Weak Coupling Phase Diagram of the Two Chain Hubbard Model

TL;DR

This paper introduces a method to analyze the phase diagram of coupled one-dimensional Hubbard-like systems, exemplified by the two-chain Hubbard model, revealing seven possible states at weak coupling and conditions for superconductivity analogs.

Contribution

The paper develops a general approach for determining phase diagrams of weakly coupled 1D Hubbard systems, providing the first controlled results for the two-chain model across doping and hopping parameters.

Findings

Seven out of nine possible states identified at weak coupling.

Detailed phase diagram for the two-chain Hubbard model.

Conditions for the model to resemble a 1D superconductor.

Abstract

We present a general method for determining the phase diagram of systems of a finite number of one dimensional Hubbard--like systems coupled by single--particle hopping with weak interactions. The technique is illustrated by detailed calculations for the two--chain Hubbard model, providing the first controlled results for arbitrary doping and inter-chain hopping. Of nine possible states which could occur in such a spin--$1/2$ ladder, we find seven at weak coupling. We discuss the conditions under which the model can be regarded as a one--dimensional analog of a superconductor.