Quantum Orders in an Exact Soluble Model
Open accessAbstract
We find all the exact eigenstates and eigenvalues of a spin-$1/2$ model on square lattice: $H=16g\ensuremath{\sum}_{\mathbit{i}}{S}_{\mathbit{i}}^{y}{S}_{\mathbit{i}+\stackrel{^}{\mathbit{x}}}^{x}{S}_{\mathbit{i}+\stackrel{^}{\mathbit{x}}+\stackrel{^}{\mathbit{y}}}^{y}{S}_{\mathbit{i}+\stackrel{^}{\mathbit{y}}}^{x}$. We show that the ground states for $g<0$ and $g>0$ have different quantum orders described by $Z2A$ and $Z2B$ projective symmetry groups. The phase transition at $g=0$ represents a new kind of phase transition that changes quantum orders but not symmetry. Both the $Z2A$ and $Z2B$ states contain ${Z}_{2}$ lattice gauge theories at low energies. They have robust topologically degenerate ground states and gapless edge excitations.
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The ZXXZ variant of the surface code helps symmetrize the X- and Z-basis logical error rates.
“We also remove certain Hadamard gates to implement the ZXXZ variant of the surface code44,45, which helps symmetrize the X- and Z-basis logical error rates.”
From Suppressing quantum errors by scaling a surface code logical qubit (2023) · cites this paper as [44]
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- Authors
- Wen, X.-G.
- Affiliations
- Massachusetts Institute of Technology (US)
- Corresponding author
- Wen, Xiao-Gang
- ORCID
- Wen, Xiao-Gang
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2003-01-10
- Volume
- 90
- Issue
- 1
- Pages
- 016803-016803
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2045176588
- Cited by
- 422
- References
- 17
- Citations by year
- 2026: 13 · 2025: 23 · 2024: 28 · 2023: 78 · 2022: 26 · 2021: 16 · 2020: 30 · 2019: 19 · 2018: 15 · 2017: 20 · 2016: 9 · 2015: 12 · 2014: 15 · 2013: 18 · 2012: 14
- FWCI
- 4.65
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- quantum order, projective symmetry group, exact eigenstates, ground state degeneracy, Z2 lattice gauge theory, quantum phase transitions, topological order
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