Absence of Translational Symmetry Breaking in Nonmagnetic Insulator Phase on Two-Dimensional Lattice with Geometrical Frustration

TL;DR

This study investigates the ground-state properties of a frustrated 2D Hubbard model, revealing that the nonmagnetic insulator phase does not exhibit translational symmetry breaking, supporting the existence of a genuine Mott insulator driven by frustration and quantum fluctuations.

Contribution

It provides evidence that the nonmagnetic insulator phase lacks translational symmetry breaking, emphasizing the role of geometrical frustration and quantum fluctuations in realizing a true Mott insulator.

Findings

No translational symmetry breaking observed in the nonmagnetic insulator phase

Supports the existence of a genuine Mott insulator driven by frustration

Phase transitions between paramagnetic metal and antiferromagnetic insulator

Abstract

The ground-state properties of the two-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hoppings at half filling are studied by the path-integral-renormalization-group method. The nonmagnetic-insulator phase sandwiched by the the paramagnetic-metal phase and the antiferromagnetic-insulator phase shows evidence against translational symmetry breaking of the dimerized state, plaquette singlet state, staggered flux state, and charge ordered state. These results support that the genuine Mott insulator which cannot be adiabatically continued to the band insulator is realized generically by Umklapp scattering through the effects of geometrical frustration and quantum fluctuation in the two-dimensional system.