Ground state wave functionals for $1+1$-dimensional fermion field theories

TL;DR

This paper derives exact ground state wave functions for various 1+1 dimensional fermion field theories using path-integral methods, revealing universal Jastrow factorized forms and matching known exponents from Bethe Ansatz solutions.

Contribution

It provides explicit ground state wave functions for several models, including Thirring, Luttinger, and Coset fermion models, and demonstrates their universal Jastrow structure.

Findings

Wave functions have Jastrow factorized form with calculated exponents.

Results agree with Bethe Ansatz exponents for Sutherland model and Haldane-Shastri chain.

Universal behavior of wave functions across different models in the same class.

Abstract

We use path-\-integral methods to derive the ground state wave functions of a number of two-\-dimensional fermion field theories and related systems in one-\-dimensional many body physics. We derive the exact wave function for the Thirring/Luttinger and Coset fermion models and apply our results to derive the universal behavior of the wave functions of the Heisenberg antiferromagnets and of the Sutherland model. We find explicit forms for the wave functions in the density and in the Grassmann representations. We show that these wave functions always have the Jastrow factorized form and calculated the exponent. Our results agree with the exponents derived from the Bethe Ansatz for the Sutherland model and the Haldane-\-Shastri spin chain but apply to all the systems in the same universality class.