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Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
by Yu-An Chen, Po-Shen Hsin
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Submission summary
| Authors (as registered SciPost users): | Yu-An Chen · Po-Shen Hsin |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2110.14644v3 (pdf) |
| Date accepted: | 2023-02-13 |
| Date submitted: | 2022-12-23 02:50 |
| Submitted by: | Hsin, Po-Shen |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary $\mathbb{Z}_2$ topological order with fermionic particle and fermionic loop excitations that have mutual $\pi$ statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary $\mathbb{Z}_2$ symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.
List of changes
- fixed the typos as requested in the first (earlier) referee report
- added a paragraph on p12 before section 2.2 as requested in the first referee report, which is the same explanation in the author reply to the first report that the referee agreed upon.
- added a paragraph on p33 as requested by the second (more recent) referee in the second report.
Published as SciPost Phys. 14, 089 (2023)