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arXiv:2509.02705

Competing Dirac masses in one dimension: Symmetry-enhanced pseudo-first-order transition and deconfined criticality

Manuel Weber

Published Sep 2, 2025• 0 citations
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Abstract

Emergent symmetries and slow crossover phenomena are central themes in quantum criticality and manifest themselves in the pseudocritical scaling experienced in the context of deconfined criticality. Here we discover its conceptual counterpart, i.e., a symmetry-enhanced pseudo-first-order transition. It emerges from a one-dimensional realization of deconfined criticality between charge- and bond-ordered states driven by competing Holstein and Su-Schrieffer-Heeger electron-phonon couplings, for which quantum fluctuations and thereby the nature of the transition can be tuned systematically via the phonon frequency $ω_0$. In the classical limit $ω_0 \to 0$, a low-energy Dirac theory predicts a direct first-order transition with emergent U(1) symmetry. Using exact quantum Monte Carlo simulations, we provide strong evidence for symmetry enhancement and even finite-size scaling on intermediate length scales but in the thermodynamic limit it turns into a narrow intermediate phase where both order parameters are finite, as chiral U(1) symmetry is weakly broken on the lattice. Including quantum lattice fluctuations diminishes the width of the intermediate phase, gradually restores the U(1) symmetry, and eventually tunes the system to a deconfined quantum critical point.

DOI
10.48550/arxiv.2509.02705

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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.
Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first-order transition, similar to the case of U(1) x U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.
We consider a model of Dirac fermions in 2+1 dimensions with dynamically generated, anticommuting SO(3) Néel and Z_{2} Kekulé mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the Néel and Kekulé phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While the bare symmetries of our model do not allow for spinon-carrying Z_{3} vortices in the Kekulé mass, the emergent SO(4) invariance permits an interpretation of the transition in terms of deconfined quantum criticality. The phase diagram also features a tricritical point at which the Néel, Kekulé, and semimetallic phases meet. The present sign-free approach can be generalized to a variety of other mass terms and thereby provides a new framework to study exotic critical phenomena.
Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first order transition, similar to the case of U(1)×\times×U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.
The fluctuations of massless Dirac fermion can not only turn a first-order bosonic phase transition (in the Landau sense) to a quantum critical point, but also work reversely to enhance the first-order transition itself, depending on the implementation of finite-size effects in the coupling corrections. Here, we report a case study of the latter by employing quantum Monte Carlo simulation upon a lattice model in which the bosonic part featuring the Landau-Devonshire first-order phase transition and Yukawa coupled to the Dirac fermions. We find that the parameter range for the first-order phase transition becomes larger as the Yukawa coupling increases, and the microscopic mechanism of this phenomena is revealed, at a quantitative level, as the interplay between the critical fluctuations and the finite-size effects. Moreover, the scaling behavior at the separation point between the first-order and the continuous phase transitions is found to belong to the chiral tricritical Gross-Neveu universality. Our results demonstrate that the interplay of massless Dirac fermions, critical fluctuations, and the finite-size effects could trigger a plethora of interesting phenomena, and therefore great care is called for when making generalizations.
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.