Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

Abstract

We investigate a model of hard-core bosons with correlated hopping on the honeycomb lattice in an external magnetic field by means of a coupled-wire approach. It has been numerically shown that this model exhibits at half filling the bosonic integer quantum Hall (BIQH) state, which is a symmetry-protected topological phase protected by the U(1) particle conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015)]. By combining the bosonization approach and a coupled-wire construction, we analytically confirm this finding and show that it even holds in the strongly anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH phase against tunnelings that break the separate particle conservations on different sublattices down to a global particle conservation. We further argue that a phase transition between two different BIQH phases is in a deconfined quantum critical point described by two copies of the (2 + 1)-dimensional O(4) nonlinear sigma model with the topological theta term at theta = pi. Finally, we predict a possible fractional quantum Hall state, the Halperin (221) state, at 1/6 filling

Deconfined Quantum Critical Points: Symmetries and Dualities

“…[65,66] using parton constructions (see also Appendix B for a different perspective) and more recently in Ref. [67] using a coupled-wire construction. This bosonic IQH transition has been seen numerically, and the results show evidence of a continuous phase transition [44,45].…”

Quantum Hall hierarchy from coupled wires

“…This transformation can be conveniently expressed in terms of the bosonic fields φ σ j = ϕ σ + θ −σ j andφ σ j = ϕ σ j − θ −σ j . The pairs of the bosonic fields {φ σ j } and {φ σ j } have the opposite chirality to each other and actually describe counter-propagating edge modes of the bosonic IQH state [74]. In terms of these fields, the PH transformation is given by φ σ j →φ σ j+1 andφ σ j → φ σ j with complex conjugation.…”

Lattice realization of a bosonic integer quantum Hall state–trivial insulator transition and relation to the self-dual line in the easy-plane NCCP1 model

“…21,22 Recent theoretical and numerical studies [23][24][25] of bilayer graphene as a plat-form for bosonic SPT states suggested a second-order bosonic topological-trivial transition, although the accessed sizes are perhaps too small to determine critical properties. In other works, DMRG and coupled-wire studies of a hard-core boson model with correlated hopping on a honeycomb lattice 19,26 found a direct transition between BIQHE states with σ xy = 2 and σ xy = −2, but more detailed studies are needed to establish the nature of the transition.…”