Universality relations in non-solvable quantum spin chains

TL;DR

This paper proves the universal relations between critical exponents and susceptibility in non-solvable quantum spin chains, confirming predictions previously verified only in special solvable models.

Contribution

It provides the first rigorous proof of the Haldane Luttinger liquid conjecture relations in generic non-solvable lattice fermionic and quantum spin models.

Findings

Validated universal relations in non-solvable models

Extended the applicability of Haldane conjecture

Confirmed theoretical predictions in more general settings

Abstract

We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models.