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 $Z_2$ 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 corner-transfer matrix method, which is computationally more efficient than previous approaches based on the tensor renormalization group.

中文翻译：

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从无偏无限投影纠缠对状态模拟中检测Z2拓扑有序的相

我们提出了一种基于无偏无限投影纠缠对状态模拟来识别拓扑顺序的方法，即，在优化张量网络ansatz的过程中，我们不对张量施加虚拟对称性。作为示例，我们考虑在磁场中表现出复曲面模型的基态${ž}_2$ 拓扑顺序。优化是通过基于张量环境之和的高效能量最小化方法来计算梯度的。我们表明，将优化的张量引入正确的量规后，大约${ž}_2$ 对称，并且它们可以完全对称地后验以生成稳定的拓扑有序状态，从而产生正确的拓扑纠缠熵和模S和U矩阵。为了计算后者，我们开发了一个转角传递矩阵方法的变体，该方法在计算上比基于张量重归一化组的先前方法更有效。