Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity

TL;DR

This paper investigates a quantum phase transition in a novel two-dimensional lattice model where interactions preserve both SU(2) and Ising-like symmetries, revealing a new universality class at the critical point.

Contribution

The study introduces a sign-free quantum Monte Carlo model with unique symmetry properties and identifies a new universality class for the quantum critical point involving antiferromagnetism and superconductivity.

Findings

Massive fermion phase breaks Ising symmetry, leading to antiferromagnetism or superconductivity.

Quantum critical point belongs to a new 'chiral spin-charge symmetric' universality class.

Effective field theory explains the observed phase transition and critical behavior.

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.