Study of the triangular-lattice Hubbard model with constrained-path quantum Monte Carlo

TL;DR

This study evaluates the constrained-path Monte Carlo method on the triangular-lattice Hubbard model, emphasizing the importance of symmetry-adapted trial wave functions for accurate results across different fillings and interaction strengths.

Contribution

It demonstrates that symmetry-adapted trial wave functions significantly improve the accuracy of CPMC in frustrated systems, providing a practical approach for studying complex ground states.

Findings

Symmetry-adapted trials are essential for accuracy.

Energy deviations are within 1% away from exact methods.

Polynomial scaling makes CPMC feasible for large systems.

Abstract

We benchmark constrained-path Monte Carlo (CPMC) on the triangular-lattice Hubbard model for several fillings and $U$ values and show that symmetry-adapted trial wave functions are essential for quantitative accuracy. Away from half-filling, simple free-electron-based trials that preserve the ground state symmetry yield energy deviations $\lesssim 1\%$ from exact diagonalization and density matrix renormalization group results. At half-filling, strong frustration in the intermediate to large $U$ regimes necessitates symmetry-projected trials to reach comparable accuracy, where both free-electron and symmetry-broken Hartree-Fock trials incur substantial constraint bias. Since the computational cost of CPMC with symmetry projection scales polynomially with system size, our results motivate its use as a practical route for studying competing ground states in strongly correlated, frustrated systems.