Using large-scale quantum Monte Carlo simulations, the authors unbiasedly demonstrate the existence of a topological Mott insulator -- an interaction-driven topological insulator emerging from a strongly correlated Dirac semimetal. The model designed here consists of Dirac fermions and fluctuating Ising fields mediating interactions between fermions. By tuning the fluctuation strength of the Ising fields, the authors show the existence of a topological quantum phase transition between the topological Mott insulator phase and the Dirac-semimetal phase. Furthermore, the quantum critical point was found to be in the (2+1)D
N=8 Chiral Ising universality class.
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)×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 toward 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 are 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.
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)
×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.
Topological phase transitions are typically associated with the formation of gapless states. Spontaneous symmetry breaking can lead to a gap opening, thereby obliterating the topological nature of the system. Here we highlight a completely different destiny for a topological transition in the presence of interaction. Solving a Bernevig-Hughes-Zhang model with local interaction, we show that dynamical quantum fluctuations can lead to the opening of a gap without any symmetry breaking. As we vary the interaction and the bare mass of the model, the continuous gapless topological transition turns into a first-order one, associated with the presence of a massive Dirac fermion at the transition point, showing a Gross-Neveu critical behavior near the quantum critical endpoint. We identify the gap opening as a condensed matter analog of the Coleman-Weinberg mechanism of mass generation.
A central question beyond the Landau paradigm is the non-perturbative critical theory of the symmetric mass generation (SMG) transition, where strong interactions gap Dirac fermions in (2+1) dimensions without triggering spontaneous symmetry breaking or topological order. While previous studies have already provided evidence for direct SMG transitions in (2+1) dimensions, the fermion scaling dimension -- the key observable for distinguishing candidate critical theories -- has not been determined in a controlled unbiased way. In this Letter, using large-scale determinant quantum Monte Carlo (DQMC) simulations of a bilayer honeycomb lattice model with
SU(2)×SU(2)×SU(2)/Z2 symmetry, we establish a direct continuous transition by observing the simultaneous opening of single-particle and bosonic gaps at a critical coupling
Jc≈2.6 with correlation length exponent
ν=1.14(2), while an exhaustive search over all 19 symmetry-inequivalent fermion bilinear order parameters confirms the absence of any symmetry breaking. We further obtain the first controlled unbiased estimate of the fermion anomalous dimension,
ηψ=0.071(1), which deviates significantly from the large-
N prediction (
ηψ≈0.595) and variational Monte Carlo estimates (
ηψ≈0.62), thereby placing direct quantitative constraints on SMG criticality. By contrasting with a related
Spin(5)×U(1)/Z2 model that develops an intermediate excitonic phase, we show that pure non-Abelian symmetry plays a decisive role in stabilizing the direct SMG transition.
Inspired by our recent works on SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase diagram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases, such as Dirac semimetals, antiferromagnetic Mott insulators, valence bond solids (VBSs), and Dirac spin liquid and phase transitions, including Gross-Neveu chiral transitions with emergent continuous symmetry, deconfined quantum criticality, and the first-order transition between an interaction-driven columnar VBS and a plaquette VBS. These rich phenomena coming from simple-looking lattice models firmly convey the message that the interplay between the
SU(N) Dirac fermions (with enhanced internal symmetries) and extended plaquette interactions (beyond the on-site Hubbard type) is the new playground to synthesize novel highly entangled quantum matter both at the model level and with experimental feasibilities.