Phase diagram of the half-filled two-dimensional SU(N) Hubbard-Heisenberg model: a quantum Monte Carlo study

TL;DR

This study maps the phase diagram of the half-filled 2D SU(N) Hubbard-Heisenberg model using quantum Monte Carlo, revealing various magnetic and insulating phases depending on N and model parameters.

Contribution

It provides the first comprehensive quantum Monte Carlo analysis of the phase transitions and ground states in the SU(N) Hubbard-Heisenberg model across different N values.

Findings

Transition from d-density wave to spin dimerized insulator at large N

Stabilization of spin density wave at N=2

Existence of a gapless spin liquid state with power-law correlations

Abstract

We investigate the phase diagram of the half-filled SU(N) Hubbard-Heisenberg model with hopping t, exchange J and Hubbard U, on a square lattice. In the large-N limit, and as a function of decreasing values of t/J, the model shows a transition from a d-density wave state to a spin dimerized insulator. A similar behavior is observed at N=6 whereas at N=2 a spin density wave insulating ground state is stabilized. The N=4 model, has a d-density wave ground state at large values of t/J which as a function of decreasing values of t/J becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power-law,resulting in gapless spin excitations at q = (pi,pi). Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors q = (0,pi) and q = (pi,0). This gapless spin liquid state is equally found in the SU(4) Heisenberg model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a pi-flux phase is offered. Our results stem from projective (T=0) quantum Monte-Carlo simulations on lattice sizes ranging up to 24 X 24.