Ground state phase diagram of the triangular lattice Hubbard model by density matrix renormalization group method

TL;DR

This study uses the density matrix renormalization group method to map the ground state phase diagram of the Hubbard model on a triangular lattice, identifying metallic, paramagnetic, and Neel ordered phases with first order transitions.

Contribution

It provides the first detailed phase diagram of the triangular lattice Hubbard model at half filling using DMRG, revealing multiple phases and transition points.

Findings

Identifies two first order phase transitions at Uc1 and Uc2.

Finds a metallic phase for 0 < U < Uc1.

Discovers a paramagnetic phase with no magnetic order between Uc1 and Uc2.

Abstract

Two-dimensional density-matrix renormalization group method is employed to examine the ground state phase diagram of the Hubbard model on the triangular lattice at half filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction U at Uc1 = 7.55 t and Uc2 = 9.65 t (t being the hopping integral), indicating that there are three phases separated by first order transitions. The absence of any singularity in physical quantities for 0 < U < Uc1 implies that this phase corresponds to a metallic phase. The local spin density induced by an applied pinning magnetic field for U > Uc2 exhibits a three sublattice feature, which is compatible with the Neel ordered state realized in the strong coupling limit. For Uc1 < U < Uc2, a response to the applied pinning magnetic field is comparable to that in the metallic phase but a relatively large spin correlation length is found with neither valence bond nor chiral magnetic order, suggesting a paramagnetic nature which resembles gapless spin liquid. The calculation also finds that the pair- ing correlation function monotonically decreases with increasing U and thus the superconductivity is unlikely in the intermediate phase.