Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model

TL;DR

This study investigates how different geometrical surface configurations affect the critical behaviors of a two-dimensional dimerized quantum XXZ model, revealing diverse surface phenomena at quantum critical points.

Contribution

It uncovers distinct surface behaviors induced by geometrical settings in the 2D dimerized quantum XXZ model, including evidence for extraordinary and extraordinary-log surface transitions.

Findings

Dangling-ladder surface exhibits ordinary transition for both S=1/2 and S=1.

Dangling-chain surface shows richer behaviors, including potential extraordinary and extraordinary-log transitions.

Surface behaviors depend strongly on the geometrical surface configuration and spin magnitude.

Abstract

We study the surface behavior of the two-dimensional columnar dimerized quantum antiferromagnetic XXZ model with easy-plane anisotropy, with particular emphasis on the surface critical behaviors of the (2+1)-dimensional quantum critical points of the model that belong to the classical three-dimensional O(2) universality class, for both $S=1/2$ and $S=1$ spins using quantum Monte Carlo simulations. We find completely different surface behaviors on two different surfaces of geometrical settings: the dangling-ladder surface, which is exposed by cutting a row of weak bonds, and the dangling-chain surface, which is formed by cutting a row of strong bonds along the direction perpendicular to the strong bonds of a periodic system. Similar to the Heisenberg limit, we find an ordinary transition on the dangling-ladder surface for both $S=1$ and $S=1/2$ spin systems. However, the dangling-chain surface shows much richer surface behaviors than in the Heisenberg limit. For the $S=1/2$ easy-plane model, at the bulk critical point, we provide evidence supporting an extraordinary surface transition with a long-range order established by effective long-range interactions due to bulk critical fluctuations. The possibility that the state is an extraordinary-log state seems unlikely. For the $S=1$ system, we find surface behaviors similar to that of the three-dimensional classical XY model with sufficiently enhanced surface coupling, suggesting an extraordinary-log state at the bulk critical point.