Exactly solvable lattice Hamiltonians and gravitational anomalies

Journal Article · 02 May 2023 · SciPost Physics

DOI: https://doi.org/10.21468/scipostphys.14.5.089 · OSTI ID:1972252

Chen, Yu-An ^[1]; Hsin, Po-Shen ^[2]

---

1. California Institute of Technology (CalTech), Pasadena, CA (United States); Univ. of Maryland, College Park, MD (United States)
2. California Institute of Technology (CalTech), Pasadena, CA (United States); Mani L. Bhaumik Institute for Theoretical Physics, Los Angeles, CA (United States)

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.

• Research Organization: California Institute of Technology (CalTech), Pasadena, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; USDOE
• Grant/Contract Number: SC0011632
• OSTI ID: 1972252
• Alternate ID(s): OSTI ID: 2420116
• Journal Information: SciPost Physics, Vol. 14, Issue 5; ISSN 2542-4653
• Publisher: SciPost FoundationCopyright Statement
• Country of Publication: United States
• Language: English