Bulk and Surface Critical Behaviors of quantum Heisenberg antiferromagnet on a two-dimensional coupled diagonal ladders

Abstract

Using Quantum Monte Carlo simulations, we study the spin-1/2 Heisenberg model on a two-dimensional lattice formed by coupling diagonal ladders. The model hosts an antiferromagnetic Néel phase, a rung singlet product phase, and a topological none trivial Haldane phase, separated by two quantum phase transitions. We show that the two quantum critical points are all in the three-dimensional O(3) universality class. The properties of the two gapped phases, including the finite-size behavior of the string orders in the Haldane phase, are studied. We show that the surface formed by the ladders ends is gapless, while the surface exposed along the ladders is gapful, in the Haldane phase. Conversely, in the gapped rung singlet phase, the former surface is gapped, and the latter is gapless. We demonstrate that, although mechanisms of the two gapless modes are different, nonordinary surface critical behaviors are realized at both critical points on the gapless surfaces exposed by simply cutting bonds without fine-tuning the surface coupling required to reach a multicritical point in classical models. We also show that, on the gapped surfaces, the surface critical behaviors are in the ordinary class.

arXiv comment12 pages, 8 figures

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Cited by in corpus (7)

• A plane defect in the 3d O$(N)$ model
• The ordinary surface universality class of the three-dimensional O($N$) model
• Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model
• Extraordinary surface critical behavior induced by symmetry-protected topological state of a two-dimensional quantum magnet
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Spontaneous continuous-symmetry breaking and tower of states in a comb chain
• Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering