Quantum Disordered Phase near the Mott Transition in the Staggered-Flux Hubbard Model on a Square Lattice

Abstract

We investigate ground state properties of the half-filled staggered-flux Hubbard model on a square lattice. Energy gaps to charge and spin excitations and magnetic as well as dimer orders are calculated as a function of interaction strength U/t by means of constrained-path quantum Monte Carlo method. It is found that the system is a semi-metal at U/t 5.6 and a Mott insulator with long-range antiferromagnetic order at U/t 6.6. In the range 5.6 U/t 6.6, the ground state is an correlated insulator where both magnetic and dimer orders are absent. Furthermore, spin excitation in the intermediate phase appears to be gapless, and the measured spin-spin correlation function exhibits power-law decaying behavior. The data suggest that the non-magnetic ground state is a possible candidate for the putative algebraic spin liquid. Model Hamiltonians have played an important role in realizing such exotic spin liquid states [4, 5]. Evidence of spin liquid phases has been found in the spin 1/2 Heisenberg model on triangular lattices[6], square lattices with frustration [7][8][9], and kagome lattices [10]. In these geometrically frustrated systems[11], antiferromagnetic (AF) orders are suppressed by strong quantum fluctuations. In addition to spin systems, there is also progress using the Hubbard model which contains spin and charge degrees of freedom. Spin liquid ground states have been identified in the model on anisotropic triangular lattices [12] and on bipartite honeycomb lattices [13].In this paper, we examine ground state properties of the half-filled staggered-flux Hubbard model (sfHM) on a square lattice. As will be seen later, low energy physics in the sfHM is described by Dirac fermions, similar to that found in the Hubbard model on honeycomb lattices [13]. The model is defined by the Hamiltonianwhere t ij = t e iθ ij is the nearest-neighbor hopping and we set t = 1 throughout this work. The operator c iσ (c iσ ) creates (annihilates) an electron with spin σ =↑, ↓ at site i on a lattice of size N = L × L. U > 0 is the onsite Coulomb repulsion. We work in the canonical ensemble.An electron gains a phase Φ = θ ij when it hops around a plaquette of the square lattice. Φ = 0 corresponds to the original Hubbard model. We focus on the case Φ = π in the present study. There is a gauge freedom in choosing θ ij . Here we distribute the phase

Phase diagram of interacting Fermi gas in spin–orbit coupled square lattices

“…8 3.9 ⩽ ⩽ [58]. Similar situations have been encountered for the staggered-flux model on a square lattice [61,62]. Here, the essential feature characterizing the present system is the considerably large space of parameters, where the NMI phase emerges.…”

Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices

“…[11], since we do not find an intermediate spin-liquid phase but a direct transition between semimetal and a Néel-ordered phase. Similar to the recent findings for the Hubbard model on the isotropic honeycomb lattice which result from numerical advancements [12,13], our findings for the π -flux square lattices also benefits from optimizations in the QMC simulations.…”

“…In this case, it is known that the semimetal phase is stable with respect to the Hubbard interaction. The transition from the semimetal to antiferromagnetic Mott insulating state has captured attention since numerical studies put forward the possibility of an intermediate disordered state [10,11]. More recent results on the honeycomb lattice [12,13] exclude this possibility, and provide an explanation of the Mott transition in terms of Gross-Neveu criticality [14], where the origin of the mass gap stems from the symmetry breaking.…”

Sign structure, electron fractionalization, and emergent gauge description of the Hubbard model

“…1). The U term is given by (12) where N e denotes the total number of electrons and N the number of lattice sites, with…”