Self-duality protected multi-criticality in deconfined quantum phase transitions

TL;DR

This paper explores how self-duality in certain quantum field theories leads to multi-critical points and different universality classes, with detailed calculations of operator scaling dimensions and implications for phase transitions.

Contribution

It provides a perturbative analysis of self-dual deconfined quantum critical points, revealing new multi-critical behavior and universality classes in 3D QED with Chern-Simons and Gross-Neveu couplings.

Findings

Identification of multi-critical points in self-dual theories.

Calculation of operator scaling dimensions in 3D QED with Chern-Simons and Gross-Neveu couplings.

Non-relativistic four-fermion interactions can induce first-order phase transitions.

Abstract

Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the self-duality can be promoted as a symmetry, this leads to the multi-criticalities. This work investigates a description of the deconfined quantum criticality, the $N_f=2$ QED$_3$, as an example of self-dual theories and its multi-critical behavior under perturbative deformations. The multi-criticality is described by the theory with Gross-Neveu couplings and falls in a different universality class than the standard deconfined quantum criticality. We systematically calculate the scaling dimensions of various operators in the 3d quantum electrodynamics with the Chern-Simons term and Gross-Neveu couplings by the large-$N$ renormalization group analysis. Specifically, we find certain non-relativistic four-fermion interactions corresponding to the dimer-dimer interactions in the lattice model will drive the deconfined quantum criticality to the first-order transition, consistent with previous numerical studies.