Hubbard ladders at small $U$ revisited

TL;DR

This paper re-examines the phase diagram of the two-leg Hubbard ladder at small interaction strength using analytical methods and DMRG, revealing a crossover in behavior and implications for related lattice models.

Contribution

It provides a detailed analysis of the small $U$ regime, identifying a crossover in correlation length behavior and challenging recent DMRG findings on related models.

Findings

Identification of a crossover at $U^igstar$ in correlation length behavior

Hierarchy of length scales for $U < U^igstar$

Implications for triangular lattice Hubbard models at small $U$

Abstract

We re-examine the zero temperature phase diagram of the two-leg Hubbard ladder in the small $U$ limit, both analytically and using density-matrix renormalization group (DMRG). We find a ubiquitous Luther-Emery phase, but with a crossover in behavior at a characteristic interaction strength, $U^\star$; for $U \gtrsim U^\star$, there is a single emergent correlation length $\log[\xi] \sim 1/U$, characterizing the gapped modes of the system, but for $U\lesssim U^\star$ there is a hierarchy of length scales, differing parametrically in powers of $U$, reflecting a two-step renormalization group flow to the ultimate fixed point. Finally, to illustrate the versatility of the approach developed here, we sketch its implications for a half-filled triangular lattice Hubbard model on a cylinder, and find results in conflict with inferences concerning the small $U$ phase from recent DMRG studies of the same problem.