Generic short-range interactions in two-leg ladders

TL;DR

This paper derives a comprehensive Hamiltonian for two-leg ladders with arbitrary interactions, exploring their phase diagrams and conditions for Tomanaga-Luttinger liquid behavior, with applications to lithium purple bronze.

Contribution

It introduces a generalized Hamiltonian for two-leg ladders with multiple interactions and analyzes their phases using renormalization group methods, highlighting conditions for exotic phases and Tomanaga-Luttinger liquids.

Findings

Increasing interactions enriches the phase diagram at half-filling.

Exotic phases emerge when the number of interactions is large and zigzag angle is small.

Tomanaga-Luttinger liquid phase occurs only with ferromagnetic rung spin interactions.

Abstract

We derive a Hamiltonian for a two-leg ladder which includes an arbitrary number of charge and spin interactions. To illustrate this Hamiltonian we consider two examples and use a renormalization group technique to evaluate the ground state phases. The first example is a two-leg ladder with zigzagged legs. We find that increasing the number of interactions in such a two-leg ladder may result in a richer phase diagram, particularly at half-filling where a few exotic phases are possible when the number of interactions are large and the angle of the zigzag is small. In the second example we determine under which conditions a two-leg ladder at quarter-filling is able to support a Tomanaga-Luttinger liquid phase. We show that this is only possible when the spin interactions across the rungs are ferromagnetic. In both examples we focus on lithium purple bronze, a two-leg ladder with zigzagged legs which is though to support a Tomanaga-Luttinger liquid phase.