scholarly journals Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems

2020 ◽  
Vol 10 (3) ◽  
Author(s):  
Qing-Rui Wang ◽  
Zheng-Cheng Gu
Keyword(s):  
Topological Phases ◽  
Fermion Systems ◽  
Symmetry Protected

scholarly journals Why are fractional charges of orientifolds compatible with Dirac quantization?

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Yuji Tachikawa ◽  
Kazuya Yonekura
Keyword(s):  
String Theory ◽  
Double Cover ◽  
Topological Phases ◽  
Duality Group ◽  
Dirac Quantization ◽  
Type Iib String Theory ◽  
Symmetry Protected

Orientifold pp-planes with p\le 4p≤4 have fractional Dpp-charges, and therefore appear inconsistent with Dirac quantization with respect to D(6{-}p)(6−p)-branes. We explain in detail how this issue is resolved by taking into account the anomaly of the worldvolume fermions using the \etaη invariants. We also point out relationships to the classification of interacting fermionic symmetry protected topological phases. In an appendix, we point out that the duality group of type IIB string theory is the  pin^++ version of the double cover of GL(2,Z).

scholarly journals Non-Abelian Three-Loop Braiding Statistics for 3D Fermionic Topological Phases

2021 ◽  
Author(s):  
Jin-Ren Zhou ◽  
Qing-Rui Wang ◽  
Chenjie Wang ◽  
Zheng-Cheng Gu
Keyword(s):  
Gauge Theories ◽  
Topological Phases ◽  
Reduction Scheme ◽  
Physical Origin ◽  
Fractional Statistics ◽  
Fermion Systems ◽  
Topological Quantum ◽  
Fermionic Systems ◽  
Topological Quantum Computation ◽  
Symmetry Protected

Abstract Fractional statistics is one of the most intriguing features of topological phases in 2D. In particular, the so-called non-Abelian statistics plays a crucial role towards realizing universal topological quantum computation. Recently, the study of topological phases has been extended to 3D and it has been proposed that loop-like extensive objects can also carry fractional statistics. In this work, we systematically study the so-called three-loop braiding statistics for 3D interacting fermion systems. Most surprisingly, we discovered new types of non-Abelian three-loop braiding statistics that can only be realized in fermionic systems (or equivalently bosonic systems with emergent fermionic particles). The simplest example of such non-Abelian braiding statistics can be realized in interacting fermionic systems with a gauge group Z2 × Z8 or Z4 × Z4, and the physical origin of non-Abelian statistics can be viewed as attaching an open Majorana chain onto a pair of linked loops, which will be naturally reduced to the well known Ising non-Abelian anyons via the standard dimension reduction scheme. Moreover, due to the correspondence between gauge theories with fermionic particles and classifying fermionic symmetry-protected topological (FSPT) phases with unitary symmetries, our study also gives rise to an alternative way to classify FSPT phases. We further compare the classification results for FSPT phases with arbitrary Abelian unitary total symmetry Gf and find systematical agreement with previous studies using other methods. We believe that the proposed framework of understanding three-loop braiding statistics (including both Abelian and non-Abelian cases) in interacting fermion systems applies for generic fermonic topological phases in 3D.

scholarly journals The classification of symmetry protected topological phases of one-dimensional fermion systems

2021 ◽  
Vol 9 ◽  
Author(s):  
Chris Bourne ◽  
Yoshiko Ogata
Keyword(s):  
Site Symmetry ◽  
Matrix Product ◽  
Translation Invariant ◽  
Fermion Systems ◽  
A Finite Group ◽  
Reduced Density ◽  
Symmetry Protected ◽  
Wall Group ◽  
Uniformly Bounded

Abstract We introduce an index for symmetry-protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group G. This index takes values in $\mathbb {Z}_2 \times H^1(G,\mathbb {Z}_2) \times H^2(G, U(1)_{\mathfrak {p}})$ with a generalised Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry.

scholarly journals Classification of subsystem symmetry-protected topological phases

2018 ◽  
Vol 98 (23) ◽  
Author(s):  
Trithep Devakul ◽  
Dominic J. Williamson ◽  
Yizhi You
Keyword(s):  
Topological Phases ◽  
Symmetry Protected
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