scholarly journals Topological invariants for gauge theories and symmetry-protected topological phases

2015 ◽  
Vol 91 (16) ◽  
Author(s):  
Chenjie Wang ◽  
Michael Levin
Keyword(s):  
Gauge Theories ◽  
Topological Invariants ◽  
Topological Phases ◽  
Symmetry Protected

scholarly journals Many-body topological invariants from randomized measurements in synthetic quantum matter

2020 ◽  
Vol 6 (15) ◽  
pp. eaaz3666 ◽  
Author(s):  
Andreas Elben ◽  
Jinlong Yu ◽  
Guanyu Zhu ◽  
Mohammad Hafezi ◽  
Frank Pollmann ◽  
...  
Keyword(s):  
Body Wave ◽  
Complete Classification ◽  
Theoretical Description ◽  
Spin Model ◽  
Topological Invariants ◽  
Topological Phases ◽  
Many Body ◽  
Topological Quantum ◽  
The Many ◽  
Symmetry Protected

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

scholarly journals Floquet Second-Order Topological Phases in Momentum Space

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1170
Author(s):  
Longwen Zhou
Keyword(s):  
Momentum Space ◽  
Bound States ◽  
Second Order ◽  
Large Integer ◽  
Open Boundary ◽  
Topological Invariants ◽  
Topological Phases ◽  
Open Boundary Conditions ◽  
Kicked Rotor ◽  
Symmetry Protected

Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.

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 Non-Abelian three-loop braiding statistics for 3D fermionic topological phases

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jing-Ren Zhou ◽  
Qing-Rui Wang ◽  
Chenjie Wang ◽  
Zheng-Cheng Gu
Keyword(s):  
Crucial Role ◽  
Gauge Theories ◽  
The Other ◽  
Topological Phases ◽  
Fractional Statistics ◽  
Fermion Systems ◽  
Topological Quantum ◽  
Fermionic Systems ◽  
Topological Quantum Computation ◽  
Symmetry Protected

AbstractFractional 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 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 discover 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). On the other hand, 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.

scholarly journals Symmetry-protected topological phases in lattice gauge theories: Topological QED2

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
G. Magnifico ◽  
D. Vodola ◽  
E. Ercolessi ◽  
S. P. Kumar ◽  
M. Müller ◽  
...  
Keyword(s):  
Gauge Theories ◽  
Topological Phases ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Symmetry Protected
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