PI: Simon Hands
Institution: University of Liverpool

The Thirring Model describes relativistic fermions moving in a two-dimensional plane and interacting via a contact term between conserved currents. The physical system it most resembles is low-energy electronic excitations in graphene. For free electrons at half-filling on a honeycomb lattice, conduction and valance bands form cones just touching at their vertices at two “Dirac points” lying within the first Brillouin zone. Since the density of states vanishes, and the effective fine structure constant is boosted by a factor v_F/c≈1/300, where the pitch of the cones v_F is the Fermi velocity, the resulting physics is described by a strongly-interacting relativistic quantum field theory, with equal likelihood of exciting electrons or holes.

Besides applications in layered condensed matter systems, the Thirring model is of interest in its own right as possibly the simplest relativistic theory of fermions requiring a computational solution. In the most recent simulation campaign we have for the first time studied the model’s spectrum in the vicinity of the phase transition, exploring both bound fermion – anti-fermion “meson” channels, with spin-0, and the spin-1/2 fermion channel. The results confirm a significant spectral gap between states with quantum numbers expected of Goldstone bosons, and non-Goldstone channels, consistent with the spontaneous breakdown of U(2) global symmetry to U(1)xU(1) accompanied by the generation of a fermion bilinear condensate <ψψ>≠0 signalling dynamical mass generation in the fermion channel.

A major highlight arises from the fermion timeslice correlator evaluated at vanishing bare mass in the vicinity of the critical interaction strength β=a/g²≈0.28, shown (left) on a log-log plot. The results are consistent with fermion propagation of the form

C_f(x)∼x^-(2+η_ψ⁾

with the fermion anomalous dimension η_ψ (plotted in the inset) taking the unexpectedly large value ≈3. This first estimate of a fermionic critical exponent suggests the emergent conformal field theory at the critical point is very strongly-interacting.

S. Hands and J. Ostmeyer, Spectroscopy in the 2+1D Thirring model with N=1 domain wall fermions

Phys.Rev.D 107 (2023) 1, 014504   2210.04790 [hep-lat]

DOI: 10.1103/PhysRevD.107.014504 (publication)