Non-equilibrium dynamics in one-dimensional constrained quantum statistical systems

Dávid X. Horváth

Federica Maria Surace

In the last decade the non-equilibrium dynamics of isolated quantum systems has raised a huge interest for both its conceptual and practical implications. Simulation of quantum dynamics represents by now a very active research effort, with highly controllable quantum devices composed of hundreds of qubits already being realized in numerous setups. These offer the unprecedented possibility to access real-time quantum dynamics and strongly correlated quantum many-body states, opening numerous avenues not only for future quantum technologies, but also for long-standing theoretical problems. One of the most sought-after applications is the computation of real-time evolution in theories of fundamental interactions. Since Wilson's proposal in 1974, the equilibrium phase diagrams of lattice gauge theories have been successfully investigated with Monte Carlo simulations in a wide range of parameters. Nonequilibrium properties, on the other hand, cannot be accessed with conventional techniques. Thanks to the recent advances in numerics (e.g. tensor networks) and experiments (quantum simulation), new promising tools are now available for tackling these questions. Remarkable works have already demonstrated that applying these techniques to simple theories, such as one-dimensional quantum electrodynamics, can help to detect the signatures of confinement and pair creation. Despite these impressive achievements, investigating the non-equilibrium dynamics of gauge theories with quantum simulators turned out to be extremely challenging. This is mostly due to the complex constrained dynamics of these theories, which make their simulation with realistic atomic platforms particularly difficult. At the same time, the dynamical constraints can play a key role in determining novel interesting phenomena and peculiar non-equilibrium properties. These phenomena -- which include, for example, quantum scars, fractons, Hilbert space fragmentation -- can lead to anomalous dynamics, eventually evading the paradigm of thermalization, which predicts the relaxation of physical observable to their thermodynamic values. The aim of this thesis is twofold: first, we want to address through a combination of numerical and analytical tools some of the open questions regarding the non-equilibrium dynamics of quantum many-body systems with constrained Hilbert spaces, including lattice gauge theories. In addition, the work reported here is part of a large effort of the community towards the quantum simulation of complex phenomena of condensed matter and high-energy physics.

William C. Schieve

Tim Langen, Michael Gring, Maximilian Kuhnert +7 more

Non-equilibrium dynamics of isolated quantum many-body systems play an important role in many areas of physics. However, a general answer to the question of how these systems relax is still lacking. We experimentally study the dynamics of ultracold one-dimensional (1D) Bose gases. This reveals the existence of a quasi-steady prethermalized state which differs significantly from the thermal equilibrium of the system. Our results demonstrate that the dynamics of non-equilibrium quantum many-body systems is a far richer process than has been assumed in the past.

Richard Tattersall, Andrew William Baggaley, T. P. Billam

Abstract When a system undergoes a rapid quench from a disordered to an ordered phase, it does not order instantly but instead relaxes towards equilibrium over time. During this relaxation, the dynamical scaling hypothesis predicts that the length scale of ordered regions increases, with later patterns statistically similar to earlier ones except for a change in global scale. Quantum gases are one of many systems in which such out of equilibrium behaviour is predicted to occur. Here, we present a method for systematically testing when dynamical scaling is taking place, by quantifying the similarity of the rescaled two-point correlation function over time using the Mahalanobis distance. Data on the velocity field of a two-dimensional quantum fluid, generated from point vortex simulations, are used to illustrate the application of this method.

Gérard G. Emch