期刊
PHYSICAL REVIEW B
卷 83, 期 7, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.83.075103
关键词
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资金
- Institute for Quantum Information under National Science Foundation [PHY-0803371]
- Direct For Mathematical & Physical Scien
- Division Of Physics [0803371] Funding Source: National Science Foundation
In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the time-reversal-invariant Majorana chain (BDI symmetry class). While the band classification yields an integer topological index k, it is known that phases characterized by values of k in the same equivalence class modulo 8 can be adiabatically transformed one to another by adding suitable interaction terms. Here we show that the eight equivalence classes are distinct and exhaustive, and provide a physical interpretation for the interacting invariant modulo 8. The different phases realize different Altland-Zirnbauer classes of the reduced density matrix for an entanglement bipartition into two half chains. We generalize these results to the classification of all one-dimensional gapped phases of fermionic systems with possible antiunitary symmetries, utilizing the algebraic framework of central extensions. We use matrix product state methods to prove our results.
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