Information scrambling in spin glasses and entanglement transition of monitored bosons

Abstract

In this thesis, I study various aspects of quantum many-body dynamics from the perspective of quantum information scrambling and entanglement dynamics in closed systems as well as systems interacting with the environment. There are five chapters. The first chapter introduces the ideas of classical, quantum many-body chaos, quantum entanglement, and the quantum dynamics of systems subjected to continuous measurements. This provides the necessary background material and gives an overview of the rest of the thesis. In the second chapter, I study the effect of quantum, thermal fluctuations, and complex relaxation dynamics on the quantum many-body chaos, across a symmetry breaking phase transition, in a random Heisenberg model of spin glass, known as Sachdev-Ye model. The chaos is characterized by the quantum Lyapunov exponent extracted from the out-of-time ordered correlation functions. I then analyze the asymptotic behavior of the Lyapunov exponent as a function of temperature and a quantum parameter S, namely the spin of the bosonic representation for the Heisenberg spins. Comparing our results with an earlier study on chaos in the p-spin glass model I f ind that the peak in the Lyapunov exponent is present only as a function of S but not as a function of temperature. From this, I conclude that the evolution of complexity with thermal fluctuations in the SY model is different from that of the p-spin model. In the third chapter, I generalize the zero-dimensional Sachdev-Ye and p-spin glass models into 1D chains of spin glass, thus paving the way for studying the spatial dynamics of information scrambling, diagnosed by butterfly velocity. Following the earlier chapter, I study the effect of quantum, thermal fluctuations, and complex relaxation dynamics on the butterfly velocity, across a symmetry breaking phase transition in the Sachdev-Ye and p-spin glass models and compare them. I employ two different methods for calculating the butterfly velocity which I refer to as real and imaginary p methods and find that the results obtained using both these methods closely agree with each other. The behavior of butterfly velocity is observed to be similar to that of the Lyapunov exponent. Further, from the knowledge of the Lyapunov exponent and the butterfly velocity, I calculate a proxy of the diffusion constant. In the fourth chapter, I explore the dynamics induced by continuous measurements in a 1D model of interacting bosons, with a three-body constraint, using the method of quantum trajectories. I use various measures of entanglement and correlation functions to characterize the nature of the dynamical phase transition. Based on earlier work on the measurement induced criticality in a hardcore boson model, in this study, I probe the effect of relaxing the hard-core constraint on the nature of the criticality. I f ind an entanglement transition from the volume law phase to the area law phase with increasing measurement strength. I then calculate various exponents and coefficients at the critical point by performing a finite-size scaling analysis. Although these values do not seem to fit into any known universality class, they appear very close to those of the case of the hardcore boson model under continuous measurements. In the last chapter, I conclude the thesis with a discussion of the important findings in the earlier chapters and possible future directions in which these works can be expanded.