Chiral eigenbases of the XX and XY quantum spin chains

TL;DR

This paper computes observable values in chiral eigenstates of the XX and XY quantum spin chains, comparing them with traditional eigenstates, and interprets the spectrum in terms of kink and antikink excitations.

Contribution

It introduces a detailed analysis of chiral eigenstates in the XX and XY chains, including diagonalization, norm calculation, and correlation functions, offering new insights into their spectrum and excitations.

Findings

Calculated observables in chiral eigenstates

Compared chiral basis results with fixed magnetization basis

Interpreted spectrum via kink and antikink scattering states

Abstract

We calculate the values of observables in chiral eigenstates of the XX quantum spin chain that were introduced in previous work and compare the form of the result with the respective expressions obtained in the more familiar eigenbasis of states with fixed magnetization in the $z$ direction. We carry out the diagonalization of the XY spin chain in the chiral basis. We calculate the norm of the chiral XY eigenstates, and the values of the one-point functions and some neighbor two-point correlation functions. We interpret the spectrum and the particle content of the XY chain in terms of scattering states of an even number of kink and antikink excitations that are created over a reduced Brillouin zone.