Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions

Journal Article · Wed May 30 00:00:00 EDT 2018 · Progress of Theoretical and Experimental Physics

DOI:https://doi.org/10.1093/ptep/pty051· OSTI ID:1499898

Wang, Juven ^[1]; Ohmori, Kantaro ^[2]; Putrov, Pavel ^[2]; Zheng, Yunqin ^[3]; Wan, Zheyan ^[4]; Guo, Meng ^[5]; Lin, Hai ^[6]; Gao, Peng ^[5]; Yau, Shing-Tung ^[6]

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1. Institute for Advanced Study, Princeton, NJ (United States); Harvard Univ., Cambridge, MA (United States)
2. Institute for Advanced Study, Princeton, NJ (United States)
3. Princeton Univ., NJ (United States)
4. Univ. of Science and Technology of China, Hefei (China)
5. Harvard Univ., Cambridge, MA (United States)
6. Harvard Univ., Cambridge, MA (United States); Tsinghua Univ., Beijing (China)

Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the partition function on various manifolds and ground state degeneracy (GSD), mainly based on continuum/cochain topological quantum field theories (TQFTs), in any dimension. This information can be related to the counting of extended operators of bosonic/fermionic TQFTs. On the lattice scale, anyonic particles/strings live at the ends of line/surface operators. Certain systems in different dimensions are related to each other through dimensional reduction schemes, analogous to (de)categorification. Examples include spin TQFTs derived from gauging the interacting fermionic symmetry-protected topological states (with fermion $$\mathbb Z$$$$f\atop{2}$$) of parity symmetry groups $$\mathbb Z{_4}$$×$$\mathbb Z{_2}$$ and ($$\mathbb Z{_4}$$)² in 3+1D, also $$\mathbb Z{_2}$$ and ($$\mathbb Z{_2}$$)² in 2+1D. Gauging the last three cases begets non-Abelian spin TQFTs (fermionic topological order). We consider situations where a TQFT lives on (1) a closed spacetime or (2) a spacetime with a boundary, such that the bulk and boundary are fully gapped and short- or long-range entangled (SRE/LRE). Anyonic excitations can be deconfined on the boundary. We introduce new exotic topological interfaces on which neither particle nor string excitations alone condense, but only fuzzy-composite objects of extended operators can end (e.g., a string-like composite object formed by a set of particles can end on a special 2+1D boundary of 3+1D bulk). We explore the relations between group extension constructions and partially breaking constructions (e.g., 0-form/higher-form/“composite” breaking) of topological boundaries, after gauging. We comment on the implications of entanglement entropy for some such LRE systems.

• Research Organization: Institute for Advanced Study, Princeton, NJ (United States)
• Sponsoring Organization: USDOE; National Science Foundation (NSF); US–Israel Binational Science Foundation
• Grant/Contract Number: SC0009988; PHY-1314311; 11431010; 11571329; PHY-1306313; PHY-0937443; DMS-1308244; DMS-0804454; DMS-1159412
• OSTI ID: 1499898
• Journal Information: Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 5; ISSN 2050-3911
• Publisher: Physical Society of Japan
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS