SU(N) fractional quantum Hall effect in topological flat bands

Abstract

We study N -component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU(N )-invariant interactions based on exact diagonalization and density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU(N ) fractional quantum Hall states can emerge at fractional filling factors ν = N/(N + 1) for bosons (ν = N/(2N + 1) for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characterization based on the K matrix, and discuss the close relationship to the fractional quantum Hall physics in topological flat bands with Chern number N .

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

“…Generally speaking, the multicomponent FQH states can be classified by a class of the integer-valued symmetric K matrix of the rank N [8][9][10][11]. The diagnosis of the topological nature of the K matrix has been discussed in our previous works [49,50]. Here we briefly summarize the main strategy.…”

Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect

“…For any FQH state, it is a common knowledge that its Hall conductance should be a universal quantized constant σ H = ν regardless of its Abelian/non-Abelian nature, which is related to the topological invariant (so called Chern number) [22]. So far, it has been successful in characterizing Abelian multicomponent quantum Hall states based on the Chern number matrix, namely the inverse of the K = C −1 matrix [23][24][25][26]. Here the diagonal and off-diagonal elements of the Chern number matrix are related to intracomponent and intercomponent Hall transports respectively.…”

Continuous phase transition between bosonic integer quantum Hall liquid and a trivial insulator: Evidence for deconfined quantum criticality

“…By inserting one flux quantum θ y ↑ = θ, θ y ↓ = 0 from θ = 0 to θ = 2π on the cylinder system, the expectation value of the total particle number N L on the left side equals to N L (θ) = tr[ ρ L (θ) N L ], where ρ L is the reduced density matrix of the corresponding left part. The net charge transfer from the right side to the left side of the system during each cycle is encoded by [46,47]…”