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Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies

Chen, Yu-An and Hsin, Po-Shen (2021) Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies. . (Unpublished)

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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 ℤ₂ topological order with fermionic particle and fermionic loop excitations that have mutual π 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 ℤ₂ symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Chen, Yu-An0000-0002-8810-9355
Hsin, Po-Shen0000-0002-4764-1476
Additional Information:We thank Anton Kapustin for his discussion and participation at the early stage of the project. We thank Alexei Kitaev, Ryan Thorngren, and Ryohei Kobayashi for the discussion. We thank Maissam Barkeshli, Xie Chen, Meng Cheng, Tyler Ellison, Anton Kapustin, Alexei Kitaev, Shu-Heng Shao, Wilbur Shirley, Nathanan Tantivasadakarn, and Cenke Xu for comments on a draft. The work of P.-S. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. Y.-A. C is supported by the JQI fellowship at the University of Maryland.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Joint Quantum Institute (JQI)UNSPECIFIED
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Record Number:CaltechAUTHORS:20211130-215749950
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112113
Deposited By: George Porter
Deposited On:30 Nov 2021 23:49
Last Modified:30 Nov 2021 23:49

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