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

Abstract

The deconfined quantum critical point, a prototype Landau-forbidden transition, could exist in principle in the phase transitions involving symmetry protected topological phase, however, examples of such kinds of transition in physical systems are rare beyond one-dimensional systems. Here, using density-matrix renormlization group calculation, we unveil a bosonic integer quantum Hall phase in two-dimensional correlated honeycomb lattice, by full identification of its internal structure from topological K matrix. Moreover we demonstrate that imbalanced periodic chemical potentials can destroy the bosonic integer quantum Hall state and drive it into a featureless trivial (Mott) insulator, where all physical observables evolve smoothly across the critical point. At the critical point the entanglement entropy reveals a characteristic scaling behavior, which is consistent with the critical field theory as an emergent QED3 with two flavors of Dirac fermions.

Building models of topological quantum criticality from pivot Hamiltonians

“…In fact, even for the triangular lattice model which we studied in detail in the present work, it would be interesting to directly simulate the dual honeycomb plaquette XY model Eq. (29). Multibranch cluster updates [103] might speed up the simulations, allowing to study larger system sizes, and compare critical exponents obtained from other models described by SO( 5) DQCP.…”

“…In fact, such quantum criticality between SPT phases is intimately related to the anomalous surface states in one higher dimension [15][16][17] and are therefore reflected in the properties of the phases themselves. Deep connections between such topological phase transitions and deconfined quantum critical points, as well as self duality, have also been explored [15,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Other theoretical developments include a study of 1+1D quantum phase transitions between SPT phases and of 2D topological transition between bosonic 'integer' quantum Hall states and other interacting SPTs [7,20,[36][37][38][39][40][41][42][43][44][45][46][47][48].…”

Bosonic fractional Chern insulating state at integer fillings in multi-band system

“…On the other hand, the FCI state is often challenged by other conventional ordered states in the strongly correlated systems [18], e.g., the charge-density wave state may be favorable when the long-range Coulomb interaction are taken into account [19,54]. We further discuss the role of NN Coulomb repulsion V [62] on the FCI state. In the large V limit, the loading bosons tend to occupy the NNN neighbors, i.e, the same sublattice, to lower energy contributed by the Coulomb repulsion.…”

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.…”