期刊
PHYSICAL REVIEW B
卷 102, 期 12, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.102.125127
关键词
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资金
- NSF [PHY-1620541, OIA-1921199]
- Constance and Walter Burke Special Projects Fund in Quantum Information Science
- Quantum Alberta Initiative by the Government of Alberta
- Office of Research Advancement, SUNY Polytechnic Institute
- DOE [DE-SC0020343]
- Office of the Vice Provost for Research through its Emerging Areas of Research program
- U.S. Department of Energy (DOE) [DE-SC0020343] Funding Source: U.S. Department of Energy (DOE)
We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary space dimension, we establish three fundamental nogo theorems that prove the absence of parity switches, symmetry-protected-topological quantum phases, and localized bosonic zero modes under open boundary conditions. We then introduce a squaring, kernel-preserving map connecting no-ninteracting Hermitian theories of fermions and stable boson systems, which serves as a playground to reveal the role of topology in bosonic phases and their localized midgap boundary modes. Finally, we determine the symmetry classes inherited from the fermionic tenfold-way classification, unveiling an elegant threefold-way topological classification of noninteracting bosons. We illustrate our main findings in one- and two-dimensional bosonic lattice and field-theory models.
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