Ising Quantum Chains

TL;DR

This paper provides a comprehensive pedagogical overview of the equilibrium and nonequilibrium properties of free fermionic quantum spin chains, including phase transitions, effects of disorder, and relaxation dynamics.

Contribution

It offers a detailed explanation of the diagonalisation method and explores the impact of aperiodicity and quenched disorder on quantum chain criticality and dynamics.

Findings

Analysis of phase transitions and phase diagram.

Effects of aperiodicity and disorder on critical properties.

Insights into relaxation and aging phenomena in quantum chains.

Abstract

The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical properties of the quantum chain. The remaining part is devoted to the nonequilibrium dynamical behaviour of such quantum chains relaxing from a nonequilibrium pure initial state. In particular, a special attention is made on the relaxation of transverse magnetization. Two-time linear response functions and correlation functions are also considered, giving insights on the nature of the final nonequilibrium stationnary state. The possibility of aging is also discussed.