TENSOR NETWORK APPROACHES IN NON-EQUILIBRIUM QUANTUM MANY-BODY DYNAMICS

Abstract

Understanding the dynamics of non-equilibrium quantum systems has been a longstanding challenge in a wide range of physical phenomena. Recent advancements in various quantum technologies have driven theoretical investigations of non-equilibrium quantum many-body dynamics. A crucial aspect of the theory is the development of computational methods, which have led to significant results and show promising directions for further development. However, simulating these complex systems using classical algorithms remains extremely difficult, primarily due to the challenge of identifying physically principled and efficient approximations capable of reducing their computational complexity.This thesis discusses theoretical and numerical studies on the non-equilibrium dynamics of quantum many-body systems, particularly focusing on the steady-state transport of conserved quantities in various one-dimensional spin systems. We study transport phenomena employing boundary-driven open quantum setups and investigate various aspects of the non-equilibrium dynamics induced by these systems. Our goal is to understand steady-state phenomena and to push the boundaries of simulation capacity using state-of-the-art technologies. In the first part, we examine the non-equilibrium steady-state (NESS) phases of an interacting Aubry-Andr´e-Harper model. This model involves a quasiperiodic potential, leading to interesting emergent collective phenomena. The observed spin transport and quantum correlation structure suggest the presence of multiple dynamical phases between the well-studied thermal and many-body-localized phases. In the second part, we study the impact of operator weight dissipation on the scaling behavior of transport in various spin models. Our findings suggest that dissipation’s effect on transport depends on the system’s conserved quantities. When dissipation preserves these symmetries, it maintains the scaling of the system’s transport properties. However, when it disrupts these conserved quantities, it leads the system towards diffusive scaling of transport. In the third part, we investigate energy transport within the non-integrable regime of the Z3 chiral clock model, utilizing Lindblad operators with adjustable size and temperature. Through scaling analysis, we extract the model’s transport coefficients at relatively high temperatures, both above its gapless and gapped low-temperature phases. Furthermore, we calculate the temperature dependence of the energy diffusion constant across various model parameters, including the regime where the model exhibits quantum critical behavior at low temperatures.