Entanglement Phase Transition of Interacting Bosons under Random Measurements

Abstract

In this thesis, we study the entanglement phase transition from volume-law to area-law entanglement in a hard-core boson chain model under continuous measurement of local occupation number. We are specifically interested in observing the effects of spatially random measurement strengths on this phase transition. We have used the quantum trajectory approach to model the measurement process. The random measurement strengths case is compared with the constant strengths case. Quantities like von Neumann Entanglement Entropy, particle densities, bipartite and tripartite mutual information, probability distribution of single site von Neumann entropy and connected correlation function of number operators are studied to get a more comprehensive look at the system under measurement. Finally, we perform the finite size scaling analysis to study scaling behaviours of entanglement entropy, bipartite mutual information and connected correlation function at the entanglement transitions. For random measurements on a purely hard-core boson chain, which can be mapped to a non-interacting model of fermions, we see entanglement entropy increasing linearly with system size for small mean values of the random strengths. The increase is suppressed for larger mean values. This suggests a possible entanglement transition, which also shows a maximum at the transition point in bipartite mutual information. We also observe significant changes in some quantities with increasing the variance of the distribution from which strengths are chosen. For interacting boson chain with the available results, we observe an increase in entanglement entropy with system size. From scaling analysis of the random case, we obtain exponents that are different from the constant case.