Study of the Hubbard model on the triangular lattice using dynamical cluster approximation and dual fermion methods

TL;DR

This paper explores the Hubbard model on a triangular lattice at half-filling using advanced computational methods to analyze electronic properties, phase transitions, and magnetic correlations, providing insights into metal-insulator transitions and magnetic ordering.

Contribution

It combines DCA, DF, CT QMC, and SCA methods to study the Hubbard model, comparing their effectiveness and revealing magnetic phases and transition behaviors.

Findings

Spectral functions agree between SCA and CT QMC methods.

Identified metal-insulator transition and hysteresis effects.

Evidence for magnetically ordered phases with enhanced AF correlations.

Abstract

We investigate the Hubbard model on the triangular lattice at half-filling using the dynamical cluster approximation (DCA) and dual fermion (DF) methods in combination with continuous-time quantum Monte carlo (CT QMC) and semiclassical approximation (SCA) methods. We study the one-particle properties and nearest-neighbor spin correlations using the DCA method. We calculate the spectral functions using the CT QMC and SCA methods. The spectral function in the SCA and obtained by analytic continuation of the Pade approximation in CT QMC are in good agreement. We determine the metal-insulator transition (MIT) and the hysteresis associated with a first-order transition in the double occupancy and nearest-neighbor spin correlation functions as a function of temperature. As a further check, we employ the DF method and discuss the advantages and limitation of the dynamical mean field theory (DMFT), DCA and recently developed DF methods by comparing Green's functions. We find an enhancement of antiferromagnetic (AF) correlations and provide evidence for magnetically ordered phases by calculating the spin susceptibility.