Exact ground and excited states of a t-J ladder doped with two holes

TL;DR

This paper provides exact analytical solutions for the ground and excited states of a two-leg t-J ladder with two holes, revealing a bound d-wave pair with superconducting correlations in the strong rung coupling limit.

Contribution

It derives exact ground and excited states for a doped t-J ladder, including wavefunctions and symmetry, and maps the model to an effective boson model showing superconducting tendencies.

Findings

Ground state is a bound pair of holes with S=0.

Charge excitation is gapless, spin excitation has a gap.

Strong rung coupling leads to effective boson model with superconducting correlations.

Abstract

A two chain ladder model is considered described by the strong coupling $t-t^\prime-J-J^\prime$ Hamiltonian. For the case of two holes moving in a background of antiferromagnetically interacting spins, exact, analytical results are derived for the ground state energy and low-lying excitation spectrum. The ground state is a bound state of two holes with total spin S=0. The charge excitation is gapless and the spin excitation has a gap. The corresponding wavefunctions are also exactly determined. The bound hole pair is found to have symmetry of the d-wave type. In the limit of strong rung coupling, the model maps onto an effective hard core boson model which exhibits dominant superconducting pairing correlations.