Erratum: Spin-singlet wave function for the half-integral quantum Hall effect [Phys. Rev. Lett. 60, 956 (1988)]

Haldane, F. D. M.; Rezayi, E. H.

doi:10.1103/physrevlett.60.1886

Cited by 496 publications

(887 citation statements)

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“…Such supersymmetric spin chains play an important role in describing some correlated systems of condensed matter physics, where holes moving in the dynamical background of spin behave as bosons and spin- 1 2 electrons behave as fermions [13]. It is worth noting that the supersymmetric SU(m|n) HS spin chain exhibits Y (gl (m|n) ) super-Yangian symmetry [3], which is also the quantum group symmetry of supersymmetric SU(m|n) Polychronakos spin chain [14,15].…”

Section: Introductionmentioning

confidence: 99%

“…Study of such HS spin- 1 2 chain with long-range interaction was originally motivated from the fact that the exact ground state wavefunction of this model coincides with the U → ∞ limit of Gutzwiller's variational wave function for the Hubbard model, and also with the one-dimensional version of the resonating valence bond state proposed by Anderson [1,2]. Remarkably, HS spin chain can be explicitly solved in much greater detail than integrable spin chains with short-range interactions, has a Yangian quantum group symmetry and interestingly shares many of the characteristics of an ideal gas, but with fractional statistics [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Exact partition function of supersymmetric Haldane–Shastry spin chain

Basu-Mallick

Bondyopadhaya

2006

Nuclear Physics B

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By taking the freezing limit of a spin Calogero-Sutherland model containing 'anyon like' representation of the permutation algebra, we derive the exact partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain. This partition function allows us to study global properties of the spectrum like level density distribution and nearest neighbour spacing distribution. It is found that, for supersymmetric HS spin chains with large number of lattice sites, continuous part of the energy level density obeys Gaussian distribution with a high degree of accuracy. The mean value and standard deviation of such Gaussian distribution can be calculated exactly. We also conjecture that the partition function of supersymmetric HS spin chain satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact partition function of supersymmetric Haldane–Shastry spin chain

Basu-Mallick

Bondyopadhaya

2006

Nuclear Physics B

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“…In one dimension, many-body Hamiltonians with pair-potentials of the form 1/r 2 (or its periodic equivalent 1/sin 2 r), where r = (u a −u b ), have exact ground state wave functions of the Jastrow form [2][3][4][5]. It has been…”

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confidence: 99%

A cross-over from Fermi-liquid to non-Fermi-liquid behaviour in a solvable one-dimensional model

Chen¹,

Muttalib²

1994

J. Phys.: Condens. Matter

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We consider a quantum many-body problem in one-dimension described by a Jastrow type wavefunction, characterized by an exponent λ and a parameter γ. In the limit γ = 0 the model becomes identical to the well known 1/r 2 pair-potential model; γ is shown to be related to the strength of a many body correction to the 1/r 2 interaction. Exact results for the one-particle density matrix are obtained for all γ when λ = 1, for which the 1/r 2 part of the interaction vanishes. We show that with increasing γ, the Fermi liquid state (at γ = 0) crosses over to distinct γ-dependent non-Fermi liquid states, characterized by effective "temperatures".

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“…Substituting (A.7) in (A.5) we obtain the effective potential in its final form as 8) which can be shown easily to coincide with (27).…”

Section: Discussionmentioning

confidence: 99%

“…The CM and its various descendants continue to draw considerable interest due to their diverse physical applications in systems such as random matrices [7], fractional statistics [8]- [11], gravity and black hole physics [12,13], spin chains [14,15], solitons [16]- [20], 2D Yang-Mills theory [21,22], lowest Landau level (LLL) anyon models [23,24], Chern-Simons matrix model [25]- [27], Laughlin-Hall states [28]- [30], and unoriented superstrings in two dimensions [31].…”

Section: Introductionmentioning

confidence: 99%

Collective field formulation of the multi-species Calogero model and its duality symmetries

2007

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We study the collective field formulation of a restricted form of the multispecies Calogero model, in which the three-body interactions are set to zero. We show that the resulting collective field theory is invariant under certain duality transformations, which interchange, among other things, particles and antiparticles, and thus generalize the well-known strong-weak coupling duality symmetry of the ordinary Calogero model. We identify all these dualities, which form an Abelian group, and study their consequences. We also study the ground state and small fluctuations around it in detail, starting with the two-species model, and then generalizing to an arbitrary number of species.

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Erratum: Spin-singlet wave function for the half-integral quantum Hall effect [Phys. Rev. Lett. 60, 956 (1988)]

Cited by 496 publications

References 0 publications

Exact partition function of supersymmetric Haldane–Shastry spin chain

Exact partition function of supersymmetric Haldane–Shastry spin chain

A cross-over from Fermi-liquid to non-Fermi-liquid behaviour in a solvable one-dimensional model

Collective field formulation of the multi-species Calogero model and its duality symmetries

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