Spinons and holons on the lattice

TL;DR

This paper explores the potential relevance of 3D compact U(1) lattice gauge theory with fermions and scalars to condensed matter physics, highlighting uncertain properties and proposing conjectures for future research.

Contribution

It conjectures the universality classes of the model at different couplings and discusses the significance of dynamical fermion mass generation and tricritical points.

Findings

Indicates possible universality with 3D four-fermion models at strong coupling.

Suggests two universality classes at intermediate and weak coupling.

Highlights the importance of dynamical fermion mass generation in compact QED_3.

Abstract

We point out that the dynamical fermion mass generation in the 3D compact U(1) lattice gauge theory with charged fermion and scalar fields (chi-U-phi_3 model) may be of relevance for the spinon-holon theory with local gauge symmetry in the condensed matter physics. However, many properties of the model are uncertain, so we make some conjectures to motivate their future investigation. Most probably, for strong gauge coupling the model is by universality equivalent to the familiar 3D four-fermion coupling models with N_f=2. Available numerical results indicate that at the intermediate and weak gauge coupling two universality classes with new interesting physics may arise. One of them is associated with a tricritical point which probably exists in the phase diagram of the model. The other one is determined by the dynamical fermion mass generation in the compact QED_3, which is insufficiently understood but of much interest by itself.