Nematic Quantum Criticality in Dirac Systems

Abstract

We investigate nematic quantum phase transitions in two different Dirac fermion models. The models feature twofold and fourfold, respectively, lattice rotational symmetries that are spontaneously broken in the ordered phase. Using negative-sign-free quantum Monte Carlo simulations and an $\epsilon$-expansion renormalization group analysis, we show that both models exhibit continuous phase transitions. In contrast to generic Gross-Neveu dynamical mass generation, the quantum critical regime is characterized by large velocity anisotropies, with fixed-point values being approached very slowly. Hence both experimental and numerical investigations will not be representative of the infrared fixed point, but of a crossover regime characterized by drifting exponents.

arXiv comment35 pages, including a 29 page supplemental information section; added notion of quasiuniversality; updated acknowledgements

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• Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Wilson-Fisher fixed points in presence of Dirac fermions
• Robust Fermi liquid instabilities in sign problem-free models
• Emus live on the Gross-Neveu-Yukawa archipelago
• Twist-tuned quantum criticality in moiré bilayer graphene
• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Spontaneous breaking of the $\text{SO}(2N)$ symmetry in the Gross-Neveu model
• Boosting quantum Monte Carlo and alleviating sign problem by Gutzwiller projection
• Quasiuniversality from all-in-all-out Weyl quantum criticality in pyrochlore iridates
• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality