Bosonization and phase Diagram of the one-dimensional t-J model

TL;DR

This paper analytically explores the phase diagram of the one-dimensional t-J model using bosonization and renormalization group techniques, introducing a deformation approach to handle constraints and comparing results with existing literature.

Contribution

The paper introduces a deformation of Hubbard operators to analyze the t-J model and combines bosonization with RG to map its phase diagram, validating the approach against previous methods.

Findings

Phase diagram mapped using bosonization and RG techniques.

Deformation parameter $\Delta$ allows perturbative analysis.

Results consistent with existing literature.

Abstract

We present an analytic study of the phase diagram of the one-dimensional t-J model and a couple of its cousins. To deal with the interactions induced by the no double occupancy constraints, we introduce a deformation of the Hubbard operators. When the deformation parameter $\Delta$ is small, the induced interactions are softened, accessible by perturbation theory. We combine bososnization with renormalization group techniques to map out the phase diagram of the system. We argue that when $\Delta\to 1$, there is no essential change in the phase diagram. Comparison with the existing results in the literature obtained by other methods justifies our deformation approach.