Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone

TL;DR

This paper uses quantum Monte Carlo simulations on a lattice with a single Dirac cone to study the chiral Heisenberg Gross-Neveu-Yukawa phase transition, providing precise critical exponents and insights into fermionic and bosonic excitations.

Contribution

It introduces a lattice model with a single Dirac cone that reduces finite size effects and accurately characterizes the quantum critical behavior of the transition.

Findings

Critical coupling U_c = 6.76(1) for antiferromagnetic order

Critical exponents: ν=0.98(1), η_φ=0.53(1), η_ψ=0.18(1), β=0.75(1)

Evidence of quasiparticle weight degradation near the transition

Abstract

We present quantum Monte Carlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with $N=4$ Dirac spinor components subject to a repulsive, local four fermion interaction in 2+1$d$. Here we employ a two dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and $\pi$-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of ${U_c = 6.76(1)}$ as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition we extract a self-consistent set of critical exponents ${\nu = 0.98(1)}$, ${\eta_{\phi} = 0.53(1)}$, ${\eta_{\psi} = 0.18(1)}$, ${\beta = 0.75(1)}$. We provide evidence for the continuous degradation of the quasi-particle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally we study the effective "speed of light" of the low-energy relativistic description, which depends on the interaction $U$, but is expected to be regular across the quantum phase transition. We illustrate that the strongly coupled bosonic and fermionic excitations share a common velocity at the critical point.