dc.contributorSilva Valencia, Jereson
dc.contributorSistemas Correlacionados (SISCO)
dc.creatorPérez Romero, Arturo
dc.date.accessioned2020-08-08T17:56:53Z
dc.date.available2020-08-08T17:56:53Z
dc.date.created2020-08-08T17:56:53Z
dc.date.issued2019-04-20
dc.identifierhttps://repositorio.unal.edu.co/handle/unal/77982
dc.description.abstractEn la presente tesis se considera fermiones con tres grados de libertad internos en una dimensión, sistema que puede ser descritos por un modelo de Fermi-Hubbard SU(3), al cual se adiciona un término de interacción a primeros vecinos. El modelo obtenido no tiene solución exacta, pero usando el método de grupo de renormalización de la matriz densidad (DMRG) se evidencia la presencia de seis fases: onda de densidad de espín (SDW), onda de densidad de carga (CDW), separación de fase (PS), metalica, apareamiento de pares (PP) y una fase que se denominó como Beat. Además, usando la entropía de von Neumann y el parámetro de Luttinger se determinó los puntos críticos entre algunas de estas fases. De tal modo que se construyó un diagrama de fases para un modelo de Hubbard extendido SU(3), el cual presenta diferencias con el mismo modelo con dos grados de libertad internos.
dc.description.abstractIn the present work we consider three-color fermions in a one-dimensional lattice. The system not only can be described by a SU(3) Fermi-Hubbard model but also is expressed by an extended model version. In our case, we add a next-neighbor interaction term at SU(3) Fermi-Hubbard model. The model obtained doesn’t have an exact solution, but we used the density matrix renormalization group method (DMRG) to find some model features. Our results reveal six different phases: spin density wave (SDW), charge density wave (CDW), phase separation (PS), metallic phase, pairing phase (PP), and a new phase which we call it Beat phase. Furthermore, we used Luttinger parameter and von Neumann entropy that worked well in determining transition points. With these results, we create the extended SU(3) Fermi-Hubbard model phases diagram, which has different from the same SU(2) model.
dc.languagespa
dc.publisherBogotá - Ciencias - Maestría en Ciencias - Física
dc.publisherDepartamento de Física
dc.publisherUniversidad Nacional de Colombia - Sede Bogotá
dc.relationRoland Assaraf, Patrick Azaria, Michel Caffarel, and Philippe Lecheminant. Metal-insulator transition in the one-dimensional su (n) hubbard model. Physical Review B, 60(4):2299, 1999.
dc.relationJJ Vicente Alvarez, CA Balseiro, and HA Ceccatto. Spin-and charge-rotation invariant approach to the hubbard model. Physical Review B, 54(16):11207, 1996.
dc.relationMatteo Acciai, Alessio Calzona, Giacomo Dolcetto, Thomas L Schmidt, and Maura Sassetti. Charge and energy fractionalization mechanism in onedimensional channels. Physical Review B, 96(7):075144, 2017.
dc.relationMike H Anderson, Jason R Ensher, Michael R Matthews, Carl E Wieman, and Eric A Cornell. Observation of bose-einstein condensation in a dilute atomic vapor. science, 269(5221):198–201, 1995.
dc.relationK Aikawa, A Frisch, M Mark, S Baier, R Grimm, and F Ferlaino. Reaching fermi degeneracy via universal dipolar scattering. Physical review letters, 112(1):010404, 2014.
dc.relationLei Ai, Guojia Fang, Longyan Yuan, Nishuang Liu, Mingjun Wang, Chun Li, Qilin Zhang, Jun Li, and Xingzhong Zhao. Influence of substrate temperature on electrical and optical properties of p-type semitransparent conductive nickel oxide thin films deposited by radio frequency sputtering. Applied Surface Science, 254(8):2401–2405, 2008.
dc.relationHenri Alloul. Strongly correlated electrons in solids. arXiv preprint arXiv:1504.05855, 2015.
dc.relationNeil W Ashcroft and N David Mermin. Solid state physics (saunders college, philadelphia, 1976). Appendix N, 2010.
dc.relationMikhail A Baranov. Theoretical progress in many-body physics with ultracold dipolar gases. Physics Reports, 464(3):71–111, 2008.
dc.relationDionys Baeriswyl, David K Campbell, and Sumit Mazumdar. An overview of the theory of π-conjugated polymers. In Conjugated conducting polymers, pages 7–133. Springer, 1992.
dc.relationJohn Bardeen, Leon N Cooper, and J Robert Schrieffer. Microscopic theory of superconductivity. Physical Review, 106(1):162, 1957.
dc.relationMikhail A Baranov, Marcello Dalmonte, Guido Pupillo, and Peter Zoller. Condensed matter theory of dipolar quantum gases. Chemical Reviews, 112(9):5012–5061, 2012.
dc.relationImmanuel Bloch, Jean Dalibard, and Wilhelm Zwerger. Many-body physics with ultracold gases. Reviews of modern physics, 80(3):885, 2008.
dc.relationJesper Fevre Bertelsen. Ultracold Atomic Gases. PhD thesis, PhD thesis, University of Aarhus, 2007.
dc.relationHans Bethe. Zur theorie der metalle. Zeitschrift für Physik, 71(3-4):205–226, 1931.
dc.relationImmanuel Bloch and Markus Greiner. Exploring quantum matter with ultracold atoms in optical lattices. Advances in Atomic, Molecular, and Optical Physics, 52:1–47, 2005.
dc.relationJames W Bray, Leonard V Interrante, Israel S Jacobs, and Jill C Bonner. The spin-peierls transition. In Extended linear chain compounds, pages 353–415. Springer, 1983.
dc.relationFelix Bloch. Über die quantenmechanik der elektronen in kristallgittern. Zeitschrift für physik, 52(7-8):555–600, 1929.
dc.relationK Buchta, Ö Legeza, E Szirmai, and J Sólyom. Mott transition and dimerization in the one-dimensional su (n) hubbard model. Physical Review B, 75(15):155108, 2007.
dc.relationMA Baranov, MS Marenko, Val S Rychkov, and GV Shlyapnikov. Superfluid pairing in a polarized dipolar fermi gas. Physical Review A, 66(1):013606, 2002.
dc.relationMax Born and Robert Oppenheimer. Zur quantentheorie der molekeln. Annalen der physik, 389(20):457–484, 1927.
dc.relationCurtis Charles Bradley, CA Sackett, and RG Hulet. Bose-einstein condensation of lithium: Observation of limited condensate number. Physical Review Letters, 78(6):985, 1997.
dc.relationCl C Bradley, CA Sackett, JJ Tollett, and Randall G Hulet. Evidence of bose-einstein condensation in an atomic gas with attractive interactions. Physical review letters, 75(9):1687, 1995.
dc.relationGuest CDT-CMP. What is condensed matter physics?, 2015.
dc.relationSteven Chu, Leo Hollberg, John E Bjorkholm, Alex Cable, and Arthur Ashkin. Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure. Physical review letters, 55(1):48, 1985.
dc.relationSylvain Capponi, Philippe Lecheminant, and Keisuke Totsuka. Phases of one-dimensional su(n) cold atomic fermi gases from molecular luttinger liquids to topological phases. Annals of Physics, 367:50–95, 2016
dc.relationJit Kee Chin, DE Miller, Y Liu, C Stan, W Setiawan, C Sanner, K Xu, and W Ketterle. Evidence for superfluidity of ultracold fermions in an optical lattice. Nature, 443(7114):961, 2006.
dc.relationJit Kee Chin, DE Miller, Y Liu, C Stan, W Setiawan, C Sanner, K Xu, and W Ketterle. Evidence for superfluidity of ultracold fermions in an optical lattice. Nature, 443(7114):961, 2006.
dc.relationRichard J Cook. Optical stern-gerlach effect. Physical Review A, 35(9):3844, 1987.
dc.relationM Cyrot. Theory of mott transition: Applications to transition metal oxides. Journal de Physique, 33(1):125–134, 1972.
dc.relationJozef Devreese. Highly conducting one-dimensional solids. Springer Science & Business Media, 2013.
dc.relationPedro M Duarte, Russell A Hart, Tsung-Lin Yang, Xinxing Liu, Thereza Paiva, Ehsan Khatami, Richard T Scalettar, Nandini Trivedi, and Randall G Hulet. Compressibility of a fermionic mott insulator of ultracold atoms. Physical review letters, 114(7):070403, 2015.
dc.relationBrian DeMarco and Deborah S Jin. Onset of fermi degeneracy in a trapped atomic gas. science, 285(5434):1703–1706, 1999.
dc.relationKendall B Davis, M-O Mewes, Michael R Andrews, NJ Van Druten, DS Durfee, DM Kurn, and Wolfgang Ketterle. Bose-einstein condensation in a gas of sodium atoms. Physical review letters, 75(22):3969, 1995.
dc.relationBrian J DeSalvo, Mi Yan, Pascal Gerry Mickelson, YN Martinez De Escobar, and Thomas C Killian. Degenerate fermi gas of sr^87 . Physical Review Letters, 105(3):030402, 2010.
dc.relationFabian HL Essler, Holger Frahm, Frank G¨ohmann, Andreas Klümper, and Vladimir E Korepin. The one-dimensional Hubbard model. Cambridge University Press, 2005.
dc.relationFabian HL Essler, Vladimir E Korepin, and Kareljan Schoutens. Complete solution of the one-dimensional hubbard model. Physical review letters, 67(27):3848, 1991.
dc.relationVJ Emery. Theory of the one-dimensional electron gas. In Highly conducting one-dimensional solids, pages 247–303. Springer, 1979.
dc.relationEnrico Fermi et al. Motion of neutrons in hydrogenous substances. Ricerca Scientifica, 7(2):13–52, 1936.
dc.relationJean-Pierre Farges. Organic conductors: fundamentals and applications. Marcel Dekker, 1994.
dc.relationPatrik Fazekas. Lecture notes on electron correlation and magnetism, volume 5. World scientific, 1999.
dc.relationPavol Farkasovský and Hana Cencariková. Ferromagnetism in the two-dimensional hubbard model with long-range hopping. Open Physics, 11(1):119–123, 2013.
dc.relationMichael E Fisher. The renormalization group in the theory of critical behavior. Reviews of Modern Physics, 46(4):597, 1974.
dc.relationB Fourcade and G Spronken. Real-space scaling methods applied to the one-dimensional extended hubbard model. ii. the finite-cell scaling method. Physical Review B, 29(9):5096, 1984.
dc.relationShi-Jian Gu, Shu-Sa Deng, You-Quan Li, and Hai-Qing Lin. Entanglement and quantum phase transition in the extended hubbard model. Physical review letters, 93(8):086402, 2004.
dc.relationFlorian Gebbhard. The mott metal-insulator transition: Models and methods, 1997.
dc.relationMarkus Greiner and Simon Fölling. Condensed-matter physics: Optical lattices. Nature, 453(7196):736, 2008.
dc.relationAlexey Vyacheslavovich Gorshkov, M Hermele, V Gurarie, C Xu, Paul S Julienne, J Ye, Peter Zoller, Eugene Demler, Mikhail D Lukin, and AM Rey. Two-orbital su (n) magnetism with ultracold alkaline-earth atoms. Nature physics, 6(4):289, 2010.
dc.relationThierry Giamarchi. Quantum physics in one dimension, volume 121. Clarendon press, 2003.
dc.relationS Glocke, A Klümper, and J Sirker. Half-filled one-dimensional extended hubbard model: Phase diagram and thermodynamics. Physical Review B, 76(15):155121, 2007.
dc.relationVitaly L Ginzburg and Lev D Landau. On the theory of superconductivity. In On Superconductivity and Superfluidity, pages 113–137. Springer, 2009.
dc.relationMarkus Greiner, Olaf Mandel, Tilman Esslinger, Theodor W Hänsch, and Immanuel Bloch. Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms. nature, 415(6867):39, 2002.
dc.relationAlexander O Gogolin, Alexander A Nersesyan, and Alexei M Tsvelik. Bosonization and strongly correlated systems. Cambridge university press, 2004.
dc.relationStefano Giorgini, Lev P Pitaevskii, and Sandro Stringari. Theory of ultracold atomic fermi gases. Reviews of Modern Physics, 80(4):1215, 2008.
dc.relationDavid J Griffiths and Darrell F Schroeter. Introduction to quantum mechanics. Cambridge University Press, 2018.
dc.relationFDM Haldane. "luttinger liquid theory" of one-dimensional quantum fluids. i. properties of the luttinger model and their extension to the general 1d interacting spinless fermi gas. Journal of Physics C: Solid State Physics, 14(19):2585, 1981.
dc.relationJE Hirsch. Charge-density-wave to spin-density-wave transition in the extended hubbard model. Physical review letters, 53(24):2327, 1984.
dc.relationChristian Hofrichter, Luis Riegger, Francesco Scazza, Moritz Höfer, Diogo Rio Fernandes, Immanuel Bloch, and Simon Fölling. Direct probing of the mott crossover in the su (n) fermi-hubbard model. Physical Review X, 6(2):021030, 2016.
dc.relationHideo Hosono, Keiichi Tanabe, Eiji Takayama-Muromachi, Hiroshi Kageyama, Shoji Yamanaka, Hiroaki Kumakura, Minoru Nohara, Hidenori Hiramatsu, and Satoru Fujitsu. Exploration of new superconductors and functional materials, and fabrication of superconducting tapes and wires of iron pnictides. Science and Technology of Advanced Materials, 16(3):033503, 2015.
dc.relationJohn Hubbard. Electron correlations in narrow energy bands. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 276(1365):238–257, 1963.
dc.relationFernando Iemini, Thiago O Maciel, and Reinaldo O Vianna. Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended hubbard model. Physical Review B, 92(7):075423, 2015.
dc.relationJanusz Jedrzejewski. On the phase diagram of the extended hubbard model. Zeitschrift für Physik B Condensed Matter, 59(3):325–332, 1985.
dc.relationAC Jacko, H Feldner, E Rose, F Lissner, M Dressel, Roser Valentí, and Harald O Jeschke. Electronic properties of fabre charge-transfer salts under various temperature and pressure conditions. Physical Review B, 87(15):155139, 2013.
dc.relationRobert Jördens, Niels Strohmaier, Kenneth Günter, Henning Moritz, and Tilman Esslinger. A mott insulator of fermionic atoms in an optical lattice. Nature, 455(7210):204, 2008.
dc.relationJunjiro Kanamori. Electron correlation and ferromagnetism of transition metals. Progress of Theoretical Physics, 30(3):275–289, 1963.
dc.relationMichael Köhl, Henning Moritz, Thilo Stöferle, Kenneth Günter, and Tilman Esslinger. Fermionic atoms in a three dimensional optical lattice: Observing fermi surfaces, dynamics, and interactions. Physical review letters, 94(8):080403, 2005.
dc.relationJ Kaczmarczyk, J Spalek, T Schickling, and J Buenemann. High-temperature superconductivity in the hubbard model: Gutzwiller wave-function solution. arXiv preprint arXiv:1210.6249, 2012.
dc.relationG. Lang. Correlations in Low-Dimensional Quantum Gases. Springer Theses. Springer International Publishing, 2018.
dc.relationMingwu Lu, Nathaniel Q Burdick, and Benjamin L Lev. Quantum degenerate dipolar fermi gas. Physical Review Letters, 108(21):215301, 2012.
dc.relationJ Levinsen, NR Cooper, and GV Shlyapnikov. Topological p x+ ip y superfluid phase of fermionic polar molecules. Physical Review A, 84(1):013603, 2011.
dc.relationJohn Edward Lennard-Jones. On the determination of molecular fields. ii. from the equation of state of gas. Proc. Roy. Soc. A, 106:463–477, 1924.
dc.relationMaciej Lewenstein, Anna Sanpera, and Veronica Ahufinger. Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems. Oxford University Press, 2012.
dc.relationElliott H Lieb and F Yu Wu. Absence of mott transition in an exact solution of the short-range, one-band model in one dimension. In Exactly Solvable Models Of Strongly Correlated Electrons, pages 9–12. World Scientific, 1994.
dc.relationGerald D Mahan. Many-particle physics. Springer Science & Business Media, 2013.
dc.relationAlbert Messiah. Quantum mechanics. vol. i. translated from the french by gm temmer. North-Holland Publishing Co., Amsterdam, 5:26, 1961.
dc.relationG Modugno, F Ferlaino, R Heidemann, G Roati, and M Inguscio. Production of a fermi gas of atoms in an optical lattice. Physical Review A, 68(1):011601, 2003.
dc.relationE Müller-Hartmann. Ferromagnetism in hubbard models: Low density route. Journal of low temperature physics, 99(3-4):349–354, 1995.
dc.relationSalvatore R Manmana, Kaden RA Hazzard, Gang Chen, Adrian E Feiguin, and Ana Maria Rey. Su (n) magnetism in chains of ultracold alkaline-earth metal atoms: Mott transitions and quantum correlations. Physical Review A, 84(4):043601, 2011.
dc.relationE Miranda. Introduction to bosonization. Brazilian Journal of Physics, 33(1):3–35, 2003.
dc.relationA Macridin, M Jarrell, Th Maier, and GA Sawatzky. Physics of cuprates with the two-band hubbard model: The validity of the one-band hubbard model. Physical Review B, 71(13):134527, 2005.
dc.relationNF Mott and R Peierls. Discussion of the paper by de boer and verwey. Proceedings of the Physical Society, 49(4S):72, 1937.
dc.relationArianna Montorsi and Marco Roncaglia. Nonlocal order parameters for the 1d hubbard model. Physical review letters, 109(23):236404, 2012.
dc.relationCA Macedo and AMC Souza. Magnetic properties of nanotube structures. Physica B: Condensed Matter, 354(1-4):290–292, 2004.
dc.relationYosuke Nagaoka. Ferromagnetism in a narrow, almost half-filled s band. Physical Review, 147(1):392, 1966.
dc.relationMasaaki Nakamura. Mechanism of cdw-sdw transition in one dimension. Journal of the Physical Society of Japan, 68(10):3123–3126, 1999.
dc.relationMasaaki Nakamura. Tricritical behavior in the extended hubbard chains. Physical Review B, 61(24):16377, 2000.
dc.relationH Nonne, P Lecheminant, Sylvain Capponi, G Roux, and E Boulat. Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The haldane-charge conjecture. Physical Review B, 84(12):125123, 2011.
dc.relationTimo Bastian Ottenstein, T Lompe, M Kohnen, AN Wenz, and S Jochim. Collisional stability of a three-component degenerate fermi gas. Physical review letters, 101(20):203202, 2008.
dc.relationHideki Ozawa, Shintaro Taie, Yosuke Takasu, and Yoshiro Takahashi. Antiferromagnetic spin correlation of su (n) fermi gas in an optical superlattice. Physical review letters, 121(22):225303, 2018.
dc.relationGuido Pagano, Marco Mancini, Giacomo Cappellini, Pietro Lombardi, Florian Schäfer, Hui Hu, Xia-Ji Liu, Jacopo Catani, Carlo Sias, Massimo Inguscio, et al. A one-dimensional liquid of fermions with tunable spin. Nature Physics, 10(3):198, 2014.
dc.relationDavid Peter, Steffen Müller, Stefan Wessel, and Hans Peter Büchler. Anomalous behavior of spin systems with dipolar interactions. Physical review letters, 109(2):025303, 2012.
dc.relationWilliam D Phillips, John V Prodan, and Harold J Metcalf. Laser cooling and electromagnetic trapping of neutral atoms. JOSA B, 2(11):1751–1767, 1985.
dc.relationStéphane Pairault, David Sénéchal, and A-MS Tremblay. Strong-coupling expansion for the hubbard model. Physical review letters, 80(24):5389, 1998.
dc.relationH Rosner, H Eschrig, R Hayn, S-L Drechsler, and J Málek. Electronic structure and magnetic properties of the linear chain cuprates sr 2 cuo 3 and ca 2 cuo 3. Physical Review B, 56(6):3402, 1997.
dc.relationC. A. Regal, M. Greiner, and D. S. Jin. Observation of resonance condensation of fermionic atom pairs. Phys. Rev. Lett., 92:040403, Jan 2004.
dc.relationS Robaszkiewicz, R Micnas, and KA Chao. Thermodynamic properties of the extended hubbard model with strong intra-atomic attraction and an arbitrary electron density. Physical Review B, 23(3):1447, 1981.
dc.relationSubir Sachdev. Quantum phase transitions. Handbook of Magnetism and Advanced Magnetic Materials, 2007.
dc.relationP Schlottmann. Exact results for highly correlated electron systems in one dimension. International Journal of Modern Physics B, 11(04n05):355–667, 1997.
dc.relationHeinz J Schulz, Gianaurelio Cuniberti, and Pierbiagio Pieri. Fermi liquids and luttinger liquids. In Field theories for low-dimensional condensed matter systems, pages 9–81. Springer, 2000.
dc.relationB Sriram Shastry. Mott transition in the hubbard model. Modern Physics Letters B, 6(23):1427–1438, 1992.
dc.relationHiroyuki Shiba. Thermodynamic properties of the one-dimensional half filled-band hubbard model. ii: Application of the grand canonical method. Progress of Theoretical Physics, 48(6):2171–2186, 1972.
dc.relationU Schneider, L Hackermüller, S Will, Th Best, Immanuel Bloch, TA Costi, RW Helmes, D Rasch, and A Rosch. Metallic and insulating phases of repulsively interacting fermions in a 3d optical lattice. Science, 322(5907):1520– 1525, 2008.
dc.relationF Schreck, Lev Khaykovich, KL Corwin, G Ferrari, Thomas Bourdel, Julien Cubizolles, and Christophe Salomon. Quasipure bose-einstein condensate immersed in a fermi sea. Physical Review Letters, 87(8):080403, 2001.
dc.relationMP López Sancho, MC Muñoz, and L Chico. Coulomb interactions in carbon nanotubes. Physical Review B, 63(16):165419, 2001.
dc.relationSeiji Sugawa, Shintaro Taie, Takeshi Fukuhara, Satoshi Uetake, Rekishu Yamazaki, Yosuke Takasu, and Yoshiro Takahashi. Ultracold ytterbium atoms in optical lattices. In Laser Spectroscopy, pages 222–231. World Scientific, 2010.
dc.relationBill Sutherland. Model for a multicomponent quantum system. In Exactly Solvable Models Of Strongly Correlated Electrons, pages 287–297. World Scientific, 1994.
dc.relationHal Tasaki. From nagaoka’s ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the hubbard model. Progress of Theoretical Physics, 99(4):489–548, 1998.
dc.relationHal Tasaki. The hubbard model-an introduction and selected rigorous results. Journal of Physics: Condensed Matter, 10(20):4353, 1998.
dc.relationAndrew G Truscott, Kevin E Strecker, William I McAlexander, Guthrie B Partridge, and Randall G Hulet. Observation of fermi pressure in a gas of trapped atoms. Science, 291(5513):2570–2572, 2001.
dc.relationYu-Chin Tzeng and Min-Fong Yang. Scaling properties of fidelity in the spin-1 anisotropic model. Physical Review A, 77(1):012311, 2008.
dc.relationGuifre Vidal. Entanglement renormalization. Physical review letters, 99(22):220405, 2007.
dc.relationJohn Von Neumann. Mathematische grundlagen der quantenmechanik, volume 38. Springer-Verlag, 2013.
dc.relationGregory H Wannier. The structure of electronic excitation levels in insulating crystals. Physical Review, 52(3):191, 1937.
dc.relationSteven R White. Density matrix formulation for quantum renormalization groups. Physical review letters, 69(19):2863, 1992.
dc.relationKenneth G Wilson. The renormalization group: Critical phenomena and the kondo problem. Reviews of modern physics, 47(4):773, 1975.
dc.relationMin-Fong Yang. Ground-state fidelity in one-dimensional gapless models. Physical Review B, 76(18):180403, 2007.
dc.relationNouredine Zettili. Quantum mechanics: concepts and applications, 2003.
dc.relationHuihuo Zheng. Entanglement in quantum phase transition. 2012.
dc.relationPaolo Zanardi and Nikola Paunkovíc. Ground state overlap and quantum phase transitions. Physical Review E, 74(3):031123, 2006.
dc.relationWilhelm Zwerger. The BCS-BEC crossover and the unitary Fermi gas, volume 836. Springer Science & Business Media, 2011.
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dc.titleModelo de Hubbard extendido para fermiones con tres grados de libertad internos
dc.typeOtro


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