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  • Open Access

Lattice field theory analysis of the chiral Heisenberg model

Simon Hands1 and Johann Ostmeyer2,*

  • *Contact author: ostmeyer@hiskp.uni-bonn.de
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Phys. Rev. B 114, 125102 – Published 5 August, 2026

DOI: https://doi.org/10.1103/pndw-743y

Abstract

Motivated by ongoing interest in the universal behavior of the Hubbard model of spinning electrons on honeycomb and π-flux lattices at the semimetal–Mott insulator phase transition, we formulate the three-dimensional (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 L3×Ls, with L∈{8,...,24} and domain wall separation Ls∈{8,16,24}. We locate the phase transition corresponding to spontaneous SU(2)→U(1) breaking, yielding critical exponent estimates ν−1=0.63(3) and ηΦ=1.42(8). These values are considerably removed from estimates obtained from simulations performed in (2+1)D, i.e., with the time and spatial directions treated differently, but align more closely with analytic estimates obtained using 3D covariant field theory. We also present results for the fermion correlator, ultimately needed for the determination of the exponent ηΨ, highlighting the need to rotate the fermion source to a common reference direction in isospace to obtain a signal.

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Phys. Rev. B 114, 125102– Published 5 August, 2026
  • Received 10 April 2026
  • Accepted 9 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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