Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations

TL;DR

This paper provides exact calculations of non-equilibrium correlation functions in quantum anisotropic XY models, expressing them as sums of Pfaffians and determinants for single particle excitations, advancing understanding of quantum dynamics.

Contribution

It introduces a method to compute non-equilibrium matrix elements in the XY model using Pfaffians, simplifying to determinants for single particle states.

Findings

Exact expressions for non-equilibrium matrix elements as sums of Pfaffians.

Simplification to determinants for single particle excitations.

Enhanced understanding of quantum dynamics in XY models.

Abstract

We calculate exactly matrix elements between states that are not eigenstates of the quantum XY model for general anisotropy. Such quantities therefore describe non equilibrium properties of the system; the Hamiltonian does not contain any time dependence. These matrix elements are expressed as a sum of Pfaffians. For single particle excitations on the ground state the Pfaffians in the sum simplify to determinants.