Critical flavor number in the 2+1D Thirring model

Simon Hands

doi:10.1103/physrevd.99.034504

Abstract

The Thirring model in 2+1 spacetime dimensions, in which $N$ flavors of relativistic fermion interact via a contact interaction between conserved fermion currents, is studied using lattice field theory simulations employing domain wall fermions, which furnish the correct U(2N) global symmetry in the limit that the wall separation $L_s\to\infty$. Attention is focussed on the issue of spontaneous symmetry breakdown via a non-vanishing fermion bilinear condensate $\langle\bar\psi\psi\rangle\not=0$. Results from quenched simulations are presented demonstrating that a non-zero condensate does indeed form over a range of couplings, provided simulation results are first extrapolated to the $L_s\to\infty$ limit. Next, results from simulations with $N=1$ using an RHMC algorithm demonstrate that U(2) symmetry is unbroken at weak coupling but plausibly broken at strong coupling. Correlators of mesons with spin zero are consistent with the Goldstone spectrum expected from U(2)$\to$U(1)$\otimes$U(1). We infer the existence of a symmetry-breaking phase transition at some finite coupling, and combine this with previous simulation results to deduce that the critical number of flavors for the existence of a quantum critical point in the Thirring model satisfies $0<N_c<2$, with strong evidence that in fact $N_c>1$.

Highlights

While the study of theories of relativistic fermions moving in the plane, i.e., in 2 þ 1 spacetime dimensions, has received a fillip over the past decade as a result of developments in the condensed matter physics of layered systems, the underlying quantum field theories continue to be of considerable theoretical interest in their own right
The mismatch between theoretical expectation and results from the staggered Thirring model has motivated us to consider alternative lattice fermion formulations with the potential to capture the requisite symmetries more faithfully. We have developed both analytical and numerical insight into how Uð2NÞ symmetry is manifested in 2 þ 1d using domain wall fermions (DWF) [15,16], which will be reviewed
This paper extends the study of spontaneous symmetry breaking in the Thirring model with DWF to N 1⁄4 1

Summary

INTRODUCTION

While the study of theories of relativistic fermions moving in the plane, i.e., in 2 þ 1 spacetime dimensions, has received a fillip over the past decade as a result of developments in the condensed matter physics of layered systems, the underlying quantum field theories continue to be of considerable theoretical interest in their own right. More interesting still is the possibility that the true ground state has a bilinear condensate hψψi ≠ 0; fermions propagating through such a vacuum incur a dynamically-generated mass This phenomenon can be described in terms of spontaneous breaking of a global Uð2NÞ symmetry. The main conclusions of that work were that in the GN model there appears to be no obstruction to studying symmetry breaking via bilinear condensation and the resulting QCP; good qualitative agreement was found with the analytical expectations of the large-N approach. Since to date Uð2NÞ symmetry breaking has not been observed with DWF, as a warm-up Sec. III presents results from a study of the quenched Thirring model, to see what broken symmetry might look like.

FORMULATION AND IMPLEMENTATION

RESULTS

Bilinear condensate hψψi

Meson correlators

DISCUSSION