UCLA

After a brief introduction that overviews quantum phase transitions and quantum criticality at finite temperatures, we begin Chapter 1 by introducing an exactly solved model with multiple critical lines - transverse field Ising model with added 3-spin interaction. We focus on the phase diagram and discuss several features associated with critical lines. Then we explicitly show how to calculate the spin-spin correlation function and dynamical structure factor S(k, ω) in terms of a Pfaffian. Next, we present the zero-temperature dynamical structure factor at various critical lines in the pure and disordered systems. Finally, this chapter concludes with a discussion about further research on similar models with quantum critical lines or quantum critical surfaces.In Chapter 2, we emphasize the finite temperature behavior of the same model as in the previous chapter by first showing any necessary modifications when the temperature is nonzero. Then we illustrate the finite temperature properties of the model in various aspects. We show how specific heat is computed and its temperature dependence at several critical points. In addition, we identify several crossovers (quantum critical to quantum disordered or renormalized classical) by classifying different temperature dependencies of the correlation length and thus constructing a quantum critical fan along one of the critical lines. In Chapter 3, we start with an introduction to show what measurement-induced entanglement transition is and its current status. Next, we discuss our model and its setup. Topological entanglement entropy and mutual information have been calculated to construct the phase diagram. We discover the system ends in different phases by applying non-commutative measurement gates at each time step on a line of qubits. Moreover, we obtain various critical exponents through finite-size scaling.