Exactly Solvable Fermionic N-chain Models

TL;DR

This paper introduces an exactly solvable model of coupled fermionic chains with gauge interactions, revealing Luttinger-liquid behavior and potential instabilities, advancing understanding of complex one-dimensional fermionic systems.

Contribution

It generalizes the Schulz-Shastry model to multiple chains with two fermion species, providing exact solutions and insights into correlation functions and phase instabilities.

Findings

Correlation functions decay as power laws with non-integer exponents

The model's ground state can be obtained via a unitary transformation

Identification of relevant perturbations indicating possible instabilities

Abstract

Motivated by the problem of N coupled Hubbard chains, we investigate a generalisation of the Schulz-Shastry model containing two species of one-dimensional fermions interacting via a gauge field that depends on the positions of all the particles of the other species. The exact many body ground state of the model can be easily obtained through a unitary transformation of the model. The correlation functions are Luttinger-like - i.e., they decay through power laws with non-integer exponents. Through the interaction dependent correlation functions of the two-particle operators, we identify the relevant perturbations and hence, possible instabilities.