Non-Abelian Holonomy of BCS and SDW Quasiparticles

Demler, Eugene; Zhang, Shou-Cheng

doi:10.1006/aphy.1998.5866

Cited by 44 publications

(79 citation statements)

References 41 publications

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“…However, this quaternionic representation is not suitable for our purpose since the objects we would like to transform to the Clifford algebra are complex 4 × 4 Hermitian matrices. The required Dirac-like matrices having positive signature (+, +, +, +, +) were given in [11,12]. As we shall see, the following set of Γ i matrices yields real coefficients at basis vectors e i , as required by Cl 5 after the decomposition of the Hamiltonian and hole spin matrices,…”

Section: Representation Of Basis Vectorsmentioning

confidence: 99%

Valence Band of Cubic Semiconductors from Viewpoint of Clifford Algebra

Dargys¹

2009

Acta Phys. Pol. A

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In this paper the properties of semiconductors having cubic symmetry are considered in a real multidimensional Euclidean space within the formalism of multivector Clifford algebra rather than, usually used for this purpose, complex Hilbert space. In particular, it is demonstrated how the valence band energy spectrum and spin properties may be calculated within Cl 5 Clifford algebra and SO(5) symmetry group related with it.

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Section: Representation Of Basis Vectorsmentioning

confidence: 99%

Valence Band of Cubic Semiconductors from Viewpoint of Clifford Algebra

Dargys¹

2009

Acta Phys. Pol. A

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“…The bosonic version of our formalism actually realizes the beautiful second Hopf map. One way to study the O(5) Nonlinear Sigma model is to decompose the O(5) vector in terms of bosonic SU(4) spinors as n a = Φ † Γ a Φ, Γ a with a = 1, 2, · · · 5 are five Gamma matrices, and Φ is a four component complex bosonic spinor 32 . After this decomposition there is a redundant SU (2) (8) vector forms a manifold of seven dimensional sphere S 7 , and the theory describes a mapping: S 7 /S 3 → S 4 , the S 3 manifold is exactly the SU(2) group manifold, and S 4 is the manifold formed by O (5) vector.…”

Section: Spin Liquid With Su(2) Gauge Field a The Majorana Fermmentioning

confidence: 99%

Renormalization group studies on four-fermion interaction instabilities on algebraic spin liquids

2008

Phys. Rev. B

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We study the instabilities caused by four fermion interactions on algebraic spin liquids. Renormalization group (RG) is used for three types of previously proposed spin liquids on the square lattice: the staggered flux state of SU(2) spin system, the π−flux state of SU(4) spin system, and the π−flux state of SU(2) spin system. The low energy field theories of the first two types of spin liquids are QED3 with emerged SU(4) and SU(8) flavor symmetries , the low energy theory of the π−flux SU(2) spin liquid is the QCD3 with SU(2) gauge field and emergent Sp(4) (SO (5)) flavor symmetry. Suitable large-N generalization of these spin liquids are discussed, and a systematic 1/N expansion is applied to the RG calculations. The most relevant four fermion perturbations are identified, and the possible phases driven by relevant perturbations are discussed.

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“…The eigenstate of P is given by 11) where N N = 2r(r + x 3 ) is a normalization factor, which ensures v|v = 1. The Berry phase is defined [58] as ǫ ab x a dx b , (B 13) which is singular at x 3 = −r. The field strength of the Dirac monopole is calculated as…”

Section: B Hopf Map and Berry Phasementioning

confidence: 99%

Nonabelian gauge field and dual description of fuzzy sphere

Kimura

2004

J. High Energy Phys.

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In matrix models, higher dimensional D-branes are obtained by imposing a noncommutative relation to coordinates of lower dimensional D-branes. On the other hand, a dual description of this noncommutative space is provided by higher dimensional D-branes with gauge fields. Fuzzy spheres can appear as a configuration of lower dimensional D-branes in a constant R-R field strength background. In this paper, we consider a dual description of higher dimensional fuzzy spheres by introducing nonabelian gauge fields on higher dimensional spherical D-branes. By using the Born-Infeld action, we show that a fuzzy 2k-sphere and spherical D2k-branes with a nonabelian gauge field whose Chern character is nontrivial are the same objects when n is large. We discuss a relationship between the noncommutative geometry and nonabelian gauge fields. Nonabelian gauge fields are represented by noncommutative matrices including the coordinate dependence. A similarity to the quantum Hall system is also studied.

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Non-Abelian Holonomy of BCS and SDW Quasiparticles

Cited by 44 publications

References 41 publications

Valence Band of Cubic Semiconductors from Viewpoint of Clifford Algebra

Valence Band of Cubic Semiconductors from Viewpoint of Clifford Algebra

Renormalization group studies on four-fermion interaction instabilities on algebraic spin liquids

Nonabelian gauge field and dual description of fuzzy sphere

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