Agnostic and efficient detection of ℤ2 symmetry-protected topological phases in projected entangled-pair states
Abstract
Symmetry-protected topological (SPT) phases are the simplest example of quantum phases that cannot be detected by local order parameters. Their classification is by now well-established from multiple perspectives, a prominent one being via tensor network states. The practical question, however, is not mere classification, but detection: given the ground state of an interacting Hamiltonian and a symmetry group G along with its representation, is there an efficient way to tell if the state is in a SPT phase with respect to G? While there exist such practical tests in one spatial dimension (1D), methods in 2D have so far been restricted to finite-size systems or require an explicit form of virtual symmetries of the tensor networks representing the ground state. Here, we develop an agnostic and efficient method to detect interacting ℤ2 2D SPT phases, using an infinite projected entangled-pair (PEPS) representation of the ground state. The method is agnostic to the symmetry representation in the virtual space of the PEPS tensor and applicable independent of the bond dimension of the tensors. Moreover, it is efficient as it does not require finite-size scalings: it works directly in the thermodynamic limit. We numerically demonstrate the procedure by mapping out phase boundaries away from fixed-point wavefunctions. We extract the SPT label cocycle data explicitly from the PEPS tensor.
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BibTeX
@misc{chaduteau2026agnostic,
title = {{Agnostic and efficient detection of $\mathbbZ_2$ symmetry-protected topological phases in projected entangled-pair states}},
author = {Alexandre Chaduteau and Hao Chen and Juraj Hasik and Titus Neupert},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07030},
eprint = {2611.07030},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07030},
}
RIS
TY - UNPB
TI - Agnostic and efficient detection of ℤ_2 symmetry-protected topological phases in projected entangled-pair states
AU - Alexandre Chaduteau
AU - Hao Chen
AU - Juraj Hasik
AU - Titus Neupert
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07030
UR - https://arxiv.org/abs/2611.07030
AB - Symmetry-protected topological (SPT) phases are the simplest example of quantum phases that cannot be detected by local order parameters. Their classification is by now well-established from multiple perspectives, a prominent one being via tensor network states. The practical question, however, is not mere classification, but detection: given the ground state of an interacting Hamiltonian and a symmetry group G along with its representation, is there an efficient way to tell if the state is in a SPT phase with respect to G? While there exist such practical tests in one spatial dimension (1D), methods in 2D have so far been restricted to finite-size systems or require an explicit form of virtual symmetries of the tensor networks representing the ground state. Here, we develop an agnostic and efficient method to detect interacting ℤ_2 2D SPT phases, using an infinite projected entangled-pair (PEPS) representation of the ground state. The method is agnostic to the symmetry representation in the virtual space of the PEPS tensor and applicable independent of the bond dimension of the tensors. Moreover, it is efficient as it does not require finite-size scalings: it works directly in the thermodynamic limit. We numerically demonstrate the procedure by mapping out phase boundaries away from fixed-point wavefunctions. We extract the SPT label cocycle data explicitly from the PEPS tensor.
ER -