Critical flavour number of the Thirring model in three dimensions

Abstract

The Thirring model is a four-fermion theory with a current-current interaction and $U(2N)$ chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition it serves as a toy model to study chiral symmetry breaking. In the limit of flavour number $N\to 1/2$ it is equivalent to the Gross-Neveu model, which shows a parity-breaking discrete phase transition. The model was already studied with different methods, including Dyson-Schwinger equations, functional renormalisation group methods and lattice simulations. Most studies agree that there is a phase transition from a symmetric phase to a spontaneously broken phase for a small number of fermion flavours, but no symmetry breaking for large $N$. But there is no consensus on the critical flavour number $N^{\text{cr}}$ above which there is no phase transition anymore and on further details of the critical behaviour. Values of $N$ found in the literature vary between $2$ and $7$. All earlier lattice studies were performed with staggered fermions. Thus it is questionable if in the continuum limit the lattice model recovers the internal symmetries of the continuum model. We present new results from lattice Monte Carlo simulations of the Thirring model with SLAC fermions which exactly implement all internal symmetries of the continuum model even at finite lattice spacing. If we reformulate the model in an irreducible representation of the Clifford algebra, we find, in contradiction to earlier results, that the behaviour for even and odd flavour numbers is very different: For even flavour numbers, chiral and parity symmetry are always unbroken. For odd flavour numbers parity symmetry is spontaneously broken below the critical flavour number $N_{\text{ir}}^{\text{cr}}=9$ while chiral symmetry is still unbroken.

arXiv comment17 pages, 9 figures, 3 tables

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Cited by in corpus (28)

• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
• On the Critical Flavor Number in the 2+1$d$ Thirring Model
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Inhomogeneities in the $2$-Flavor Chiral Gross-Neveu Model
• Momentum dependence of quantum critical Dirac systems
• Critical Behaviour in the Single Flavor Thirring Model in 2+1d
• Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions
• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• From Domain Wall to Overlap in 2+1d
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Validity of SLAC fermions for the (1 + 1)-dimensional helical Luttinger liquid
• Symmetries of Thirring models on 3d lattices
• The Planar Thirring Model with Kähler-Dirac Fermions
• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• The relevance of the three dimensional Thirring coupling at finite temperature and density
• Bosonization of the Thirring Model in 2+1 Dimensions
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Evaluation of the Bilinear Condensate of the Planar Thirring Model in the Strongly Coupled Region
• Nature of the Topological Transition of the Kitaev Model in [111] Magnetic Field
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors