A stochastic approach to quantum spin systems

Abstract

In this Thesis, we investigate an exact stochastic approach to quantum spins systems [2–4], in which the unitary time evolution of interacting spins is mapped onto the stochastic dynamics of classical variables and the interactions play the role of noise. We study this approach both in real and imaginary time, focussing in particular on the quantum Ising model. In real time, we demonstrate that the stochastic approach is capable of accessing a wide range of systems, including higher dimensional and disordered ones, by numerically computing time-dependent quantum expectation values from stochastic processes. Furthermore, we show that the dynamics of the classical variables contains signatures of dynamical quantum phase transitions [5]. We then consider imaginary time evolution, showing how the stochastic approach can be used to compute grounds state expectation values. In this context, we introduce a measure transformation by means of which we are able to access large systems, as we demonstrate for N = 150 spins. We conclude our discussion by outlining directions for further developments.

Date of Award	1 Feb 2019
Original language	English
Awarding Institution	King's College London
Supervisor	Joe Bhaseen (Supervisor) & Benjamin Doyon (Supervisor)