Construction of bosonic symmetry-protected-trivial states and their topological invariants via<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mo>×</mml:mo><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>∞</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>nonlinear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi></mml:math>models

Wen, Xiao-Gang

doi:10.1103/physrevb.91.205101

Cited by 81 publications

(117 citation statements)

References 118 publications

(256 reference statements)

Supporting

Mentioning

114

Contrasting

Order By: Relevance

“…Another way to define E(d) is a specific subgroup of O(d) × Z4 given in [40]. 33 We compute the co/bordism group in whose bordism invariants are generated by three generators of mod 2 class:…”

Section: Enumeration Of Gauge Theories From Dynamically Gauging 4d Sptsmentioning

confidence: 99%

Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory

2019

View full text Add to dashboard Cite

We explore various 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at θ = π (SU(2) θ=π YM), by turning on the background fields for both the time-reversal (i.e., on unorientable manifolds) and the 1-form center global symmetry. We find Four Siblings of SU(2) θ=π YM with distinct couplings to background fields, labeled by (K 1 , K 2 ): K 1 = 0, 1 specifies Kramers singlet/doublet Wilson line and new mixed higher 't Hooft anomalies; K 2 = 0, 1 specifies boson/fermionic Wilson line and a new Wess-Zumino-Witten-like counterterm. Higher anomalies indicate that to realize all higher nglobal symmetries locally on n-simplices, the 4d theory becomes a boundary of a 5d higher-symmetryprotected topological state (SPTs, as an invertible topological quantum field theory in math, or as a 5d higher-symmetric interacting topological superconductor in condensed matter). Via Weyl's gauge principle, by dynamically gauging the 1-form symmetry, we transform a 5d bulk SRE SPTs into an LRE symmetry-enriched topologically ordered state (SETs); thus we obtain the 4d SO(3) θ=π YM-5d LREhigher-SETs coupled system with dynamical higher-form gauge fields. We further derive new exotic anyonic statistics of extended objects such as 2-worldsheet of strings and 3-worldvolume of branes, physically characterizing the 5d SETs. We discover triple and quadruple link invariants potentially associated with the underlying 5d higher-gauge TQFTs, hinting a new intrinsic relation between nonsupersymmetric 4d pure YM and topological links in 5d. We provide 4d-5d lattice simplicial complex regularizations and bridge to 4d SU(2) and SO(3)-gauged quantum spin liquids as 3+1 dimensional realizations.

show abstract

Section: Enumeration Of Gauge Theories From Dynamically Gauging 4d Sptsmentioning

confidence: 99%

Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory

2019

View full text Add to dashboard Cite

show abstract

“…We allow only the fluctuations of the higher Z 2 -flux, and try to use them to drive a phase transition. Such a system has the Z 2 k-symmetry (56). Using the anomaly matching condition, we find that the phase transition can nerve produce the confined phase with topological order, when m = 1.…”

Section: Higher Anomaly and Phase Transitionmentioning

confidence: 91%

“…where dâ Z2 k describes the higher Z 2 -flux on the boundary. The above model has a Z 2 k-symmetry (56). The Z 2 ksymmetry is anomalous for m = 1 and anomaly-free for m = 0.…”

Section: The Bulk Theory and The Boundary Theorymentioning

confidence: 93%

See 1 more Smart Citation

Emergent anomalous higher symmetries from topological order and from dynamical electromagnetic field in condensed matter systems

Wen

2019

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

IX. Lattice models that realize higher SPT phasessystematic constructions 21 A. Models realizing bosonic SPT phases 21 B. Models realizing bosonic higher SPT phases 21 C. More general bosonic hSPT phases 22 D. Fermionic hSPT phases 23 E. The usefulness of hSPT phases 24 X. Lattice models that realize topological orders with higher symmetry 24 A. The first type of constructions 24 B. The second type of constructions 24 XI. EM condensed matter systems and their higher symmetry 25 A. Space-time complex, cochains, and cocycles 27 B. Path integral and Hamiltonian 30 References 31 arXiv:1812.02517v5 [cond-mat.str-el] 21 Apr 2019 R/Z J− a R/Z J ) e i 2π B 3 I≤J k IJ a R/Z I ( da R/Z J − da R/Z J )− da R/Z I a R/Z J e − B 3 I R/Z J − da R/Z J )− da R/Z I a R/Z J = e i 2π M 4 k IJ ( da R/Z I − da R/Z I )( da R/Z J − da R/Z J R/Z I )( da R/Z J − da R/Z J ) = e − i 2π M 4 I,J K IJ a R/Z I d da R/Z J , (81) where d da R/Z J can be viewed as the Poincaré dual of the worldline of the U (1) monoples. This implies that the effect of the topological term e i 2π M 4 I≤J k IJ ( da R/Z I − da R/Z I )( da R/Z J − da R/Z J

show abstract

“…A set of wavefunctions which are all mutually equivalent in this sense constitutes an SPT phase. (Note that in this paper, the theoretical framework covers only pure SPTs, which excludes systems with mixed gauge-gravity anomalies and surface intrinsic topological order [50][51][52][53]. )…”

Section: Projective Representations and 1d Spt Phasesmentioning

confidence: 99%

Interacting symmetry-protected topological phases out of equilibrium

McGinley

Cooper

2019

Phys. Rev. Research

View full text Add to dashboard Cite

We show that the dynamics of generic isolated quantum systems admits a topological classification which captures universal features of many-body wavefunctions far from equilibrium. Specifically, we consider two short-ranged entangled wavefunctions to be topologically equivalent if they can be interconverted via finite-time unitary evolution governed by a symmetry-respecting Hamiltonian. By analogy to the classification of symmetry-protected topological phases, we consider the projective action of the symmetry group on a time-evolved wavefunction to explicitly calculate this nonequilibrium topological classification, focussing on systems of strongly interacting bosons in a variety of symmetry classes. The physical consequences of the non-equilibrium classification are described. In particular, we show that the characteristic zero-frequency spectroscopic peaks associated with topologically protected edge modes will be broadened by external noise only when the system is trivial in the non-equilibrium classification. arXiv:1908.06875v1 [cond-mat.str-el]

show abstract

Construction of bosonic symmetry-protected-trivial states and their topological invariants viaG×SO(∞)nonlinearσmodels

Cited by 81 publications

References 118 publications

Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory

Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory

Emergent anomalous higher symmetries from topological order and from dynamical electromagnetic field in condensed matter systems

Interacting symmetry-protected topological phases out of equilibrium

Contact Info

Product

Resources

About