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Prog. Theor. Phys. Vol. 122 No. 4 (2009) pp. 953-967

Spherical Deformation for One-Dimensional Quantum Systems

Andrej Gendiar,^1,2 Roman Krcmar¹ and Tomotoshi Nishino^2,3

¹Institute of Electrical Engineering, Slovak Academy of Sciences,
Dúbravská cesta 9, SK-841 04, Bratislava, Slovakia
²Institute for Theoretical Physics C, RWTH University Aachen,
D-52056 Aachen, Germany
³Department of Physics, Graduate School of Science, Kobe University,
Kobe 657-8501, Japan

(Received March 31, 2009; Revised July 15, 2009)

Abstract:

System-size dependence of the ground-state energy E^N is investigated for N-site one-dimensional (1D) quantum systems with open boundary condition, where the interaction strength decreases towards the both ends of the system. For the spinless Fermions on the 1D lattice we have considered, it is shown that the finite-size correction to the energy per site, which is defined as E^N / N - lim _{N →∞} E^N / N, is of the order of 1 / N² when the reduction factor of the interaction is expressed by a sinusoidal function. We discuss the origin of this fast convergence from the viewpoint of the spherical geometry.

Subject Index : 021, 047, 397
URL : http://ptp.ipap.jp/link?PTP/122/953/
DOI : 10.1143/PTP.122.953

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See Also:

• Progress of Theoretical Physics Vol. 123 No. 2 (2010) pp. 393-393 :

  Erratum : Spherical Deformation for One-Dimensional Quantum Systems

  Andrej Gendiar, Roman Krcmar and Tomotoshi Nishino

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Citing Article(s) :

1. Journal of the Physical Society of Japan 80 (2011) 094001 (5 pages) :

   Hyperbolic Deformation Applied to S = 1 Spin Chains – Scaling Relation in Excitation Energy –

   Hiroshi Ueda, Hiroki Nakano, Koichi Kusakabe, and Tomotoshi Nishino

2. Progress of Theoretical Physics Vol. 124 No. 3 (2010) pp. 389-398 :

   Scaling Relation for Excitation Energy under Hyperbolic Deformation

   Hiroshi Ueda, Hiroki Nakano, Koichi Kusakabe and Tomotoshi Nishino

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