Order parameter statistics in the critical quantum Ising chain

TL;DR

This paper derives the universal scaling function of total magnetization distribution at criticality in the quantum Ising chain, linking it to the Kondo problem's partition function through integrability.

Contribution

It provides an exact calculation of the magnetization distribution's scaling function for the quantum Ising chain at criticality, connecting it to the Kondo problem.

Findings

Exact scaling function for magnetization distribution obtained

Relation established between quantum Ising chain and Kondo problem

Results applicable to ground and first excited states

Abstract

In quantum spin systems obeying hyperscaling, the probability distribution of the total magnetization takes on a universal scaling form at criticality. We obtain this scaling function exactly for the ground state and first excited state of the critical quantum Ising spin chain. This is achieved through a remarkable relation to the partition function of the anisotropic Kondo problem, which can be computed by exploiting the integrability of the system.