Integrable spin chain with reflecting end

Yamamoto, Takashi; Tsuchiya, Osamu

doi:10.1088/0305-4470/29/14/021

Cited by 40 publications

(58 citation statements)

References 45 publications

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“…As mentioned above, this problem is equivalent to the triangularization of the extensionsH andH sc acting on their respective Hilbert spaces H ≡ Λ εε (L 2 (C (B) ) ⊗ Σ) and H sc ≡ Λ sc (L 2 (C (B) )), which can be carried out without difficulty with the help of Eq. (39).…”

Section: Triangularization Of H (B) and H (B)mentioning

confidence: 99%

“…Spin generalizations of the BC N Calogero-Sutherland model have been extensively studied in the last few years, and various properties of their related spin chains of HS type have been analyzed with the help of the freezing trick [37][38][39][40][41][42][43][44]. Among the other classical root systems, the exceptional ones are comparatively less interesting in this context, since their associated models consist of at most 8 particles.…”

Section: Introductionmentioning

confidence: 99%

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The exactly solvable spin Sutherland model of type and its related spin chain

Basu-Mallick¹,

Finkel²,

González‐López³

2013

Nuclear Physics B

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We compute the spectrum of the su(m) spin Sutherland model of B N type, including the exact degeneracy of all energy levels. By studying the large coupling constant limit of this model and of its scalar counterpart, we evaluate the partition function of their associated spin chain of Haldane-Shastry type in closed form. With the help of the formula for the partition function thus obtained we study the chain's spectrum, showing that it cannot be obtained as a limiting case of its BC N counterpart. The structure of the partition function also suggests that the spectrum of the Haldane-Shastry spin chain of B N type is equivalent to that of a suitable vertex model, as is the case for its A N−1 counterpart, and that the density of its eigenvalues is normally distributed when the number of sites N tends to infinity. We analyze this last conjecture numerically using again the explicit formula for the partition function, and check its validity for several values of N and m.

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Section: Triangularization Of H (B) and H (B)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The exactly solvable spin Sutherland model of type and its related spin chain

Basu-Mallick¹,

Finkel²,

González‐López³

2013

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…They are all associated with the root system A N−1 , in the sense that the interactions J i j depend only on the differences of the site coordinates ξ k . Although several generalizations of these chains to the BC N and D N root systems have been considered in the literature [7][8][9][10][11], in this paper we shall restrict ourselves to the above A N−1 -type models. Spin chains of HS type are the simplest models in condensed matter physics exhibiting fractional statistics [12].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of spin chains of Haldane–Shastry type and one-dimensional vertex models

2012

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We study the thermodynamic properties of spin chains of Haldane-Shastry type associated with the A N−1 root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that these chains are equivalent to a suitable inhomogeneous classical Ising model in a spatially dependent magnetic field, generalizing the results of Basu-Mallick et al. for the zero magnetic field case. Using the standard transfer matrix approach, we are able to compute in closed form the free energy per site in the thermodynamic limit. We perform a detailed analysis of the chains' thermodynamics in a unified way, with special emphasis on the zero field and zero temperature limits. Finally, we provide a novel interpretation of the thermodynamic quantities of spin chains of Haldane-Shastry type as weighted averages of the analogous quantities over an ensemble of classical Ising models.

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“…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%

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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Integrable spin chain with reflecting end

Cited by 40 publications

References 45 publications

The exactly solvable spin Sutherland model of type and its related spin chain

The exactly solvable spin Sutherland model of type and its related spin chain

Thermodynamics of spin chains of Haldane–Shastry type and one-dimensional vertex models

The spin Sutherland model of type and its associated spin chain

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