Surface critical behaviors of coupled Haldane chains

Abstract

The special surface transition at (2+1)-dimensional quantum critical point is precluded in corresponding classical critical point. The mechanism of such behavior which is only found in dimerized Heisenberg models so far is still under debate. To illuminate the role of symmetry protected topological (SPT) phase in inducing such nonordinary behaviors, we study a system on a two-dimensional square lattice consisted by interacting spin-1 Haldane chains, which has a genuine SPT phase-the Haldane phase-at weak interchain interactions and a quantum critical point belonging to the classical 3D O(3) universality class to the Néel phase. Different from models studied previously, there is no dimerization in the current model. Cutting the system along the chain direction or perpendicular to the chain direction exposes two different surfaces. Using unbiased quantum Monte Carlo simulations, we find that the two different types of surface show completely different surface critical behaviors at the bulk critical point, resulted from different surface states in the SPT phase. For the system with surfaces along the chain direction, the surface critical behavior is of ordinary type of the bulk 3D O(3) critical point, while for the surfaces perpendicular to the chain direction, the surface critical behavior is nonordinary, consistent with special transitions found in dimerized Heisenberg models. Our numerical results demonstrate that the gapless surface state in the gapped SPT phase together with the gapless mode of critical point is a pure quantum scenario that leads to the nonordinary transition.

Boundary Critical Behavior of the Three-Dimensional Heisenberg Universality Class

“…[22]. These findings provide a explanation to recent MC results on the boundary critical behavior of quantum spin models [13][14][15][16][18][19][20]. The exponent η reported for such models is close to that of the special transition, Eq.…”

“…This plausibly explains at least the results for S = 1 quantum models of Ref. [18,20], where a topological θ−term is absent. Also, we observe that the exponent η reported in Refs.…”

“…Nevertheless, quite remarkably a MC study of a dimerized S = 1 system reported a surface critical exponent close (although not identical) to that of the S = 1/2 case [18], whereas VBS correlations decay faster than for the S = 1/2 case [19]. Similar exponents have been found at the boundary of coupled Haldane chains [20]. For a S = 1 system a topological θ−term is absent, and so via a standard quantum-to-classical mapping [21] it should correspond to a classical 3D O(3) model with a surface.…”

“…Also, we observe that the exponent η reported in Refs. [18,20] deviates for about 15% from η at the special point (Eq. ( 9)), suggesting that the models are not exactly at the special transition.…”

Spin versus bond correlations along dangling edges of quantum critical magnets

“…Recent numerical studies of two-dimensional quantum Heisenberg antiferromagnets (AFM) have, however, called the current understanding of quantum surface critical phenomena into question [10][11][12][13][14]. These magnets feature a bulk quantum critical point in the 3D O(3) universality class, precisely implementing the purely ordinary case discussed above.…”