Detecting a Z_{2} topologically ordered phase from unbiased infinite projected entangledpair state simulations
Abstract
We present an approach to identify topological order based on unbiased infinite projected entangledpair 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 Z_{2} 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 Z_{2} 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 cornertransfer matrix method, which is computationally more efficient than previous approaches based on the tensor renormalization group.
 Publication:

Physical Review B
 Pub Date:
 March 2020
 DOI:
 10.1103/PhysRevB.101.115143
 arXiv:
 arXiv:1912.00908
 Bibcode:
 2020PhRvB.101k5143C
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Quantum Physics
 EPrint:
 16 pages, 14 figures