Composite Fermions as Deformed Oscillators: Wavefunctions and Entanglement
Keywords:composite fermions (cofermions), composite bosons (cobosons, quasibosons), realization by deformed oscillators, bipartite entanglement, entanglement entropy, purity
Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, п-mesons, excitons, Cooper pairs are not ideal bosons, and, likewise, baryons are not pure fermions. In our preceding papers, we studied bipartite composite boson (i.e. quasiboson) systems via a realization by deformed oscillators. Therein, the interconstituent entanglement characteristics such as entanglement entropy and purity were found in terms of the parameter of deformation. Herein, we perform an analogous study of composite Fermi-type particles, and explore them in two major cases: (i) “boson + fermion” composite fermions (or cofermions, or CFs); (ii) “deformed boson + fermion” CFs. As we show, cofermions in both cases admit only the realization by ordinary fermions. Case (i) is solved explicitly, and admissible wavefunctions are found along with entanglement measures. Case (ii) is treated within few modes both for CFs and constituents. The entanglement entropy and purity of CFs are obtained via the relevant parameters and illustrated graphically.
J.K. Jain. Composite Fermions (Cambridge Univ. Press, 2007) [ISBN: 978-0-521-86232-5]. https://doi.org/10.1017/CBO9780511607561
D. Hadjimichef et al. Mapping of composite hadrons into elementary hadrons and effective hadronic hamiltonians. Ann. Phys. 268, 105 (1998). https://doi.org/10.1006/aphy.1998.5825
Y. Oh, H. Kim. Pentaquark baryons in the SU(3) quark model. Phys. Rev. D 70, 094022 (2004). https://doi.org/10.1103/PhysRevD.70.094022
T.E. Browder, I.R. Klebanov, D.R. Marlow. Prospects for pentaquark production at meson factories. Phys. Lett. B 587, 62 (2004). https://doi.org/10.1016/j.physletb.2004.03.003
A.M. Gavrilik, I.I. Kachurik, Yu.A. Mishchenko. Quasibosons composed of two q-fermions: realization by deformed oscillators. J. Phys. A: Math. Theor. 44, 47530 (2011). https://doi.org/10.1088/1751-8113/44/47/475303
A.M. Gavrilik, I.I. Kachurik, Yu.A. Mishchenko. Two-fermion composite quasibosons and deformed oscillators. Ukr. J. Phys. 56, 948 (2011).
A.M. Gavrilik, Yu.A. Mishchenko. Entanglement in composite bosons realized by deformed oscillators. Phys. Lett. A 376 (19), 1596 (2012). https://doi.org/10.1016/j.physleta.2012.03.053
A.M. Gavrilik, Yu.A. Mishchenko. Energy dependence of the entanglement entropy of composite boson (quasiboson) systems. J. Phys. A: Math. Theor. 46 (14), 145301 (2013). https://doi.org/10.1088/1751-8113/46/14/145301
R. Horodecki et al. Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009). https://doi.org/10.1103/RevModPhys.81.865
M.C. Tichy, F. Mintert, A. Buchleitner. Essential entanglement for atomic and molecular physics. J. Phys. B: At. Mol. Opt. Phys. 44, 192001 (2011). https://doi.org/10.1088/0953-4075/44/19/192001
C.K. Law. Quantum entanglement as an interpretation of bosonic character in composite two-particle systems. Phys. Rev. A 71, 034306 (2005). https://doi.org/10.1103/PhysRevA.71.034306
C. Chudzicki, O. Oke, W.K. Wootters. Entanglement and composite bosons. Phys. Rev. Lett. 104, 070402 (2010). https://doi.org/10.1103/PhysRevLett.104.070402
Z. Lasmar et al. Assembly of 2N entangled fermions into multipartite composite bosons. Phys. Rev. A 100, 032105 (2019). https://doi.org/10.1103/PhysRevA.100.032105
T. Morimae. Vacuum entanglement governs the bosonic character of magnons. Phys. Rev. A 81, 060304 (2010). https://doi.org/10.1103/PhysRevA.81.060304
R. Ramanathan, P. Kurzynski, T.K. Chuan et al. Criteria for two distinguishable fermions to form a boson. Phys. Rev. A 84, 034304 (2011). https://doi.org/10.1103/PhysRevA.84.034304
R. Weder. Entanglement creation in low-energy scattering. Phys. Rev. A 84, 062320 (2011). https://doi.org/10.1103/PhysRevA.84.062320
R.O. Esquivel et al. Quantum entanglement and the dissociation process of diatomic molecules. J. Phys. B: At. Mol. Opt. Phys. 44, 175101 (2011). https://doi.org/10.1088/0953-4075/44/17/175101
P. Kurzynski et al. Particle addition and subtraction channels and the behavior of composite particles. New J. Phys. 14, 093047 (2012). https://doi.org/10.1088/1367-2630/14/9/093047
T.J. Bartley et al. Strategies for enhancing quantum entanglement by local photon subtraction. Phys. Rev. A 87, 022313 (2013). https://doi.org/10.1103/PhysRevA.87.022313
D. Gioev, I. Klich. Entanglement entropy of fermions in any dimension and the widom conjecture. Phys. Rev. Lett. 96, 100503 (2006). https://doi.org/10.1103/PhysRevLett.96.100503
J. Shao, E.-A. Kim, F.D.M. Haldane, E.H. Rezayi. Entanglement entropy of the v = 1/2 composite fermion non-fermi liquid state. Phys. Rev. Lett. 114, 206402 (2015). https://doi.org/10.1103/PhysRevLett.114.206402
S. Meljanac, M. Milekovic, S. Pallua. Unified view of deformed single-mode oscillator algebras. Phys. Lett. B 328, 55 (1994). https://doi.org/10.1016/0370-2693(94)90427-8
D. McHugh, M. Ziman, V. Buˇzek. Entanglement, purity, and energy: Two qubits versus two modes. Phys. Rev. A 74, 042303 (2006). https://doi.org/10.1103/PhysRevA.74.042303
F.R. Gantmacher. The Theory of Matrices (AMS Chelsea Publishing, 2000), Vol. 1 [ISBN: 0-8218-1376-5].
J.B. Bronzan. Parametrization of SU(3). Phys. Rev. D 38, 1994 (1988). https://doi.org/10.1103/PhysRevD.38.1994
A.T. Bolukbasi, T. Dereli. On the SU(3) parametrization of qutrits. J. Phys.: Conf. Ser. 36, 28 (2006). https://doi.org/10.1088/1742-6596/36/1/006
G.G. Spink, P.L'opez R'ıos, N.D. Drummond, R.J. Needs. Trion formation in a two-dimensional hole-doped electron gas. Phys. Rev. B 94, 041410 (2016). https://doi.org/10.1103/PhysRevB.94.041410
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