Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models

TL;DR

This paper investigates a symplectic fermion model with second-order derivatives, exploring its semi-Lorentz invariance, unitarity, and critical behavior, with potential relevance to condensed matter systems.

Contribution

It introduces a fermionic model with a pseudo-Hermitian Hamiltonian and analyzes its renormalization group fixed points and critical exponents.

Findings

Identifies a low-energy fixed point analogous to Wilson-Fisher in fermionic systems

Calculates critical exponents to two-loop order

Demonstrates unitarity despite semi-Lorentz invariance

Abstract

We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with rotational spin of spin-1/2 particles. Since the spin-1/2 representation is not promoted to a representation of the Lorentz group, the model is not fully Lorentz invariant, although it has a relativistic dispersion relation. The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a unitary time evolution. Renormalization-group analysis shows the model has a low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed points. The critical exponents are computed to two-loop order. Possible applications to condensed matter physics in 3 space-time dimensions are discussed.