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We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the two-dimensional Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature T = 0. From a scaling analysis when T → 0 at different annealing velocities v, we find power-law scaling in the system size for the velocity required in order to relax toward the ground state; v ∼ L −(z+1/ν) , the Kibble-Zurek ansatz where z is the dynamic critical exponent and ν the previously known correlation-length exponent, ν ≈ 3.6. We find z ≈ 13.6 for both the Edwards-Anderson spin-glass order parameter and the excess energy. This is different from a previous study of the system with bimodal couplings [S. J. Rubin, N. Xu, and A. W. Sandvik, Phys. Rev. E 95, 052133 (2017)] where the dynamics is faster (z is smaller) and the above two quantities relax with different dynamic exponents (with that of the energy being larger). We argue that the different behaviors arise as a consequence of the different low-energy landscapes-for normal-distributed couplings the ground state is unique (up to a spin reflection) while the system with bimodal couplings is massively degenerate. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results presented here also indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasi-degenerate states, and the scaling function takes a different form.

We present a deep reinforcement learning framework where a machine agent is trained to search for a policy to generate a ground state for the square ice model by exploring the physical environment. After training, the agent is capable of proposing a sequence of local moves to achieve the goal. Analysis of the trained policy and the state value function indicates that the ice rule and loop-closing condition are learned without prior knowledge. We test the trained policy as a sampler in the Markov chain Monte Carlo and benchmark against the baseline loop algorithm. This framework can be generalized to other models with topological constraints where generation of constraint-preserving states is difficult. arXiv:1903.04698v2 [cond-mat.dis-nn]

Quantum effect is expected to dictate the behaviour of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy (TEE) and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a Z2 topological order down to extremely low temperature, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates an intricate competition of off-diagonal and diagonal quantum processes leading to the quasi-degeneracy of states and effectively, the classical degeneracy is restored.If we further let h = J z provided the system is within the lobe, we obtain,Appendix B: Thermal entropy measurement using Wang-Landau method