Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations

TL;DR

This paper develops effective Hamiltonians for hole dispersions in antiferromagnetic spin-1/2 two-leg ladders using self-similar continuous unitary transformations, providing insights into charge dynamics relevant for high-$T_c$ superconductors.

Contribution

It introduces a method to derive effective models in the thermodynamic limit for doped ladders, enabling detailed analysis of hole dispersions in these systems.

Findings

Calculated single-hole dispersions in the ladder system.

Method allows exploration of experimentally relevant parameter space.

Lays groundwork for studying two-hole interactions and Cooper pairing.

Abstract

The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important model system for the high-$T_c$ superconductors based on cuprates. Using the technique of self-similar continuous unitary transformations we derive effective Hamiltonians for the charge motion in these ladders. The key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit. A real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space. From the effective Hamiltonians we calculate the dispersions for single holes. Further calculations will enable the calculation of the interaction of two holes so that a handle of Cooper pair formation is within reach.