Heisenberg XX0 Chain and Random Walks on a Ring

We obtain and investigate mean values of the exponential of the centroid operator for the periodic Heisenberg XX0 chain on a ring. The generating function of directed lattice paths is obtained in terms of circulant matrices which leads to generalizations of the Ramus identity. The two-time correlati...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-06, Vol.264 (3), p.232-243
Main Authors: Bogoliubov, N. M., Malyshev, C. L.
Format: Article
Language:English
Subjects:
Centroids
Chains
Mathematics
Mathematics and Statistics
Operators (mathematics)
Random walk
Time correlation functions
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Summary:We obtain and investigate mean values of the exponential of the centroid operator for the periodic Heisenberg XX0 chain on a ring. The generating function of directed lattice paths is obtained in terms of circulant matrices which leads to generalizations of the Ramus identity. The two-time correlation function of the exponential of the centroid operator is expressed in terms of the Cauchy determinant and thus explicitly calculated.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05994-7