Interplay of Topological Order and Spin Glassiness in the Toric Code under Random Magnetic Fields

Abstract

We analyze the toric code model in the presence of quenched disorder, which is introduced via different types of random magnetic fields. In general, close to a quantum phase transition between a spin polarized phase and a topologically ordered one, we find that increasing the amount of disorder favors the topological phase. For some realizations of disorder, topological order can be robust against arbitrarily strong magnetic fields. In the case of the toric code in a random \pm h field, we show that the system exhibits a quantum phase transition to a spin glass phase in an appropriate dual variables description. The survival of topological order in the spin glass phase is directly related to the percolation properties of the rigid lattice in the Edwards-Anderson bimodal spin glass model. According to recent numerical results for this model [Phys. Rev. B 82, 214401 (2010)], it is likely that the rigid lattice does not percolate and, as a result, a new intermediate quantum phase appears in the random-field toric code. In this intermediate quantum phase, topological order coexists with spin glassiness.

7 pages, 4 figures; published version focusing on the topological spin glass phase and percolation properties of the rigid lattice in the random-field toric code model

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• Destabilization of U(1) Dirac spin-liquids on two dimensional non-bipartite lattices by quenched disorder
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries
• Tunable anyonic permeability across ${\mathbb{Z}}_2$ spin liquid junctions