The ground state of the two-leg Hubbard ladder: a density--matrix renormalization group study

TL;DR

This study uses density-matrix renormalization group techniques to analyze the ground state properties of two-leg Hubbard ladders, revealing phases with spin gaps, pairing correlations, and Luttinger liquid behavior.

Contribution

It provides detailed numerical insights into the phase diagram and correlation functions of doped and half-filled two-leg Hubbard ladders, highlighting the nature of spin gaps and pairing.

Findings

Half-filled ladder is an insulating spin-gapped system.

Doped holes form singlet pairs with power-law decay of pairing correlations.

Large interband hopping leads to Luttinger liquid phases.

Abstract

We present density-matrix renormalization group results for the ground state properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an insulating spin-gapped system, exhibiting a crossover from a spin-liquid to a band-insulator as a function of the interchain hopping matrix element. When the system is doped, there is a parameter range in which the spin gap remains. In this phase, the doped holes form singlet pairs and the pair-field and the "$4 k_F$" density correlations associated with pair density fluctuations decay as power laws, while the "$2 k_F$" charge density wave correlations decay exponentially. We discuss the behavior of the exponents of the pairing and density correlations within this spin gapped phase. Additional one-band Luttinger liquid phases which occur in the large interband hopping regime are also discussed.