Geodesic
Heisenberg $XX0$ chain and random walks on a ring
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 48-63

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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's 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. 
@article{ZNSL_2020_494_a2,
     author = {N. M. Bogoliubov and C. L. Malyshev},
     title = {Heisenberg $XX0$ chain and random walks on a ring},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {48--63},
     publisher = {mathdoc},
     volume = {494},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a2/}
}
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N. M. Bogoliubov; C. L. Malyshev. Heisenberg $XX0$ chain and random walks on a ring. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 48-63. http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a2/