Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
| dc.contributor.author | Finkel Morgenstern, Federico | |
| dc.contributor.author | González López, Artemio | |
| dc.date.accessioned | 2023-06-19T14:54:26Z | |
| dc.date.available | 2023-06-19T14:54:26Z | |
| dc.date.issued | 2014-12 | |
| dc.description | © IOP Publishing. This work was supported in part by Spains MINECO under grant no. FIS2011-22566 | |
| dc.description.abstract | We solve in closed form the simplest (su(1 vertical bar 1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1 vertical bar 1) elliptic chain behaves as a critical XX model and deviates in an essential way from the Haldane-Shastry chain. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spains MINECO | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/30699 | |
| dc.identifier.doi | 10.1088/1742-5468/2014/12/P12014 | |
| dc.identifier.issn | 1742-5468 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1088/1742-5468/2014/12/P12014 | |
| dc.identifier.relatedurl | http://iopscience.iop.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/34701 | |
| dc.journal.title | Journal of statistical mechanics : theory and experiment | |
| dc.language.iso | eng | |
| dc.publisher | IOP Publishing | |
| dc.relation.projectID | FIS2011-22566 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Inverse-square exchange | |
| dc.subject.keyword | Haldane-shastry type | |
| dc.subject.keyword | Heisenberg chain | |
| dc.subject.keyword | Yangian symmetry | |
| dc.subject.keyword | Exact spectrum | |
| dc.subject.keyword | Systems | |
| dc.subject.keyword | Models | |
| dc.subject.keyword | Gas | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Exact solution and thermodynamics of a spin chain with long-range elliptic interactions | |
| dc.type | journal article | |
| dc.volume.number | 2014 | |
| dcterms.references | [1] Haldane F D M, Exact Jastrow–Gutzwiller resonating-valence- bond ground state of the spin-1/2 antiferromagnetic Heisenberg chain with 1/r_2 exchange, 1988 Phys. Rev. Lett. 60 635 [2] Shastry B S, Exact solution of an S = 1/2 Heisenberg antiferromagnetic chain with long-ranged interactions, 1988 Phys. Rev. Lett. 60 639 [3] Polychronakos A P, Exact spectrum of SU(n) spin chain with inverse-square exchange, 1994 Nucl. Phys. B 419 553 [4] Haldane F D M, Physics of the ideal semion gas: Spinons and quantum symmetries of the integrable Haldane–Shastry spin chain, in A Okiji and N Kawakami, eds., Correlation Effects in Lowdimensional Electron Systems, Springer Series in Solid-state Sciences, volume 118, 1994, pp. 3–20 [5] Göhmann F and Wadati M, A note on inverse-square exchange models, 1995 J. Phys. Soc. Jpn. 64 3585 [6] Basu-Mallick B and Bondyopadhaya N, Exact partition functions of SU(m|n) supersymmetric Haldane–Shastry spin chain, 2006 Nucl. Phys. B 757 280 [7] Gebhard F and Ruckenstein A E, Exact results for a Hubbard chain with long-range hopping, 1992 Phys. Rev. Lett. 68 244 [8] Haldane F D M, “Fractional statistics” in arbitrary dimensions: a generalization of the Pauli principle, 1991 Phys. Rev. Lett. 67 937 [9] Greiter M and Schuricht D, No attraction between spinons in the Haldane–Shastry model, 2005 Phys. Rev. B 71 224424(4) [10] Greiter M, Statistical phases and momentum spacings for one-dimensional anyons, 2009 Phys. Rev. B 79 064409(5) [11] Haldane F D M, Ha Z N C, Talstra J C, Bernard D and Pasquier V, Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory, 1992 Phys. Rev. Lett. 69 2021 [12] Fowler M and Minahan J A, Invariants of the Haldane–Shastry SU(n) chain, 1993 Phys. Rev. Lett. 70 2325 [13] Haldane F D M, “Spinon gas” description of the S = 1 /2 Heisenberg chain with inverse-square exchange: exact spectrum and thermodynamics, 1991 Phys. Rev. Lett. 66 1529 [14] Kawakami N, Asymptotic Bethe-ansatz solution of multicomponent quantum systems with 1/r_2 long-range interaction, 1992 Phys. Rev. B 46 1005 [15] Ha Z N C and Haldane F D M, Squeezed strings and Yangian symmetry of the Heisenberg chain with long-range interaction, 1993 Phys. Rev. B 47 12459 [16] Finkel F and González-López A, Global properties of the spectrum of the Haldane–Shastry spin chain, 2005 Phys. Rev. B 72 174411(6) [17] Polychronakos A P, Lattice integrable systems of Haldane–Shastry type, 1993 Phys. Rev. Lett. 70 2329 [18] Inozemtsev V I, On the connection between the one- dimensional S = 1/2 Heisenberg chain and Haldane–Shastry model, 1990 J. Stat. Phys. 59 1143 [19] Whittaker E T and Watson G N, A Course of Modern Analysis (Cambridge University Press) 1927 [20] Maldacena J M, The large N limit of superconformal field theories and supergravity, 1998 Adv. Theor. Math. Phys. 2 231 [21] Witten E, Anti-de Sitter space and holography, 1998 Adv. Theor. Math. Phys. 2 253 [22] Gubser S S, Klebanov I R and Polyakov A M, Gauge theory correlators from non-critical string theory, 1998 Phys. Lett. B 428 105 [23] Berenstein D, Maldacena J and Nastase H, Strings in flat space and pp waves from N = 4 Super Yang Mills, 2002 J. High Energy Phys. 04 013(29) [24] Minahan J A and Zarembo K, The Bethe-ansatz for N = 4 super Yang–Mills, 2003 J. High Energy Phys. 303 013(27) [25] Serban D and Staudacher M, Planar N = 4 gauge theory and the Inozemtsev long range spin chain, 2004 J. High Energy Phys. 06 001(31) [26] Beisert N, ed., Special Volume: Review on AdS/CFT Integrability, Lett. Math. Phys., volume 99 (Springer) 2012 [27] Inozemtsev V I, Integrable Heisenberg–van Vleck chains with variable range exchange, 2003 Phys. Part. Nucl. 34 166 [28] Finkel F and González-López A, A new perspective on the integrability of Inozemtsev’s elliptic spin chain, 2014 Ann. Phys.-New York 351 797 [29] Basu-Mallick B, Bondyopadhaya N and Sen D, Low energy properties of the SU(m|n) supersymmetric Haldane–Shastry spin chain, 2008 Nucl. Phys. B 795 596 [30] Enciso A, Finkel F and González-López A, Spin chains of Haldane–Shastry type and a generalized central limit theorem, 2009 Phys. Rev. E 79 060105(4) [31] Enciso A, Finkel F and González-López A, Level density of spin chains of Haldane–Shastry type, 2010 Phys. Rev. E 82 051117(6) [32] Basu-Mallick B and Bondyopadhaya N, Spectral properties of supersymmetric Polychronakos spin chain associated with AN−1 root system, 2009 Phys. Lett. A 373 2831 [33] Göhmann F and Murakami S, Fermionic representations of integrable lattice systems, 1998 J. Phys. A: Math. Gen. 31 7729 [34] Inozemtsev V I, The eigenvectors of the Heisenberg Hamiltonian with elliptic form of the exchange spin interaction, 2005 J. Nonlin. Math. Phys. 12 395 [35] Sachdev S, Quantum Phase Transitions (Cambridge University Press), second edition 2011 [36] Olver F W J, Lozier D W, Boisvert R F and Clark C W, eds., NIST Handbook of Mathematical Functions (Cambridge Univeristy Press) 2010 [37] Enciso A, Finkel F and González-López A, Thermodynamics of spin chains of Haldane–Shastry type and one-dimensional vertex models, 2012 Ann. Phys.-New York 327 2627 [38] Stein E M and Shakarchi R, Complex Analysis (Princeton, N.J.: Princeton University Press) 2003 [39] Barba J C, Finkel F, González-López A and Rodr´ıguez M A, The Berry–Tabor conjecture for spin chains of Haldane–Shastry type, 2008 Europhys. Lett. 83 27005(6) [40] Barba J C, Finkel F, González-López A and Rodríguez M A, 1/f ^α noise and integrable systems, 2009 Phys. Rev. E 80 047201(4) [41] Latorre J I and Riera A, A short review on entanglement in quantum spin systems, 2009 J. Phys. A: Math. Theor. 42 504002(33) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 207092a4-0443-4336-a037-15936f8acc25 | |
| relation.isAuthorOfPublication | 7f260dbe-eebb-4d43-8ba9-d8fbbd5b32fc | |
| relation.isAuthorOfPublication.latestForDiscovery | 207092a4-0443-4336-a037-15936f8acc25 |
Download
Original bundle
1 - 1 of 1
