TY - BOOK

T1 - Non-Equilibrium Dynamics in One-Dimensional Quantum Many-Body Systems

AU - Gawatz, Raffael

PY - 2021

Y1 - 2021

N2 - Periodically driven quantum systems are inherently out of equilibrium. This provides a fertile ground for phases and phenomena to occur, some of which unprecedented in equilibrium. These phases and phenomena, however, are challenging to realize. Considering very well isolated systems, as found in cold atoms or trapped-ion experiments, a periodically driven system will tend to an unfavorable infinite temperature state, which omits the existence of non-trivial correlations. Numerous concepts aimed at tackling this dilemma have been proposed in recent years. One approach is to damp the heating process such that long-lived, non-trivial transients emerge. In the first part of this talk, we will discuss a one-dimensional interacting, charge pump system, in which heating is only suppressed for parts of the degrees of freedom. Here, the system can prethermalize into a quasi-steady state which can host universal charge transport for a long period of time. We will examine the many-body nature of the quasi-steady state by several one-body and many-body signatures and report on the stability of the non-equilibrium pump under the influence of local disorder. Another way to prevent heating towards a featureless state is to couple the system to baths. Here the out of equilibrium dynamics allows the system to dissipate excess heat into the baths. When studying the dynamics of interacting open many-body systems coupled to Markovian baths, one often relies on numerical tools and approximation, such as the evolution of an ensemble of quantum trajectories mimicking the evolution of the reduced system density matrix. In the second part, we will incorporate the evolution of quantum trajectories into another highly successful numerical concept of matrix product states and report on its accuracy. The evolution scheme thereby relies on a recently established novel master equation in Lindblad form, referred to as the "Universal Lindblad equation", which does not impose further conditions on the system and can thus be used for general, many-body models.

AB - Periodically driven quantum systems are inherently out of equilibrium. This provides a fertile ground for phases and phenomena to occur, some of which unprecedented in equilibrium. These phases and phenomena, however, are challenging to realize. Considering very well isolated systems, as found in cold atoms or trapped-ion experiments, a periodically driven system will tend to an unfavorable infinite temperature state, which omits the existence of non-trivial correlations. Numerous concepts aimed at tackling this dilemma have been proposed in recent years. One approach is to damp the heating process such that long-lived, non-trivial transients emerge. In the first part of this talk, we will discuss a one-dimensional interacting, charge pump system, in which heating is only suppressed for parts of the degrees of freedom. Here, the system can prethermalize into a quasi-steady state which can host universal charge transport for a long period of time. We will examine the many-body nature of the quasi-steady state by several one-body and many-body signatures and report on the stability of the non-equilibrium pump under the influence of local disorder. Another way to prevent heating towards a featureless state is to couple the system to baths. Here the out of equilibrium dynamics allows the system to dissipate excess heat into the baths. When studying the dynamics of interacting open many-body systems coupled to Markovian baths, one often relies on numerical tools and approximation, such as the evolution of an ensemble of quantum trajectories mimicking the evolution of the reduced system density matrix. In the second part, we will incorporate the evolution of quantum trajectories into another highly successful numerical concept of matrix product states and report on its accuracy. The evolution scheme thereby relies on a recently established novel master equation in Lindblad form, referred to as the "Universal Lindblad equation", which does not impose further conditions on the system and can thus be used for general, many-body models.

M3 - Ph.D. thesis

BT - Non-Equilibrium Dynamics in One-Dimensional Quantum Many-Body Systems

PB - Niels Bohr Institute, Faculty of Science, University of Copenhagen

ER -