Abstract:
We define a class of $Y(sl_{(m|n)})$ Yangian invariant Haldane–Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials.
Using some properties of the super Schur polynomials, we show that the partition functions of this class of
spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with
one-dimensional vertex models.
Citation:
Bireswar Basu-Mallick, Nilanjan Bondyopadhaya, Kazuhiro Hikami, “One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane–Shastry Like Spin Chains”, SIGMA, 6 (2010), 091, 13 pp.
This publication is cited in the following 19 articles:
Bireswar Basu-Mallick, Federico Finkel, Artemio González-López, “A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality”, J. Stat. Mech., 2024:11 (2024), 113102
Federico Finkel, Artemio González-López, “The open Haldane–Shastry chain: thermodynamics and criticality”, J. Stat. Mech., 2022:9 (2022), 093102
Federico Finkel, Artemio González-López, “Thermodynamics and criticality of
su(m)
spin chains of Haldane-Shastry type”, Phys. Rev. E, 106:5 (2022)
Basu-Mallick B., Finkel F., Gonzalez-Lopez A., “A Novel Class of Translationally Invariant Spin Chains With Long-Range Interactions”, J. High Energy Phys., 2020, no. 8, 099
Basu-Mallick B., Sinha M., “Appearance of Branched Motifs in the Spectra of Bcn Type Polychronakos Spin Chains”, Nucl. Phys. B, 952 (2020), 114914
Basu-Mallick B., Bondyopadhaya N., Carrasco J.A., Finkel F., Gonzalez-Lopez A., “Supersymmetric T-J Models With Long-Range Interactions: Partition Function and Spectrum”, J. Stat. Mech.-Theory Exp., 2019, 043105
Basu-Mallick B., Bondyopadhaya N., Carrasco J.A., Finkel F., Gonzalez-Lopez A., “Supersymmetric T-J Models With Long-Range Interactions: Thermodynamics and Criticality”, J. Stat. Mech.-Theory Exp., 2019, 073104
Finkel F., Gonzalez-Lopez A., Leon I., Rodriguez M.A., “Thermodynamics and Criticality of Supersymmetric Spin Chains With Long-Range Interactions”, J. Stat. Mech.-Theory Exp., 2018, 043101
Carrasco J.A., Finkel F., Gonzalez-Lopez A., “Generalized Lipkin-Meshkov-Glick Models of Haldane-Shastry Type”, J. Stat. Mech.-Theory Exp., 2017, 103102
Basu-Mallick B., Datta C., “Super Rogers-Szego Polynomials Associated With Bcn Type of Polychronakos Spin Chains”, Nucl. Phys. B, 921 (2017), 59–85
Banerjee P., Basu-Mallick B., Bondyopadhaya N., Datta C., “Supersymmetric Analogue of Bcn Type Rational Integrable Models With Polarized Spin Reversal Operators”, Nucl. Phys. B, 904 (2016), 297–326
Basu-Mallick B., Finkel F., Gonzalez-Lopez A., “Integrable open spin chains related to infinite matrix product states”, Phys. Rev. B, 93:15 (2016), 155154
Finkel F., Gonzalez-Lopez A., “Yangian-Invariant Spin Models and Fibonacci Numbers”, Ann. Phys., 361 (2015), 520–547
Basu-Mallick B., Datta C., Finkel F., Gonzalez-Lopez A., “Rational Quantum Integrable Systems of D-N Type With Polarized Spin Reversal Operators”, Nucl. Phys. B, 898 (2015), 53–77
Finkel F., Gonzalez-Lopez A., “a New Perspective on the Integrability of Inozemtsev'S Elliptic Spin Chain”, Ann. Phys., 351 (2014), 797–827
Basu-Mallick B., Bondyopadhaya N., Banerjee P., “Partition Functions of Polychronakos Like Spin Chains Associated With Polarized Spin Reversal Operators”, Nucl. Phys. B, 883 (2014), 501–528
Banerjee P., Basu-Mallick B., “Asymptotic Form of Level Density Distributions for a Class of Inhomogeneous 1D Vertex Models”, Xxth International Conference on Integrable Systems and Quantum Symmetries (Isqs-20), Journal of Physics Conference Series, 411, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013, 012005
Enciso A., Finkel F., Gonzalez-Lopez A., “Thermodynamics of Spin Chains of Haldane-Shastry Type and One-Dimensional Vertex Models”, Ann. Phys., 327:11 (2012), 2627–2665
Banerjee P., Basu-Mallick B., “Level Density Distribution for One-Dimensional Vertex Models Related to Haldane-Shastry Like Spin Chains”, J. Math. Phys., 53:8 (2012), 083301
Citation in format AMSBIB
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