Boson–fermion duality in supersymmetric Haldane–Shastry spin chain

Basu-Mallick, B.; Bondyopadhaya, Nilanjan; Hikami, Kazuhiro; Sen, Diptiman

doi:10.1016/j.nuclphysb.2007.05.007

Cited by 33 publications

(111 citation statements)

References 40 publications

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“…, 1) we obtain the equality of the zero-field partition functions Z 0 and Z V 0 , which is in fact the main result in Ref. [35]. On the other hand, if we evaluate the identity (3.4) at the point (q −B 1 , .…”

Section: The Associated Vertex Modelssupporting

confidence: 66%

“…As pointed out in Ref. [35], Eq. (1.12) defines a classical inhomogeneous onedimensional vertex model with bonds n 1 , .…”

Section: Introductionmentioning

confidence: 71%

“…One of the fundamental results in Ref. [35] is the fact that the generating functions (3.1) and (3.3) are identically equal, i.e.,…”

Section: The Associated Vertex Modelsmentioning

confidence: 99%

“…Using the previous expression for the partition function, Basu-Mallick et al [35] showed that the spectrum of the spin chains of HS type is given by…”

Section: Introductionmentioning

confidence: 99%

“…Following the approach of Ref. [35], in Section 3 we construct a generating function for the partition function in terms of complete homogeneous symmetric polynomials. We then define a similar function for the corresponding vertex models, and prove that both generating functions coincide for arbitrary values of their arguments.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Associated Vertex Modelssupporting

confidence: 66%

“…As pointed out in Ref. [35], Eq. (1.12) defines a classical inhomogeneous onedimensional vertex model with bonds n 1 , .…”

Section: Introductionmentioning

confidence: 71%

“…One of the fundamental results in Ref. [35] is the fact that the generating functions (3.1) and (3.3) are identically equal, i.e.,…”

Section: The Associated Vertex Modelsmentioning

confidence: 99%

“…Using the previous expression for the partition function, Basu-Mallick et al [35] showed that the spectrum of the spin chains of HS type is given by…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations