Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2024
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| author | Guo, Yuchen Zhang, Jian-Hao Zhang, Hao-Ran Yang, Shuo Bi, Zhen |
| author_facet | Guo, Yuchen Zhang, Jian-Hao Zhang, Hao-Ran Yang, Shuo Bi, Zhen |
| contents | We propose a tensor network approach known as the locally purified density operator (LPDO) to investigate the classification and characterization of symmetry-protected topological (SPT) phases in open quantum systems. We extend the concept of injectivity, originally associated with matrix product states and projected entangled pair states, to LPDOs in $(1+1)D$ and $(2+1)D$ systems, unveiling two distinct types of injectivity conditions inherent in short-range entangled density matrices. Within the LPDO framework, we outline a classification scheme for decohered average symmetry-protected topological (ASPT) phases, consistent with earlier results obtained through spectrum sequence techniques. We first illustrate our framework with ASPT phases protected by fermion parity symmetry, then extend the classification of ASPT phases to a general group extension. We demonstrate examples of explicit construction of fixed-point LPDOs for ASPT phases including intrinsic ASPTs in both $(1+1)D$ and $(2+1)D$ systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States Guo, Yuchen Zhang, Jian-Hao Zhang, Hao-Ran Yang, Shuo Bi, Zhen Strongly Correlated Electrons We propose a tensor network approach known as the locally purified density operator (LPDO) to investigate the classification and characterization of symmetry-protected topological (SPT) phases in open quantum systems. We extend the concept of injectivity, originally associated with matrix product states and projected entangled pair states, to LPDOs in $(1+1)D$ and $(2+1)D$ systems, unveiling two distinct types of injectivity conditions inherent in short-range entangled density matrices. Within the LPDO framework, we outline a classification scheme for decohered average symmetry-protected topological (ASPT) phases, consistent with earlier results obtained through spectrum sequence techniques. We first illustrate our framework with ASPT phases protected by fermion parity symmetry, then extend the classification of ASPT phases to a general group extension. We demonstrate examples of explicit construction of fixed-point LPDOs for ASPT phases including intrinsic ASPTs in both $(1+1)D$ and $(2+1)D$ systems. |
| title | Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2403.16978 |