Emergent particle-hole symmetry in spinful bosonic quantum Hall systems

Abstract

When a fermionic quantum Hall system is projected into the lowest Landau level, there is an exact particle-hole symmetry between filling fractions ν and 1 − ν. We investigate whether a similar symmetry can emerge in bosonic quantum Hall states, where it would connect states at filling fractions ν and 2 − ν. We begin by showing that the particle-hole conjugate to a composite fermion 'Jain state' is another Jain state, obtained by reverse flux attachment. We show how information such as the shift and the edge theory can be obtained for states which are particle-hole conjugates. Using the techniques of exact diagonalization and infinite density matrix renormalization group, we study a system of two-component (i.e., spinful) bosons, interacting via a δ-function potential. We first obtain real-space entanglement spectra for the bosonic integer quantum Hall effect at ν = 2, which plays the role of a filled Landau level for the bosonic system. We then show that at ν = 4/3 the system is described by a Jain state which is the particle-hole conjugate of the Halperin (221) state at ν = 2/3. We show a similar relationship between non-singlet states at ν = 1/2 and ν = 3/2. We also study the case of ν = 1, providing unambiguous evidence that the ground state is a composite Fermi liquid. Taken together our results demonstrate that there is indeed an emergent particle-hole symmetry in bosonic quantum Hall systems.

Collective modes of vortex lattices in two-component Bose–Einstein condensates under synthetic gauge fields

“…It is thus interesting to investigate how quantum corrections affect the rich vortex-lattice phase diagrams in the two cases. The present work would be a step toward understanding how the systems evolve from equivalent phase diagrams in the mean-field regime to markedly different phase diagrams in the quantum Hall regime [45,[52][53][54][55] as the filling factor is lowered. In the last line, we have used Appendix B. Derivation of the interaction matrix element (12) Here we derive the representation (12) of the interaction matrix element from equation (11).…”

“…It is thus interesting to ask whether and how the difference between the two types of systems arises in other properties such as collective modes. In this context, it is worth noting that in the quantum Hall regime, which is far beyond the mean-field description, the two types of systems exhibit markedly different phase diagrams [45,[52][53][54][55], which has been interpreted in light of pseudopotentials and entanglement formation [55].…”

Dynamics and level statistics of interacting fermions in the lowest Landau level

“…, whereas K 2 and K 2 +N give the same T 2 q eigenvalue, reducing K 2 to K 2 =0, K, N−1. Finally, since (K 1 , K 2 ) and (K 1 +N, K 2 ) have the same energy spectrum, we may define a reduced many-body Brillouin zone using (K 1 , K 2 ), where K 1 , K 2 =0, K, N−1, as in previous work [12,59,[72][73][74].…”

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

“…A special QCP known as the deconfined quantum critical point, provides an opportunity to study the properties of deconfined excitations and emergent gauge fields [29,30] as such a QCP controls the scaling behavior of physics quantities. Recent discovery of the connection between symmetry and duality [31][32][33] has stimulated additional numerical studies [34,35]. Moreover, it has been proposed that a class of Landauforbidden transitions with deconfined quantum criticality occurs between bosonic SPT phases in two dimensions [36,37].…”

“…Moreover, it has been proposed that a class of Landauforbidden transitions with deconfined quantum criticality occurs between bosonic SPT phases in two dimensions [36,37]. However, numerical Monte Carlo simulations on a designed lattice model with U (1) × U (1) symmetry gives a weakly first-order transition from BIQH to trivial insulator [35], at odds with the continuous scenario. For another two-dimensional model with discrete Z 2 symmetry, only a first-order transition was observed [38].…”