Critical Exponents for the SC-Model in the Zero Sector

TL;DR

This paper analyzes a one-dimensional quantum many-body system with specific pair potentials, calculating critical exponents for correlation functions at zero temperature using conformal field theory, revealing connections to the Hubbard model.

Contribution

It provides explicit calculations of critical exponents for a two-component quantum system with unique interactions, extending understanding of its conformal structure.

Findings

Identifies gapless excitations for different s regimes.

Calculates asymptotic correlation functions and critical exponents.

Establishes a link to the Hubbard model with repulsive interactions.

Abstract

In this paper, we continue our investigation of a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential $s(s+1)/{\rm sinh}^{2}(r)$, while unlike particles interact with a pair potential $-s(s+1)/{\rm cosh}^{2}(r)$. For an equal number of particles of the two components, the ground state for $s>0$ corresponds to an antiferromagnet/insulator. Excitations consist of a gapless pair-hole--pair continuum, a two-particle continuum with gap and excitons with gap. For $-1<s<0$, the system has two gapless excitations --- a particle-hole continuum and a two spin-wave continuum. Using finite-size scaling methods of conformal field theory, we calculate the asymptotic expressions and critical exponents for correlation functions of these gapless excitations at zero temperature. The conformal structure is closely related to the Hubbard model with repulsive on-site interaction.