Exact solution of an<i>S</i>=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions

Shastry, B. Sriram

doi:10.1103/physrevlett.60.639

Cited by 735 publications

(575 citation statements)

References 12 publications

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“…The particles in this so-called Sutherland model move on a circle, with two-body interactions proportional to the inverse square of their chord distances. In a parallel development, Haldane and Shastry found an exactly solvable quantum spin- 1 2 chain with long-range interactions [5,6]. The lattice sites of this su(2) Haldane-Shastry (HS) spin chain are equally spaced on a circle, all spins interacting with one another through pairwise exchange interactions inversely proportional to the square of their chord distances.…”

Section: Introductionmentioning

confidence: 99%

“…Recent studies have revealed that exactly solvable and integrable one-dimensional quantum many body systems with long-range interactions [1][2][3][4][5][6][7][8] are closely connected with a wide range of topics in modern physics as well as mathematics. In particular, this type of exactly solv-able systems have appeared as prototype models of various condensed matter systems exhibiting generalized exclusion statistics [8][9][10], quantum Hall effect [11] and quantum electric transport phenomena [12,13].…”

Section: Introductionmentioning

confidence: 99%

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The spin Sutherland model of type and its associated spin chain

2011

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In this paper we study the su(m) spin Sutherland (trigonometric) model of D N type and its related spin chain of Haldane-Shastry type obtained by means of Polychronakos's freezing trick. As in the rational case recently studied by the authors, we show that these are new models, whose properties cannot be simply deduced from those of their well-known BC N counterparts by taking a suitable limit. We identify the Weyl-invariant extended configuration space of the spin dynamical model, which turns out to be the N-dimensional generalization of a rhombic dodecahedron. This is in fact one of the reasons underlying the greater complexity of the models studied in this paper in comparison with both their rational and BC N counterparts. By constructing a non-orthogonal basis of the Hilbert space of the spin dynamical model on which its Hamiltonian acts triangularly, we compute its spectrum in closed form. Using this result and applying the freezing trick, we derive an exact expression for the partition function of the associated Haldane-Shastry spin chain of D N type.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The spin Sutherland model of type and its associated spin chain

2011

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“…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%

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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“…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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Exact solution of anS=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions

Cited by 735 publications

References 12 publications

The spin Sutherland model of type and its associated spin chain

The spin Sutherland model of type and its associated 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

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