Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study

Abstract

We study a generalized Kane-Mele-Hubbard model with third-neighbor hopping, an interacting two-dimensional model with a topological phase transition as a function of third-neighbor hopping, by means of the determinant projector Quantum Monte Carlo (QMC) method. This technique is essentially numerically exact on models without a fermion sign problem, such as the one we consider. We determine the interaction-dependence of the Z2 topological insulator/trivial insulator phase boundary by calculating the Z2 invariants directly from the single-particle Green's function. The interactions push the phase boundary to larger values of third-neighbor hopping, thus stabilizing the topological phase. The observation of boundary shifting entirely stems from quantum fluctuations. We also identify qualitative features of the single-particle Green's function which are computationally useful in numerical searches for topological phase transitions without the need to compute the full topological invariant.

Interaction-driven phases in the half-filled spinless honeycomb lattice from exact diagonalization

“…Indeed, ED has proven useful in studies of the Haldane-Hubbard model [17][18][19] and the π -flux model, 20 complementing other techniques such as quantum Monte Carlo and variational cluster approximation used in studies of the Hubbard and Kane-Mele-Hubbard models in the honeycomb lattice. 6,8,[21][22][23][24][25][26][27][28][29] Motivated by these results, and in particular by the interaction-driven phases found in existing mean-field calculations, in this work we study the spinless extended Hubbard model with both NN and NNN interactions in the honeycomb lattice at half-filling via ED of small finite-size systems. We will investigate and characterize the phase diagram for electronic phases that are driven by Coulomb interactions in the honeycomb lattice as an independent check for the mean-field picture.…”

Valence bond phases inS= 1/2 Kane–Mele–Heisenberg model

“…Kane-Mele-Hubbard model, is an example of such models which recently has been studied by various methods [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] . The strong coupling (large Coulomb interaction) and weak coupling (small Coulomb interaction) limits of this model are charachterized by anti-ferromagnetic Mott insulator (AFMI) and topological band insulator (TBI) phases, respectively.…”

Correlation effects in pyrochlore iridate thin films grown along the [111] direction

“…[1][2][3][4][5][6][7][8][9] Recently, significant effort has been made to investigate the role of electron-electron interactions in topological states of of matter. [10][11][12][13][14][15][16][17] Though it is generally understood that topological phases described by electronic band structure are robust to weak electronelectron interactions, the full many-body problem of a strongly interacting system remains far from completely understood. 17,18 One possible effect of electronic interactions is magnetic order that carries with it a topological phase transition (either from a non-topological system to a topological one, or from a TI to a non-topological magnetically ordered state).…”