Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

TL;DR

The paper demonstrates a continuous quantum phase transition between a Dirac semimetal and a featureless Mott insulator in a 2+1D lattice model with SU(4) symmetry, driven purely by interactions and without any fermion bilinear condensation. It employs sign-problem-free projector QMC to map the ground-state phase diagram and analyzes a complete set of potential symmetry-breaking channels, finding no long-range order at the transition. The critical point exhibits a large anomalous dimension (η ≈ 0.7), signaling unconventional critical behavior distinct from the familiar O(6) Wilson-Fisher class. The work supports mass generation without symmetry breaking and aligns with recent findings in interacting topological phases and lattice QCD, providing quantitative benchmarks for future studies.

Abstract

We study a lattice model of interacting Dirac fermions in $(2+1)$ dimension space-time with an SU(4) symmetry. While increasing interaction strength, this model undergoes a {\it continuous} quantum phase transition from the weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progresses in lattice QCD community.

Figures (11)

• Figure 1: (color online) Lattice geometry and phase diagram for the $SU(4)$ symmetric model in Eq. (\ref{['eq:SU4Model']}). (a) The honeycomb lattice, whose unit cell is denoted by the yellow shaded rectangle. (b) The Brillouin zone. (c) Phase diagram for the model Eq. (\ref{['eq:SU4Model']}) obtained from QMC simulations. Two quantum phases, Dirac semimetal and featureless Mott insulator, are observed, which are connected by a continuous quantum phase transition located at $V_c/t = 2.00\pm 0.05$.
• Figure 2: (color online) Extrapolation of structure factors (a) $P(\boldsymbol{\Gamma})/N$ and (b) $Q(\boldsymbol{\Gamma})/N$ over the inverse system size $1/L$ by cubic polynomials. The insets show the extrapolated values at the thermodynamic limit. From the results, both of the $O(6)$ orders are absent across the DSM-FMI phase transition.
• Figure 3: (color online) Extrapolation of (a) single-particle (fermionic) gap $\Delta_{sp}(\mathbf{K})$ and (b) O(6) order correlation (bosonic) gap $\Delta_{b}(\boldsymbol{\Gamma})$ over the inverse system size $1/L$ by linear and quadratic polynomials, respectively. The insets show the extrapolated gap values at the thermodynamic limit. Both excitation gaps open at $V_c/t= 2.00\pm0.05$.
• Figure 4: (color online) Extrapolation of structure factors divided by $N$ for (a) plaquette/columnar VBS order, (b) density wave order, over inverse system size $1/L$ by cubic polynomials, across the DSM-FMI phase transition. The results show that neither of these two long-range orders exists near the DSM-FMI phase transition.
• Figure 5: (color online) Blue line: fit of the spatial correlation of $O(6)$ order parameter $\boldsymbol{\phi}$ along $\mathbf{a}_1$ direction for $L=12,15$ systems as $\langle\phi(0,0)\cdot\phi(x,0)\rangle$ at $V=V_c$. The obtained anormalous dimension $\eta=0.7\pm0.1$. Dark green line: $\frac{1}{x^{4}}$, the behavior of $O(6)$ correlation at $V=0$. Violet line: $\frac{1}{x^{1.035}}$, the behavior of $O(6)$ correlation at the $(2+1)$D Wilson-Fisher $O(6)$ transition.