Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands

Abstract

Recent proposals of topological flat band (TFB) models have provided a new route to realize the fractional quantum Hall effect (FQHE) without Landau levels. We study hard-core bosons with short-range interactions in two representative TFB models, one of which is the well known Haldane model (but with different parameters). We demonstrate that FQHE states emerge with signatures of even number of quasi-degenerate ground states on a torus and a robust spectrum gap separating these states from higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases. Introduction.-The fractional quantum Hall effect (FQHE), one of the most fascinating discoveries in twodimensional (2D) electron gas, has set up a paradigm to explore new topological phases in other strongly correlated systems. As commonly believed, the FQHE requires two basic ingredients: single-particle states with nontrivial topology, and quenching of the kinetic energy compared to interaction energy scale. However, despite of the seemingly universal theoretical concepts, the FQHE has only been found in 2D systems under a strong perpendicular magnetic field, i.e., in which particles move in Landau levels (LLs). In rotating Bose-Einstein condensate [1] and optical lattice systems [2,3], researchers have been interested in generating an artificial uniform magnetic field, thus the bosonic FQHE states are expected, but still due to the existence of LLs.

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

“…More interesting physics occurs when the nearly flat 'Chern' band is partially filled (see Figs 2e and 4). In this case, as pointed out recently, fractional quantum Hall (FQH) states are likely to be realized [39][40][41][42][43][44] . To elaborate this possibility, we perform exact diagonalization calculation after projecting on-site repulsion and NN repulsion into the 1/3 filled highest Chern band (that is, at e g 3.5 + 1/6 ).…”

Elementary formula for the Hall conductivity of interacting systems

“…Equation (3b) predicts the following results for fractional Chern insulators. [11][12][13][14][15][16][17][18][19][20][21] 1. The integral over the Brillouin zone of F (k) ×n(k) equals a rational number p/q, since Laughlin's gauge argument for quantization then applies.…”

D-algebra structure of topological insulators

“…Evidence for their existence has been provided in a series of analytical and numerical works in twodimensional Chern insulators [3][4][5][6][7][8][9][10][11] and time-reversal invariant topological insulators [12][13][14]. The plethora of new experimental facts and theoretical ideas discovered in the non-interacting topological insulators suggests that their fractional (i.e.…”