[Paper Review] Chiral symmetry breaking in lattice QED model with fermion brane

Eigo Shintani, T. Onogi|arXiv (Cornell University)|Mar 6, 2012

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper proposes a 4D lattice QED model with a 2+1D fermion brane to study chiral symmetry breaking in graphene-like systems, incorporating finite fermion velocity and dynamical gauge fields. Hybrid Monte Carlo simulations reveal that chiral symmetry breaking occurs at critical coupling αc ≈ 1.5–1.59 for v = 0.1, with velocity playing a dominant role in enhancing dynamics, consistent with Schwinger-Dyson predictions and suggesting the physical graphene point lies in the broken phase.

ABSTRACT

We propose a novel approach to the Graphene system using a local field theory of 4 dimensional QED model coupled to 2+1 dimensional Dirac fermions, whose velocity is much smaller than the speed of light. Performing hybrid Monte Carlo simulations of this model on the lattice, we compute the chiral condensate and its susceptibility with different coupling constant, velocity parameter and flavor number. We find that the chiral symmetry is dynamically broken in the small velocity regime and obtain a qualitatively consistent behavior with the prediction from Schwinger-Dyson equations.

Motivation & Objective

• To investigate chiral symmetry breaking in graphene beyond non-relativistic approximations using a relativistic, gauge-invariant field theory.
• To clarify the role of fermion velocity and vacuum polarization in inducing a semimetal-insulator transition.
• To provide a non-perturbative lattice simulation of QED with 2+1D fermions coupled to 4D gauge fields, capturing realistic graphene dynamics.
• To compare results with Schwinger-Dyson and mean-field predictions, particularly regarding critical coupling αc.
• To assess whether the physical graphene point lies within the chiral symmetry broken phase.

Proposed method

• Formulate a 4D non-compact QED action with a 2+1D Dirac fermion brane, explicitly including fermion velocity as a parameter.
• Implement anisotropic gauge coupling to reflect the velocity difference between fermions and photons.
• Perform hybrid Monte Carlo simulations on the lattice to compute the chiral condensate and its susceptibility.
• Vary the gauge coupling β, fermion mass m, and velocity v to probe phase structure.
• Use the peak of chiral susceptibility to identify the critical coupling αc for chiral symmetry breaking.
• Compare results between quenched and full QED to assess dynamical fermion effects on criticality.

Experimental results

Research questions

• RQ1 Does chiral symmetry breaking occur in a relativistic 4D QED model with a 2+1D fermion brane at finite fermion velocity?
• RQ2 How does the critical coupling αc for chiral symmetry breaking depend on the fermion velocity v and dynamical fermion effects?
• RQ3 Is the critical coupling αc in the model consistent with predictions from Schwinger-Dyson equations and large-N methods?
• RQ4 What is the role of vacuum polarization and velocity renormalization in shifting the critical point?
• RQ5 Does the physical graphene point (v ≈ 1/300c) lie within the chiral symmetry broken phase?

Key findings

• Chiral symmetry breaking is dynamically generated in the small-velocity regime (v = 0.1), with a critical coupling αc ≈ 1.5–1.59, indicating a phase transition to a gapped state.
• The inclusion of dynamical fermions shifts the critical coupling βv from 0.093 (quenched) to 0.062 (full QED) at v = 0.1, consistent with a 40–50% increase in αc.
• Reducing velocity from v = 0.1 to v = 0.05 shifts the critical coupling by only 5–7%, indicating a weak dependence on v in this range.
• Extrapolating to v ≈ 1/300 (physical graphene), the critical coupling is estimated at αc ≈ 1.5 (full QED), comparable to the TB model value of α ≈ 2.2.
• The peak of chiral susceptibility shifts toward stronger coupling with decreasing v, suggesting velocity renormalization may play a key role in infrared dynamics.
• The results qualitatively match predictions from Schwinger-Dyson equations and gap equations, supporting the existence of a semimetal-insulator transition in graphene.