Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices

TL;DR

This study explores the phase diagram of the half-filled Hubbard model on vortex-full square lattices, revealing four phases and the nature of phase transitions using quantum Monte Carlo and continuous unitary transformations.

Contribution

It introduces a combined QMC and CUT approach to analyze the Hubbard model on vortex-full lattices, detailing the phase transitions and effective spin models in this context.

Findings

Identified four distinct phases: semi-metal, band insulator, Néel order, and valence bond crystal.

Mapped phase transitions, including direct and two-step transitions, depending on interaction strength.

Confirmed the absence of spin-liquid phases across the entire phase diagram.

Abstract

We study the half-filled Hubbard model on a one-parameter family of vortex-full square lattices ranging from the isotropic case to weakly coupled Hubbard dimers. The ground-state phase diagram consists of four phases: A semi-metal and a band insulator which are connected to the weak-coupling limit, and a magnetically ordered N\'eel phase and a valence bond crystal (VBC) which are linked to the strong-coupling Mott limit. The phase diagram is obained by quantum Monte Carlo (QMC) and continuous unitary transformations (CUTs). The CUT is performed in a two-step process: Non-perturbative graph-based CUTs are used in the Mott insulating phase to integrate out charge fluctuations. The resulting effective spin model is tackled by perturbative CUTs about the isolated dimer limit yielding the breakdown of the VBC by triplon condensation. We find three scenarios when varying the interaction for a fixed anisotropy of hopping amplitudes: i) one direct phase transition from N\'eel to semi-metal, ii) two phase transitions VBC to N\'eel and N\'eel to semi-metal, or iii) a smooth crossover from VBC to the band insultor. Our results are consistent with the absence of spin-liquid phases in the whole phase diagram.