Simulation of Non-Equilibrium Quantum Dynamics in Monitored and Quenched Systems

Understanding the interaction and dynamics of quantum many-body systems is a longstanding research interest that has led to numerous theoretical, experimental and technological advances. However, the quantum Hilbert space of quantum many-body systems scales exponentially with the number of degrees of freedom, making direct brute-force approaches intractable to understand the non-equilibrium quantum dynamics exhibited in these systems. Furthermore, the study of out-of-equilibrium quantum dynamics is further enriched by taking into account external interactions and manipulations on an otherwise closed quantum systems. In this dissertation, we investigate and simulate the non-equilibrium quantum dynamics of both closed and open quantum systems, where we study quenched dynamics in the former case, and the effect of quantum measurements for the latter case. We first examine non-interacting fermionic lattice systems subject to quantum measurements (as well as other quantum operations such as particle injection). Repeated, periodic sequence of quantum measurements can induce effective new non-equilibrium dynamics in matter with chiral edge transport via measurement alone. We consider the additional diffusion transport that is present in these systems with measurement-induced chiral transport, providing analytical and numerical treatments to describe these diffusive modes. In addition, we consider the effects of various types of disorder in these systems: site dilution, lattice distortion, and disorder in onsite chemical potential. In the quantum Zeno limit, the effective descriptions for the disordered measurement system with lattice distortions and random onsite potential can be modelled as a classical stochastic model, and the overall effect of increasing these disorders induces a crossover from perfect flow to zero transport. On the other hand if vacancies are present in the lattice the flow of particles per measurement cycle undergoes a percolation phase transition from unity to zero with percolation threshold pc = 0.26, with critical exponent v = 1.35. We also present numerical results away from Zeno limit and note that the overall effect of moving away from the Zeno effect is to reduce particle flow per cycle when the measurement frequency in our protocol is reduced. In the second part of this thesis, we attempt to simulate quark confinement dynamics in low-dimensional systems by framing the problem in a condensed matter setting. More precisely, we provide an analogous description of quark confinement by studying the quenched dynamics of domain walls in the Mixed Field Ising Model. We explore the interplay of confinement, string breaking and entanglement asymmetry in this setting. First, we consider the evolution of an initial domain wall and show that, surprisingly, while the introduction of confinement through a longitudinal field typically suppresses entanglement generation, it can also serve to increase it beyond a bound set for free particles. Our model can be tuned to conserve the number of domain walls, which gives an opportunity to explore entanglement asymmetry associated with link variables. We study two approaches to deal with the non-locality of the link variables, either directly or following a Kramers-Wannier transformation that maps bond variables (kinks) to site variables (spins). We develop a numerical procedure for computing the asymmetry using tensor network methods and use it to demonstrate the different types of entanglement and entanglement asymmetry.