×

Composite fermion basis for \(M\)-component Bose gases. (English) Zbl 1378.82048

Summary: The composite fermion (CF) formalism produces wave functions that are not always linearly independent. This is especially so in the low angular momentum regime in the lowest Landau level, where a subclass of CF states, known as simple states, gives a good description of the low energy spectrum. For the two-component Bose gas, explicit bases avoiding the large number of redundant states have been found. We generalize one of these bases to the \(M\)-component Bose gas and prove its validity. We also show that the numbers of linearly independent simple states for different values of angular momentum are given by coefficients of \(q\)-multinomials.

MSC:

82D05 Statistical mechanics of gases
82B26 Phase transitions (general) in equilibrium statistical mechanics

Software:

OpenCourseWare
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Viefers S 2008 J. Phys.: Condens. Matter20 123202 · doi:10.1088/0953-8984/20/12/123202
[2] Cooper N 2008 Adv. Phys.57 539 · doi:10.1080/00018730802564122
[3] Fetter A L 2009 Rev. Mod. Phys.81 647 · doi:10.1103/RevModPhys.81.647
[4] Myatt C J, Burt E A, Ghrist R W, Cornell E A and Wieman C E 1997 Phys. Rev. Lett.78 586 · doi:10.1103/PhysRevLett.78.586
[5] Hall D S, Matthews M R, Ensher J R, Wieman C E and Cornell E A 1998 Phys. Rev. Lett.81 1539 · doi:10.1103/PhysRevLett.81.1539
[6] Barrett M D et al 2001 Phys. Rev. Lett.87 010404 · doi:10.1103/PhysRevLett.87.010404
[7] Stamper-Kurn D M et al 1998 Phys. Rev. Lett.80 2027 · doi:10.1103/PhysRevLett.80.2027
[8] Stenger J et al 1998 Nat. London396 345 · doi:10.1038/24567
[9] Miesner H-J et al 1999 Phys. Rev. Lett.82 2228 · doi:10.1103/PhysRevLett.82.2228
[10] Roati G, Zaccanti M, D’Errico C, Catani J, Modugno M, Simoni A, Inguscio M and Modugno G 2007 Phys. Rev. Lett.99 010403 · doi:10.1103/PhysRevLett.99.010403
[11] Thalhammer G, Barontini G, De Sarlo L, Catani J, Minardi F and Inguscio M 2008 Phys. Rev. Lett.100 210402 · doi:10.1103/PhysRevLett.100.210402
[12] Papp S B, Pino J M and Wieman C E 2008 Phys. Rev. Lett.101 040402 · doi:10.1103/PhysRevLett.101.040402
[13] Gemelke N, Sarajlic E and Chu S 2010 (arXiv:1007.2677)
[14] Laughlin R B 1983 Phys. Rev. Lett.50 1395 · doi:10.1103/PhysRevLett.50.1395
[15] Jain J K 1989 Phys. Rev. Lett.63 199 · doi:10.1103/PhysRevLett.63.199
[16] Jain J K 2007 Composite Fermions (Cambridge: Cambridge University Press) · doi:10.1017/CBO9780511607561
[17] Moore G and Read N 1991 Nucl. Phys. B 360 361 · doi:10.1016/0550-3213(91)90407-O
[18] Read N and Rezayi E H 1999 Phys. Rev. B 59 8084 · doi:10.1103/PhysRevB.59.8084
[19] Ardonne E and Schoutens K 1999 Phys. Rev. Lett.82 5096 · doi:10.1103/PhysRevLett.82.5096
[20] Meyer M L, Sreejith G J and Viefers S 2014 Phys. Rev. A 89 043625 · doi:10.1103/PhysRevA.89.043625
[21] Meyer M L, Liabøtrø O and Viefers S 2016 J. Phys. A: Math. Theor.49 395201 · doi:10.1088/1751-8113/49/39/395201
[22] Liabøtrø O and Meyer M L 2017 Phys. Rev. A 95 033633 · doi:10.1103/PhysRevA.95.033633
[23] Girvin S M and Jach T 1984 Phys. Rev. B 29 5617 · doi:10.1103/PhysRevB.29.5617
[24] Foata D and Han G-N 2004 The q-series in Combinatorics; permutation statistics (preliminary version, available online at http://www-irma.u-strasbg.fr/ foata/qseries.html) Lecture Notes
[25] Stanley R 2006 Topics in Algebraic Combinatorics(Lecture Notes) (Massachusetts Institute of Technology: MIT OpenCourseWare)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.