Unconventional Surface Critical Behaviors Induced by Quantum Phase Transition from Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to N\'eel Order

TL;DR

This paper investigates how gapless surface states at quantum phase transitions in a 2D topological phase induce unconventional surface critical behaviors, challenging traditional Landau theory predictions.

Contribution

It reveals that gapless surface states at bulk quantum phase transitions lead to novel universality classes of surface critical behavior in a 2D topological phase.

Findings

Gapless surface states induce unconventional surface critical behaviors.

Surface critical behaviors differ from bulk Landau phase transition predictions.

Quantum Monte Carlo simulations confirm the novel universality classes.

Abstract

A symmetry-protected topological phase has nontrivial surface states in the presence of certain symmetries, which can either be gapless or be degenerate. In this work, we study the physical consequence of such gapless surface states at the bulk quantum phase transition (QPT) that spontaneously breaks these symmetries. The two-dimensional Affleck-Kennedy-Lieb-Tasaki phase on a square lattice and its QPTs to N\'eel ordered phases are realized with the spin-$1/2$ Heisenberg model on a decorated square lattice. With large-scale quantum Monte Carlo simulations, we show that even though the bulk QPTs are governed by the conventional Landau phase transition theory, the gapless surface state induces unconventional universality classes of the surface critical behaviors.