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arXiv:1908.02490 · Physical review. B./Physical review. B

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

Tian-Sheng Zeng, D. N. Sheng, W. Zhu

Published Jan 23, 2020• 16 citations
arXivHTMLPDF

Abstract

The deconfined quantum critical point, a prototype Landau-forbidden transition, could exist, in principle, in the phase transitions involving a symmetry-protected topological phase; however, examples of such kinds of transitions in physical systems are rare beyond one-dimensional systems. Here, using a density-matrix renormalization-group calculation, we unveil a bosonic integer quantum Hall phase in a two-dimensional correlated honeycomb lattice, by full identification of its internal structure from the topological $\mathbf{K}$ 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 ${\mathrm{QED}}_{3}$ with two flavors of Dirac fermions.

DOI
10.1103/physrevb.101.035138

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We study a bosonic model with correlated hopping on a honeycomb lattice, and show that its ground state is a bosonic integer quantum Hall (BIQH) phase, a prominent example of a symmetry-protected topological (SPT) phase. By using the infinite density matrix renormalization group method, we establish the existence of the BIQH phase by providing clear numerical evidence: (i) a quantized Hall conductance with |σ_{xy}|=2, (ii) two counterpropagating gapless edge modes. Our simple model is an example of a novel class of systems that can stabilize SPT phases protected by a continuous symmetry on lattices and opens up new possibilities for the experimental realization of these exotic phases.
Continuous quantum phase transitions beyond the conventional paradigm of fluctuations of a symmetry-breaking order parameter are challenging for theory.These phase transitions often involve emergent deconfined gauge fields at the critical points as demonstrated in phase transitions between different broken-symmetry states of 2 þ 1-dimensional quantum magnets, as well as those between symmetry-protected topological (SPT) phases.In this paper, we present several examples of deconfined quantum critical points between SPT phases in 3 þ 1-D for both bosonic and fermionic systems.These critical theories can be formulated as non-Abelian gauge theories either in the infrared-free regime or in the conformal window when they flow to the Banks-Zaks fixed points.We explicitly demonstrate several interesting quantum critical phenomena.We describe situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points.We exhibit the possibility-which we dub "unnecessary quantum critical points"-of stable generic continuous phase transitions within the same phase.We present examples of interaction-driven, band-theory-forbidden, continuous phase transitions between two distinct band insulators.The understanding we develop leads us to suggest an interesting possible 3 þ 1-D field theory duality between SUð2Þ gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.
We study the phase transitions of bosonic $\ensuremath{\nu}=1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and density matrix renormalization group methods, we demonstrate that the many-body ground state undergoes a continuous phase transition between bosonic FQH liquid and a trivial (Mott) insulator induced by the periodic potential, characterized by the smooth crossover of energy and entanglement entropy. When the Hubbard repulsion decreases, we claim that this bosonic FQH liquid would turn into a superfluid state with a direct energy level crossing and a discontinuous leap of off-diagonal long-range order.
Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)×\times×U(1) symmetry. Using large-scale auxiliary- field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly-interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition towards an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data is consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.
Emergent QED3_33​ at the bosonic Laughlin state to superfluid transition
Quantum phase transitions between topologically ordered and symmetry-broken phases lie beyond Landau theory. A prime example is the conjectured continuous transition from the bosonic ν=1/2ν= 1/2ν=1/2 Laughlin state to a superfluid, proposed to be governed by a QED3_33​--Chern--Simons (CS) critical point whose stability remains uncertain. We study half-filled bosons in the lowest Landau level subject to a lattice potential. Infinite-cylinder DMRG reveals a single continuous Laughlin--to--superfluid transition. Adiabatic flux insertion collapses the many-body gap and exposes massless Dirac quasiparticles, while momentum-resolved correlation lengths show that three lattice-related density modes share the same critical exponent, evidencing an emergent SO(3)SO(3)SO(3) symmetry. The joint appearance of Dirac dispersion and symmetry enlargement provides microscopic support for a stable QED3_33​--CS fixed point. Our numerical strategy also offers a blueprint for exploring Landau-forbidden transitions in fractional Chern insulators and composite Fermi liquids realised in moire and cold-atom systems.
We propose that quantum Hall bilayers in the presence of a periodic potential at the scale of the magnetic length can host examples of a deconfined metal-insulator transition (DMIT), where a Fermi-liquid (FL) metal with a generic electronic Fermi surface evolves into a gapped insulator (or an insulator with Goldstone modes) through a continuous quantum phase transition.The transition can be accessed by tuning a single parameter, and its universal critical properties can be understood using a controlled framework.At the transition, the two layers are effectively decoupled, where each layer undergoes a continuous transition from a FL to a generalized composite Fermi liquid (gCFL).The thermodynamic and transport properties of the gCFL are similar to the usual CFL, while its spectral properties are qualitatively different.The FL-gCFL quantum critical point hosts a sharply defined Fermi surface without long-lived electronic quasiparticles.Immediately across the transition, the two layers of gCFL are unstable to forming an insulating phase.We discuss the topological properties of the insulator and various observable signatures associated with the DMIT.