Abstract
We present an approach to identify topological order based on unbiased infinite projected entangled-pair states simulations, i.e., where we do not impose a virtual symmetry on the tensors during the optimization of the tensor network ansatz. As an example we consider the ground state of the toric code model in a magnetic field exhibiting topological order. The optimization is done by an efficient energy minimization approach based on a summation of tensor environments to compute the gradient. We show that the optimized tensors, when brought into the right gauge, are approximately symmetric, and they can be fully symmetrized a posteriori to generate a stable topologically ordered state, yielding the correct topological entanglement entropy and modular S and U matrices. To compute the latter we develop a variant of the corner-transfer matrix method, which is computationally more efficient than previous approaches based on the tensor renormalization group.
7 More- Received 6 December 2019
- Revised 21 February 2020
- Accepted 21 February 2020
DOI:https://doi.org/10.1103/PhysRevB.101.115143
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