Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity

Abstract

We study a quantum phase transition from a massless to massive Dirac fermion phase in a new two-dimensional bipartite lattice model of electrons that is amenable to sign-free quantum Monte Carlo simulations. Importantly, interactions in our model are not only invariant under $\SU(2)$ symmetries of spin and charge like the Hubbard model, but they also preserve an Ising like electron spin-charge flip symmetry. From unbiased fermion bag Monte Carlo simulations with up to 2304 sites, we show that the massive fermion phase spontaneously breaks this Ising symmetry, picking either anti-ferromagnetism or superconductivity and that the transition at which both orders are simultaneously quantum critical, belongs to a new "chiral spin-charge symmetric" universality class. We explain our observations using effective potential and renormalization group calculations within the framework of a continuum field theory.

arXiv comment12 pages, 6 figures, correction to flow equations

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Cited by in corpus (8)

• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• SO(4) multicriticality of two-dimensional Dirac fermions
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling
• Instabilities of a Generalized Gross-Neveu Quantum Criticality
• Transverse Field $\gamma$-Matrix Spin Chains