Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: Application to the square lattice bilayer and honeycomb lattice

Abstract

We consider an efficient scheme to simulate fermionic Hubbard models with nonlocal densitydensity interactions in two dimensions, based on bond-centered auxiliary-field quantum Monte Carlo. The simulations are shown to be sign-problem free within a finite, restricted parameter range. Using this approach, we first study the Hubbard model on the half-filled square lattice bilayer, including an interlayer repulsion term in addition to the local repulsion, and present the ground state phase diagram within the accessible parameter region. Starting from the antiferromagnetically ordered state in the absence of interlayer repulsion, the interlayer interactions are found to destabilize the antiferromagnetic order, leading to a band insulator state. Moreover, for sufficiently strong interlayer tunneling, we also observe the emergence of a direct dimer product state of mixed D-Mott and S-Mott character along the equal coupling line. We discuss the stability range of this state within strongcoupling perturbation theory. Furthermore, we consider the Hubbard model on the honeycomb lattice with next-nearest-neighbor interactions. Such an interaction is found to enhance both charge density and spin-current correlations within the semimetallic region. However, inside the accessible parameter region, they do not stabilize long-ranged charge density wave order nor a quantum spin Hall state, and the only insulating state that we observe exhibits long-range antiferromagnetism.

Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model

“…As a result, when U is fixed, a metallic phase is expected to be more stable for larger V 2 . Such behavior is already observed in recent AFQMC calculations [28], and our VMC phase diagram Let us focus on the parameter region along V 2 /t = 4, where the CDW phases are dominant. The charge-order parameters n α as a function of U/t are given in Fig.…”

“…Recent extensive research on the honeycomb extended Hubbard model by ED [17][18][19], iDMRG [20], auxiliaryfield quantum Monte Carlo (AFQMC) [28], variational Monte Carlo (VMC) [24], and functional renormalization group (fRG) [25,26,29] suggests that TMI is less likely than conventional ordered states, often CDW, at half filling. This fact leads us to ask the following questions: and CDW states.…”

Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional renormalization group calculation with high-wave-vector resolution

“…We analyze the possible groundstates of extended Hubbard models on the two-dimensional honeycomb lattice at charge neutrality, focusing on implications for single-layer graphene. Considerable effort has been put through a diversity of methods to address this matter [3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization

“…Further, in the spinless as well as in the spin-1/2 case, an analysis of the problem by means of quantum Monte Carlo (QMC) approaches is typically inhibited by the fermion sign problem. On the other hand, recent QMC studies 15 have also taken into account non-local density-density interactions on the honeycomb lattice, however, a definite statement about the quantum many-body ground state in the presence of sizable second-nearest neighbor interactions is hindered by limitations on the accessible parameter range.…”