Density-matrix renormalization study of the frustrated fermions on the triangular lattice

TL;DR

This study employs density-matrix renormalization to analyze fermionic models on a triangular lattice, revealing how boundary conditions and size scaling can detect symmetry breaking and phase transitions.

Contribution

It demonstrates the effectiveness of 2D density-matrix renormalization in identifying symmetry breaking and phase boundaries in frustrated fermionic systems on a triangular lattice.

Findings

Open edges act as perturbations to select correlations only with long-range order.

Charge gap and local charge density scaling determine the metal-insulator boundary.

Phase boundary scales with density of states and exact solutions.

Abstract

We show that the two-dimensional density-matrix renormalization analysis is useful to detect the symmetry breaking in the fermionic model on a triangular lattice. Under the cylindrical boundary conditions with chemical potentials on edge sites, we find that the open edges work as perturbation to select the strongest correlations {\it only in the presence of a long range order}. We also demonstrate that the ordinary size scaling analysis on the charge gap as well as that of the local charge density under this boundary condition could determine the metal-insulator phase boundary, which scales almost perfectly with the density of states and the exact solutions in the weak and strong coupling region, respectively.