Lattice Field Theory Analysis of the Chiral Heisenberg Model

Abstract

Motivated by ongoing interest in the universal behaviour of the Hubbard model of spinning electrons on honeycomb and $\pi$-flux lattices at the semi-metal -- Mott insulator phase transition, we formulate the 3D chiral Heisenberg model, a theory of relativistic fermions in three spacetime dimensions, as a lattice field theory using domain wall fermions. The contact interaction term preserves an SU(2) global symmetry. We perform numerical simulations using the Rational Hybrid Monte Carlo algorithm on system sizes $L^3\times L_s$ with $L\in \{8,\dots ,24\}$ and domain wall separation $L_s\in \{8,16,24\}$. We locate the phase transition corresponding to spontaneous SU(2)$\to$U(1) breaking, yielding critical exponent estimates ${\nu }^{-1}=0.63(3)$, ${\eta }_{\Phi }=1.42(8)$. These values are considerably removed from estimates obtained from simulations performed in (2+1)D, ie. with the time and spatial directions treated differently, but align more closely with analytic estimates obtained using 3D covariant field theory. We also present first results for the fermion correlator, ultimately needed for the determination of the exponent ${\eta }_{\Psi }$, highlighting the need to rotate the fermion source to a common reference direction in isospace in order to obtain a signal.

arXiv comment28 pages, 9 figures, 3 tables

References in corpus (26)

• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• A New Exact Method for Dynamical Fermion Computations with Non-Local Actions
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited
• Competing nodal d-wave superconductivity and antiferromagnetism
• Numerical evidence of conformal phase transition in graphene with long-range interactions
• On the Critical Flavor Number in the 2+1$d$ Thirring Model
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1d
• Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
• From Domain Wall to Overlap in 2+1d
• Fermion-scalar interactions with domain wall fermions
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Spectroscopy in the 2+1$d$ Thirring Model with $N=1$ Domain Wall Fermions
• The Physicist's Guide to the HMC
• Critical Behaviour in the Single Flavor Thirring Model in 2+1$d$ with Wilson Kernel Domain Wall Fermions