journal article·2024-02

Bound state attraction threshold in the layered Hubbard model

Maciej Bak

Publisher page

Abstract

The condition of the existence of a bound 2-particle state (BS) is examined in the empty lattice limit within the attractive Hubbard model on layered systems. It is known, that in low-dimensional systems an infinitesimal attraction suffices to form BS, while in three dimensions (3d), a threshold must be reached. Current results indicate an abrupt transition between “infinitesimal” and “finite threshold” regimes with an increasing number of layers for infinite systems and smooth crossover for finite ones.
Source: expertdata · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Cold Atom Physics and Bose-Einstein Condensates · Quantum many-body systems · Physics of Superconductivity and Magnetism

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (42)

Show source-provided references
1. Zur theorie der metalle: I. eigenwerte und eigenfunktionen der linearen atomkette10.1007/BF01341708 ↗
2. General theory of spin-wave interactions10.1103/PhysRev.102.1217 ↗
3. Exact evaluation of the Green functions for the anisotropic face-centred and simple cubic lattices10.1088/0305-4470/36/32/307 ↗
4. M. Wortis, “Bound states of two spin waves in the Heisenberg ferromagnet,” Physical Review, vol. 132, no. 1, 1963, doi: 10.1103/PhysRev.132.85.10.1103/PhysRev.132.85 ↗
5. Wave functions for impurity levels10.1103/PhysRev.95.1167 ↗
6. Simplified impurity calculation10.1103/PhysRev.96.1208 ↗
7. Theory of scattering in solids10.1063/1.1704180 ↗
8. The few-body problem on a lattice10.1103/RevModPhys.58.361 ↗
9. Theory of superconductivity10.1103/PhysRev.96.1442 ↗
10. Bose-Einstein condensation of trapped electron Pairs. Phase separation and superconductivity of metal-ammonia solutions10.1103/PhysRev.69.243 ↗
11. P.E. Kornilovitch, J.P. Hague, “Optimal interlayer hopping and high temperature Bose–Einstein condensation of local pairs in quasi 2D superconductors,” J. Phys.: Condens. Matter, vol. 27, no. 7, p. 075602, Feb. 2015, doi: 10.1088/0953-8984/27/7/075602.10.1088/0953-8984/27/7/075602 ↗
12. A.J. Leggett, Cooper pairing in spin-polarized fermi systems, J. Phys. Colloques, vol. 41, no. C7, pp. C7-19-C7-26, Jul. 1980, doi: 10.1051/jphyscol:1980704.10.1051/jphyscol:1980704 ↗
13. Bose condensation in an attractive fermion gas: from weak to strong coupling superconductivity10.1007/BF00683774 ↗
14. Superconductivity in a two-dimensional Fermi gas: evolution from cooper pairing to bose condensation10.1103/PhysRevB.41.327 ↗
15. J. K. Chin et al., “Evidence for superfluidity of ultracold fermions in an optical lattice,” Nature, vol. 443, no. 7114, 2006, doi: 10.1038/nature05224.10.1038/nature05224 ↗
16. Dimer of two bosons in a one-dimensional optical lattice10.1103/PhysRevA.81.043609 ↗
17. Feshbach molecules in a one-dimensional optical lattice10.1103/PhysRevA.77.021601 ↗
18. Scattering and binding of different atomic species in a one-dimensional optical lattice10.1103/PhysRevA.78.033611 ↗
19. Fermi-Hubbard physics with atoms in an optical lattice10.1146/annurev-conmatphys-070909-104059 ↗
20. Repulsively bound atom pairs in an optical lattice10.1038/nature04918 ↗
21. Observation of the sign reversal of the magnetic correlation in a driven-dissipative fermi gas in double wells10.1103/PhysRevLett.130.063001 ↗
22. Liouvillian gap and single spin-flip dynamics in the dissipative Fermi-Hubbard model10.1103/PhysRevA.107.033332 ↗
23. Two-body problem in a multiband lattice and the role of quantum geometry10.1103/PhysRevA.103.053311 ↗
24. Exact solutions of two-hole and hole-magnon bound states in a ferromagnet10.1103/PhysRevB.41.7061 ↗
25. Two-particle excitations in antiferromagnetic insulators10.1103/PhysRevLett.60.740 ↗
26. F.H.L. Essler, H. Frahm, F. Göhmann, A. Klümper, V.E. Korepin, Eds., The one-dimensional Hubbard model, 1. paperback printing. Cambridge: Cambridge University Press, 2010.
27. R. Micnas, J. Ranninger, S. Robaszkiewicz, Superconductivity in narrow-band systems with local nonretarded attractive interactions, Reviews of Modern Physics, vol. 62, no. 1, 1990, doi: 10.1103/RevModPhys.62.113.10.1103/RevModPhys.62.113 ↗
28. Effective mass of bound and resonant two-electron pairs in a simple cubic lattice10.12693/APhysPolA.127.290 ↗
29. Dilute gas of electron pairs in the t - J model10.1103/PhysRevB.44.4674 ↗
30. M.Y. Kagan, T.M. Rice, Superconductivity in the two-dimensional t-J model at low electron density, J. Phys.: Condens. Matter, vol. 6, no. 20, pp. 3771–3780, May 1994, doi: 10.1088/0953-8984/6/20/016.10.1088/0953-8984/6/20/016 ↗
31. Increasing superconducting T c ’s by a factor of 1000 with large hopping anisotropies in two-dimensional t − J model systems10.1103/PhysRevB.66.144507 ↗
32. P.E. Kornilovitch, “Two-particle bound states on a lattice.” arXiv, May 04, 2023. Accessed: Nov. 02, 2023. [Online]. Available: http://arxiv.org/abs/2305.02548.10.2139/ssrn.4554256 ↗
33. The rise of graphene10.1038/nmat1849 ↗
34. Green functions of graphene: an analytic approach10.1016/j.physb.2015.01.032 ↗
35. Electronic properties of twisted multilayer graphene10.1088/2515-7639/ac6c4a ↗
36. A. Blaer, H. Ren, Extended bound states and resonances of two fermions on a periodic lattice, Physical Review B - Condensed Matter and Materials Physics, vol. 55, no. 9, 1997, doi: 10.1103/PhysRevB.55.6035.10.1103/PhysRevB.55.6035 ↗
37. Economou · 2006
38. Bound states in the phase diagram of the extended Hubbard model10.1002/pssb.200460049 ↗
39. Double-time green functions in statistical physics10.1070/PU1960v003n03ABEH003275 ↗
40. New green’s-function method for canonical ensembles. I. interacting particle-phonon system10.1103/PhysRevA.3.437 ↗
41. Bound electron pairs on a triangular lattice in an extended Hubbard model10.1002/pssb.200674603 ↗
42. Kittel · 2004