Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions

Abstract

Interacting theories of N relativistic fermion flavors in reducible spinor representations in 2+1 spacetime dimensions are formulated on a lattice using domain wall fermions (DWF), for which a U(2N) global symmetry is recovered in the limit that the wall separation $L_s$ is made large. The Gross-Neveu (GN) model is studied in the large-N limit and an exponential acceleration of convergence to the large-$L_s$ limit is demonstrated if the usual parity-invariant mass $m\bar{\psi }\psi$ is replaced by the U(2N)-equivalent $i{m}_3\bar{\psi }{\gamma }_3\psi$. The GN model and two lattice variants of the Thirring model are simulated for N = 2 using a hybrid Monte Carlo algorithm, and studies made of the symmetry-breaking bilinear condensate and its associated susceptibility, the axial Ward identity, and the mass spectrum of both fermion and meson excitations. Comparisons are made with existing results obtained using staggered fermions. For the GN model a symmetry-breaking phase transition is observed, the Ward identity is recovered, and the spectrum found to be consistent with large-N expectations. There appears to be no obstruction to the study of critical UV fixed-point physics using DWF. For the Thirring model the Ward identity is not recovered, the spectroscopy measurements are inconclusive, and no symmetry breaking is observed all the way up to the effective strong coupling limit. This is consistent with a critical Thirring flavor number $N_c<2$, contradicting earlier staggered fermion results.

arXiv comment31 pages, 15 figures

References in corpus (24)

• The electronic properties of graphene
• A Method for Simulating Chiral Fermions on the Lattice
• Quantum Orders and Symmetric Spin Liquids
• Chiral Fermions from Lattice Boundaries
• Axial symmetries in lattice QCD with Kaplan fermions
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• QED3 theory of underdoped high temperature superconductors
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Four - Fermi Theories in Fewer Than Four Dimensions
• Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions
• Chiral Symmetry Breaking and Phase Fluctuations in Cuprate Superconductors: A QED${}_3$ Unified Theory of the Pseudogap State
• Fermion bags, duality and the three dimensional massless lattice Thirring model
• Critical Flavor Number in the Three Dimensional Thirring Model
• The Three Dimensional Thirring Model for Small N_f
• Thirring Model as a Gauge Theory
• Chiral Symmetry Restoration and Realisation of the Goldstone Mechanism in the U(1) Gross-Neveu Model at Non-Zero Chemical Potential
• The Three Dimensional Thirring Model for N_f=4 and N_f=6
• Interplay of universality classes in a three-dimensional Yukawa model
• Fermion Mass Generation in the D-dimensional Thirring Model as a Gauge Theory
• The U(1) Gross-Neveu Model at Non-Zero Chemical Potential
• From Domain Wall to Overlap in 2+1d
• Fermion-scalar interactions with domain wall fermions

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• A functional perspective on emergent supersymmetry
• Hunting Quantum Gravity with Analogs: the case of graphene
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• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• Cascade of phase transitions in a planar Dirac material
• 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
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