Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU( N ) symmetry

Abstract

We study the many-body ground states of SU(N ) symmetric hardcore bosons on the topological flat-band model by using controlled numerical calculations. By introducing strong intracomponent and intercomponent interactions, we demonstrate that a hierarchy of bosonic SU(N ) fractional quantum Hall (FQH) states emerges at fractional filling factors ν = N/(M N + 1) (odd M = 3). In order to characterize this series of FQH states, we figure the effective K matrix from the inverse of the Chern number matrix. The topological characterization of the K matrix also reveals quantized drag Hall responses and fractional charge pumping that could be detected in future experiments. In addition, we address the general one-to-one correspondence to the spinless FQH states in topological flat bands with Chern number C = N at fillings ν = 1/(M C + 1).

Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice

“…Nevertheless, the topological order of multicomponent bosons in topological flat bands discloses a fertile vein to be uncovered with many possible intriguing topological phases [28], aside from the theoretical interest. In a series of works, quantum Hall effects of multicomponent bosons including Halperin (mmn) states [29,30] and their multicomponent generalizations (including Bose-Fermi mixtures and non-Abelian spin-singlet clusters) [31][32][33][34] in topological flat bands with C = 1 are numerically demonstrated through ED and DMRG calculations of both intracomponent and intercomponent Hall transport responses. The versatile experimental ability in the design and control of different iconic topological models in cold atoms, such as Haldanehoneycomb [35] and Harper-Hofstadter models [36][37][38][39], is exemplified as a valuable platform for studying such topological phases in Chern bands for bosons in cold atoms systems.…”

Bosonic Halperin fractional quantum Hall effect at filling factor $ν=2/5$

“…The emergence of FQH effect in topological flat bands (namely "fractional Chern insulators") requires a demanding understanding of the internal topological structure of interacting fractionalised phases, where an integer valued symmetric K matrix was proposed to characterize different topological orders for Abelian multicomponent systems according to the Chern-Simons theory [34][35][36][37][38]. Indeed, at partial fillings ν = 1/(kC + 1) (odd k for hardcore bosons and even k for spinless fermions ) in topological flat bands with higher Chern numbers C, there fractionalised Abelian C-color-entangled states host a close relationship to C-component FQH states [39][40][41][42][43][44][45][46][47][48], where the general one-to-one correspondence is built up based on the classification of their K matrices from the inverse of Chern number matrix for these gapped topological phases [49][50][51][52], where the quantized intercomponent drag Hall transport is identified as a primary evidence for the emergence of exotic correlated many-body topological states in multicomponent systems [11,12]. Together with synthetic magnetic gauge fields in cold atomic neutral systems, these related progresses, thus enable new relevant prospects for the study of two-component bosonic FQH effects in both lattice and continuum models, which is the focus of our work.…”

Quantum Hall effects of exciton condensate in topological flat bands

“…To gain a better understanding of the internal structure of multicomponent quantum Hall states, it is highly desirable to investigate the diagonal and off-diagonal elements of the K matrix which describe intracomponent and intercomponent Chern-Simons gauge-field couplings respectively, and can be derived from the inverse of the Chern number matrix for gapped quantum Hall states [16][17][18][19]. However a peculiar property of Halperin (mmm) quantum Hall states is that they host intercomponent tunneling and counterflow transport anomalies in Hall resistance measurements [20], due to the superfluidity of exciton condensate in which particles in one component are coupled to holes in the other component.…”