disorder and connected to an environment. The objectives of this PhD

project are (1) to devise efficient computer codes to simulate arbitrary QS models on the honeycomb lattice; (2) to investigate the modifications to the equilibrium properties introduced by real-space disorder due to random point defects; (3) to investigate the transport of spin-based information and the generation of long distance entanglement using time-evolution methods; and (4) to investigate the dissipative dynamics generated by the coupling of localised and itinerants electrons. Applications will include problems of great interest in CMP and QIS, such as the driven dynamics of quantum antiferromagnets and spin liquids.

A major outcome of this project will be an open-source code, supported by the quantum KITE network (https://quantum-kite.com/background/). The code development phase of the project will be pursued in collaboration with the CMP theory group at the University of Porto, Portugal. The project is aligned with multiple EPSRC priority areas, including ICT, physical sciences and quantum technologies, and the following strategic priorities: (i) the physical and mathematical sciences powerhouse; (ii) quantum technologies; and (iii) ensuring an effective ecosystem for engineering and physical sciences.