SU(2) gauge symmetry of the large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi></mml:math>limit of the Hubbard model

Affleck, Ian; Zou, Zheguang; Hsu, T. C.; Anderson, Philip W.

doi:10.1103/physrevb.38.745

Cited by 445 publications

(384 citation statements)

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“…The A phase is topologically trivial and gapped. It is the strong-coupling limit of SU(2) like the antiferromagnetic Heisenberg model [26] and can be explained as the strong paring phase in the p wave sence [21]. After perturbed by an external magentic field, the B phase is gapped and has a non-zero spectral Chern number and then is topologically non-trivial citeki.…”

Section: Kitaev Modelmentioning

confidence: 99%

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

2008

Nuclear Physics B

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We construct an exactly soluble spin-1 2 model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating phase. The B phase may be either gapped or gapless determined by the generalized inversion symmetry is broken or not. The gapped B is the weak pairing phase described by either the Moore-Read Pfaffian state of the spinless fermions or anti-Pfaffian state of holes depending on the sign of the next nearest neighbor hopping amplitude. A phase transition between Pfaffian and anti-Pfaffian states are found in the gapped B phase. Furthermore, we show that there is a hidden SU(2) gauge symmetry in our model. In the gapped B phase, the ground state has a non-trivial topological number, the spectral first Chern number or the chiral central charge, which reflects the chiral anomaly of the edge state. We proved that the topological number is identified to the reduced eta-invariant and this anomaly may be cancelled by a bulk Wess-Zumino term of SO(3) group through an index theorem in 2+1 dimensions.

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Section: Kitaev Modelmentioning

confidence: 99%

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

2008

Nuclear Physics B

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“…In the next section, we shall study the Heisenberg model in different representations and shall construct a mixed path-integral representation which restored particle-hole symmetry, and the internal symmetry group becomes "almost" a gauge symmetry. 8 The mixed representation is studied in Sec. IV where a distinct mean-field theory is proposed which recovers Haldane conjecture at 1D for the Heisenberg model.…”

Section: ͑1͒mentioning

confidence: 99%

“…9 and introduce different fermion operators for different S z states. We find that for half-odd-integer spins, the spin operator thus constructed is invariant under a SU͑2͒ transformations, 8 i.e., the symmetry group is SU͑2͒ group whereas for integer spins the symmetry group is U͑1͒¯Z 2 . Fermionic path-integral formulations for spin systems with arbitrary spin S can then be formulated and the corresponding mean-field theories can be studied.…”

mentioning

confidence: 99%

“…Following Affleck et al, 8 To examine whether C is really a spinor, we construct a spin singlet state for two spins at site i and j,…”

Section: ͑1͒mentioning

confidence: 99%

“…Up to now, the fermionic approach is mainly restricted to S = 1 2 spin systems. 6,8 Because of the Pauli exclusion principle, we cannot put more than two spin up or down fermions on a site to form S Ͼ 1 2 objects as in bosonic approach. One way out is to introduce more species of fermions.…”

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confidence: 99%

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Fermionic theory for quantum antiferromagnets with spinS>12

Liu

Zhou

2010

Phys. Rev. B

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The fermion representation for S = 1 2 spins is generalized to spins with arbitrary magnitudes. The symmetry properties of the representation is analyzed where we find that the particle-hole symmetry in the spinon Hilbert space of S = 1 2 fermion representation is absent for S Ͼ 1 2 . As a result, different path-integral representations and mean-field theories can be formulated for spin models. In particular, we construct a Lagrangian with restored particle-hole symmetry, and apply the corresponding mean-field theory to one-dimensional ͑1D͒ S = 1 and S =3/ 2 antiferromagnetic ͑AFM͒ Heisenberg models, with results that agree with Haldane's conjecture. For a S = 1 open chain, we show that Majorana fermion edge states exist in our mean-field theory. The generalization to spins with arbitrary magnitude S is discussed. Our approach can be applied to higher dimensional spin systems. As an example, we study the geometrically frustrated S = 1 AFM on triangular lattice. Two spin liquids with different pairing symmetries are discussed: the gapped p x + ip y -wave spin liquid and the gapless f-wave spin liquid. We compare our mean-field result with the experiment on NiGa 2 S 4 , which remains disordered at low temperature and was proposed to be in a spin-liquid state. Our fermionic mean-field theory provide a framework to study S Ͼ 1 2 spin liquids with fermionic spinon excitations.

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