Boundary critical phenomena in the quantum Ashkin-Teller model

TL;DR

This paper studies boundary critical phenomena in the 1D quantum Ashkin-Teller model using boundary conformal field theory and DMRG, identifying boundary conditions and phase diagrams.

Contribution

It constructs microscopic boundary terms that correspond to stable conformal boundary conditions and characterizes boundary fixed points explicitly.

Findings

Validated boundary conditions via finite-size energy spectra

Confirmed symmetry and duality properties of boundary fixed points

Proposed a global phase diagram for boundary criticality

Abstract

We investigate the boundary critical phenomena of the one-dimensional quantum Ashkin-Teller model using boundary conformal field theory and density matrix renormalization group (DMRG) simulations. Based on the $\mathbb{Z}_2$-orbifold of the $c=1$ compactified boson boundary conformal field theory, we construct microscopic lattice boundary terms that renormalize to the stable conformal boundary conditions, utilizing simple current extensions and the underlying $\mathrm{SU}(2)$ symmetry to explicitly characterize the four-state Potts point. We validate these theoretical identifications via finite-size spectroscopy of the lattice energy spectra, confirming their consistency with $D_4$ symmetry and Kramers-Wannier duality. Finally, we discuss the boundary renormalization group flows among these identified fixed points to propose a global phase diagram for the boundary criticality.