Self-Duality and Phase Structure of the 4D Random-Plaquette Z_2 Gauge Model

Abstract

In the present paper, we shall study the 4-dimensional Z_2 lattice gauge model with a random gauge coupling; the random-plaquette gauge model(RPGM). The random gauge coupling at each plaquette takes the value J with the probability 1-p and -J with p. This model exhibits a confinement-Higgs phase transition. We numerically obtain a phase boundary curve in the (p-T)-plane where T is the "temperature" measured in unit of J/k_B. This model plays an important role in estimating the accuracy threshold of a quantum memory of a toric code. In this paper, we are mainly interested in its "self-duality" aspect, and the relationship with the random-bond Ising model(RBIM) in 2-dimensions. The "self-duality" argument can be applied both for RPGM and RBIM, giving the same duality equations, hence predicting the same phase boundary. The phase boundary curve obtained by our numerical simulation almost coincides with this predicted phase boundary at the high-temperature region. The phase transition is of first order for relatively small values of p < 0.08, but becomes of second order for larger p. The value of p at the intersection of the phase boundary curve and the Nishimori line is regarded as the accuracy threshold of errors in a toric quantum memory. It is estimated as p=0.110\pm0.002, which is very close to the value conjectured by Takeda and Nishimori through the "self-duality" argument.

arXiv comment14 pages, 7 figures

References in corpus (8)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
• Duality and Multicritical Point of Two-Dimensional Spin Glasses
• Symmetry, complexity and multicritical point of the two-dimensional spin glass
• Self-dual random-plaquette gauge model and the quantum toric code
• Energy fluctuations at the multicritical point in two-dimensional spin glasses

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• Duality in finite-dimensional spin glasses
• Perturbative stability and error correction thresholds of quantum codes
• Learning to find order in disorder
• Phase diagram of the three-dimensional subsystem toric code