Symmetries of Thirring models on 3d lattices

Abstract

We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_{\mathrm{crit}}$ of Thirring models in three dimensions. Only models with flavor number below $N_{\mathrm{crit}}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_{\mathrm{crit}}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_{\mathrm{crit}}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.

arXiv comment19 pages, 9 figures, Prepared for the 2021 Special Issue of the journal Symmetry on New Applications of Symmetry in Lattice Field Theory. In this replacement we corrected some errors (concerning the SLAC lattice-derivative), some misprints (mixup of numbers) and emphasized the link to random matrix theory. In addition we deleted some obsolete references and added relevant new ones

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Cited by in corpus (8)

• Induced topological gravity and anomaly inflow from Kaehler-Dirac fermions in odd dimensions
• The magnetized (2+1)-dimensional Gross-Neveu model at finite density
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Spectroscopy in the 2+1$d$ Thirring Model with $N=1$ Domain Wall Fermions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1$d$ with Wilson Kernel Domain Wall Fermions
• Higher-Dimensional Chirally Stabilized Fixed Points and Their Deformations