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

Abstract

We provide an explicit lattice model of bosons with two separately conserved boson species [U (1) × U (1) global symmetry] realizing a direct transition between an integer quantum Hall effect of bosons and a trivial phase, where any intermediate phase is avoided by an additional symmetry interchanging the two species. If the latter symmetry is absent, we find intermediate superfluid phases where one or the other boson species condenses.We know the precise location of the transition since at this point our model has an exact nonlocal antiunitary particle-hole-like symmetry that resembles particle-hole symmetry in the lowest Landau level of electrons. We exactly map the direct transition to our earlier study of the self-dual line of the easy-plane NCCP1 model, in the mathematically equivalent reformulation in terms of two (new) particles with π statistics and identical energetics. While the transition in our model is first order, we hope that our mappings and recent renewed interest in such self-dual models will stimulate more searches for models with a continuous transition.

Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points

“…Thus, we conclude that the transition in the effective no-instanton RP 1 model (i.e., the gauged Ashkin-Teller model with no instantons, which emerges at the Ising DQCP) corresponds also to the criticality between the trivial and SPT phases in a different system with the Z 2 × Z 2 symmetry [86][87][88]. This structure is similar to recent observations in 2d [89,90], where the transition in the NCCP 1 model (which is conjectured to describe the EP DQCP) maps exactly to criticality between trivial and SPT phases [91,92] in a different physical system with a U (1)×U (1) symmetry, where the SPT phase is an integer quantum Hall state of bosons [93][94][95].…”

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

“…The fact that this phase transition is continuous is in itself an important discovery, given that Uð1Þ deconfined quantum criticality had essentially been declared nonexistent, due to unexplained hints of first-order transitions in some other planar models and what seems like definite proofs in other cases [35,37,38,83]. Here (as further discussed in Appendix B), we show that the EPJQ model defined in Eq.…”

Deconfined quantum critical point in one dimension

“…The original work predicted such a transition from a Neel phase to a Valence Bond Solid phase in a spin-1/2 system on a two-dimensional (2d) square lattice, and extensive numerical studies have provided evidence for a continuous (or weakly first order) transition [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. This DQCP was revisited recently in light of improvements in the understanding of the interplay between symmetries and dualities [21][22][23][24], stimulating additional numerical studies [25][26][27], although some questions about the transition remain (for a very recent review, see Ref. 28).…”