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 nontrivial 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 ladder ends is gapless, while the surface exposed along the ladder 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 the 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.

• Received 21 July 2022
• Revised 8 September 2022
• Accepted 29 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.134407