Haldane–Shastry spin chains of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>B</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:math> type

Enciso, Alberto; Finkel, Federico; González‐López, A.; Rodrı́guez, Miguel Á.

doi:10.1016/j.nuclphysb.2004.10.064

Cited by 45 publications

(135 citation statements)

References 34 publications

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“…It also accounts for the greater complexity of the partition function of the associated chain of D N type (which we have also computed in closed form by means of the freezing trick) compared to its BC N version studied in Ref. [42].…”

Section: Introductionmentioning

confidence: 93%

“…Our starting point will be a brief review of the su(m) spin Sutherland model of BC N type, with Hamiltonian [39,42] …”

Section: The Modelsmentioning

confidence: 99%

“…The spectrum of the spin model (1) was computed in Ref. [42] by constructing a suitable basis of its Hilbert space in which the Hamiltonian H (B) is represented by a triangular matrix. Applying the so-called freezing trick [7] to the Hamiltonian (1) with b = βa and b = β a one obtains the su(m) Haldane-Shastry (antiferromagnetic) spin chain of BC N type, whose Hamiltonian we shall take as…”

Section: The Modelsmentioning

confidence: 99%

“…, N, obtained from their BC N counterparts in Ref. [42] by setting b = b = 0. Note that the set C is invariant under all the generators K ij , K i of the Weyl group of BC N type W (B) , and hence the operator J k is actually defined in a suitable dense subspace of L 2 (C).…”

Section: Triangularization Of Hmentioning

confidence: 99%

“…Indeed, Olshanetsky and Perelomov established the existence of an underlying A N root system structure for both the spinless Calogero and Sutherland models, and constructed generalizations thereof associated with any (extended) root system [4]. Spin generalizations of the BC N Calogero and Sutherland models have also been proposed, and various properties of the related lattice models of HS type have been studied with the help of the freezing trick [38][39][40][41][42][43]. Among the other classical root systems, the exceptional ones are comparatively less interesting, since their associated models consist of at most 8 particles.…”

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: 93%

“…Our starting point will be a brief review of the su(m) spin Sutherland model of BC N type, with Hamiltonian [39,42] …”

Section: The Modelsmentioning

confidence: 99%

Section: The Modelsmentioning

confidence: 99%

Section: Triangularization Of Hmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The spin Sutherland model of type and its associated spin chain

2011

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On the Thermodynamics of Supersymmetric Haldane–Shastry Spin Chains

Finkel

González‐López

León

et al. 2019

Springer Proceedings in Physics

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A novel class of translationally invariant spin chains with long-range interactions

Basu-Mallick

Finkel

González‐López

2020

J. High Energ. Phys.

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We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under "twisted" translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and su(m/2) motifs when the number m of internal degrees of freedom is even. This implies that the even m model is invariant under the direct sum of the Yangians Y (gl(1|1)) and Y (gl(0|m/2)). We also analyze several statistical properties of the new chain's spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd m.

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Haldane–Shastry spin chains of BCN type

Cited by 45 publications

References 34 publications

The spin Sutherland model of type and its associated spin chain

The spin Sutherland model of type and its associated spin chain

On the Thermodynamics of Supersymmetric Haldane–Shastry Spin Chains

A novel class of translationally invariant spin chains with long-range interactions

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