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.

12 pages, 6 figures, correction to flow equations

References in corpus (15)

• The electronic properties of graphene
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Is graphene in vacuum an insulator?
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Critical Temperature Curve in the BEC-BCS Crossover
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• A simple fermionic model of deconfined phases and phase transitions
• Massive fermions without fermion bilinear condensates
• Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models

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