RT Journal Article
T1 Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
A1 Barba, J. C:
A1 Finkel Morgenstern, Federico
A1 González López, Artemio
A1 Rodríguez González, Miguel Ángel
AB We compute the partition function of the su(m) Polychronakos-Frahm spin chain of BC_N type by means of the freezing trick. We use this partition function to study several statistical properties of the spectrum, which turn out to be analogous to those of other spin chains of Haldane-Shastry type. In particular, we find that when the number of particles is sufficiently large the level density follows a Gaussian distribution with great accuracy. We also show that the distribution of (normalized) spacings between consecutive levels is of neither Poisson nor Wigner type but is qualitatively similar to that of the original Haldane-Shastry spin chain. This suggests that spin chains of Haldane-Shastry type are exceptional integrable models since they do not satisfy a well-known conjecture of Berry and Tabor, according to which the spacings distribution of a generic integrable system should be Poissonian. We derive a simple analytic expression for the cumulative spacings distribution of the BC_N-type Polychronakos-Frahm chain using only a few essential properties of its spectrum such as the Gaussian character of the level density and the fact that the energy levels are equally spaced. This expression is shown to be in excellent agreement with the numerical data.
PB American Physical Society
SN 1098-0121
YR 2008
FD 2008-06
LK https://hdl.handle.net/20.500.14352/51490
UL https://hdl.handle.net/20.500.14352/51490
LA eng
NO ©2008 The American Physical Society.This work was partially supported by the DGI under Grant No. FIS2005-00752, and by Complutense University and the DGUI under Grant No. GR74/07-910556. J.C.B. acknowledges the financial support of the Spanish Ministry of Science and Innovation through an FPU scholarship.
NO DGI
NO Complutense University
NO DGU
NO Ministry of Science and Innovation, España
DS Docta Complutense
RD 6 abr 2025