Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929258981490688 |
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| author | Kuno, Yoshihito Orito, Takahiro Ichinose, Ikuo |
| author_facet | Kuno, Yoshihito Orito, Takahiro Ichinose, Ikuo |
| contents | Study of boundary phase transition in toric code under cylinder geometry via bulk projective measurement is reported. As the frequency of local measurement for bulk qubits is increased, spin-glass type long-range order on the boundaries emerges indicating spontaneous-symmetry breaking (SSB) of $Z_2$ symmetry. From the lattice-gauge-theory viewpoint, this SSB is a signal of a transition to Higgs phase with symmetry protected topological order. We numerically elucidate the properties of this phase transition in detail, especially its criticality, and give a physical picture using non-local gauge-invariant symmetry operators. Phase transition in the bulk is also studied and its relationship to the boundary transition is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16651 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model Kuno, Yoshihito Orito, Takahiro Ichinose, Ikuo Statistical Mechanics Disordered Systems and Neural Networks High Energy Physics - Lattice Quantum Physics Study of boundary phase transition in toric code under cylinder geometry via bulk projective measurement is reported. As the frequency of local measurement for bulk qubits is increased, spin-glass type long-range order on the boundaries emerges indicating spontaneous-symmetry breaking (SSB) of $Z_2$ symmetry. From the lattice-gauge-theory viewpoint, this SSB is a signal of a transition to Higgs phase with symmetry protected topological order. We numerically elucidate the properties of this phase transition in detail, especially its criticality, and give a physical picture using non-local gauge-invariant symmetry operators. Phase transition in the bulk is also studied and its relationship to the boundary transition is discussed. |
| title | Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model |
| topic | Statistical Mechanics Disordered Systems and Neural Networks High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2311.16651 |