Gapless spin liquid and pair density wave of the Hubbard model on three-leg triangular cylinders

TL;DR

This study uses large-scale simulations to explore the Hubbard model on three-leg triangular cylinders, revealing a gapless spin liquid phase with unique correlation properties and a striped pair-density wave upon doping.

Contribution

It identifies a novel intermediate gapless spin liquid phase and characterizes its properties and transitions in the Hubbard model on three-leg triangular cylinders.

Findings

Discovery of a gapless spin liquid phase with algebraic spin correlations.

Observation of striped pair-density wave with oscillating superconducting correlations.

Identification of phase transitions between metallic, spin liquid, and dimer phases.

Abstract

We study the ground state properties of the Hubbard model on three-leg triangular cylinders using large-scale density-matrix renormalization group simulations. At half-filling, we identify an intermediate gapless spin liquid phase between a metallic phase at weak coupling and Mott insulating dimer phase at strong interaction, which has one gapless spin mode and algebraic spin-spin correlations but exponential decay scalar chiral-chiral correlations. Upon light doping the gapless spin liquid, the system exhibits power-law charge-density-wave (CDW) correlations but short-range single-particle, spin-spin, and chiral-chiral correlations. Similar to CDW correlations, the superconducting correlations are also quasi-long-ranged but oscillate in sign as a function of distance, which is consistent with the striped pair-density wave. When further doping the gapless spin liquid phase or doping the dimer order phase, another phase takes over, which has similar CDW correlations but all other correlations decay exponentially.