Topological phase transitions for interacting finite systems

Abstract

In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the topological transition, even in finite-size systems. Spatial symmetries are argued to play a fundamental role in the selection of the boundary conditions to be used to locate topological transitions in finite systems. We discuss the theoretical implications of these results, and utilize exact diagonalization to demonstrate its manifestations in the Haldane-Fermi-Hubbard model. Our findings provide an efficient way to detect topological transitions in experiments and in numerical calculations that cannot access the ground-state wave function.

Competing chiral orders in the topological Haldane-Hubbard model of spin-12fermions and bosons

“…For small t 2 = 0, and φ = 0, π, the Dirac fermions acquire a mass, leading to a quantized Hall effect σ xy = ±e 2 /h at half-filling. For spin-1/2 fermions, with each species at half-filling, σ For spinless fermions, nearest-neighbor repulsion induces a topologically trivial charge density wave insulator, 25,26 while spinless bosons with a local Hubbard repulsion form a plaquette Mott insulator with loop currents. 27 A slave-spin approach to the HaldaneHubbard model suggests the appearance of topological Néel order at moderate coupling with a staggered sublattice potential.…”

Universality of the Hall Conductivity in Interacting Electron Systems

“…In particular, our result applies to the interacting versions of the Hofstadter [1,39] and Haldane [37] models. See also [54] and [41] for numerical and experimental results on the interacting Haldane model. We stress that our proof does not require any a priori assumption on the interacting spectrum of the system.…”

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

“…Phases that can not be easily detected with neither ED nor the mean-field approach include those with incommensurate long-range order. For example, depending on the system size and the particular geometry, ED might favor commensurate phases against frustrated phases and one has to be careful to explore (whenever possible) different sizes and/or aspect ratios 17,18 to pin down the relevant competing phases. 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.…”

“…For example, depending on the system size and the particular geometry, ED might favor commensurate phases against frustrated phases and one has to be careful to explore (whenever possible) different sizes and/or aspect ratios 17,18 to pin down the relevant competing phases. 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.…”