Geodesic
Semi-infinite Heisenberg XX0 chain and random walks
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 91-108 Cet article a éte moissonné depuis la source Math-Net.Ru

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Heisenberg XX0 chain on semi-infinte interval enables modelling of random walks restricted by presence of impenetrable wall. The state vectors of the Hamiltonian are represented in terms of symplectic Schur functions. The transition amplitudes of the model are obtained in the integral form and are estimated in the case of unlimited increasing of the number of steps of random walks. 
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N. M. Bogoliubov; C. L. Malyshev. Semi-infinite Heisenberg XX0 chain and random walks. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 91-108. http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a3/

[1] E. Lieb, T. Schultz, D. Mattis, “Two soluble models of an antiferromagnetic chain”, Ann. Physics, 16 (1961), 407–466 | DOI | MR | Zbl

[2] F. Colomo, A. G. Izergin, V. E. Korepin, V. Tognetti, “Correlators in the Heisenberg XX0 chain as Fredholm determinants”, Phys. Lett. A, 169 (1992), 243–247 | DOI | MR

[3] D. Pérez-García, M. Tierz, “Mapping between the Heisenberg XX spin chain and low-energy QCD”, Phys. Rev. X, 4 (2014), 021050

[4] M. Saeedian, A. Zahabi, “Phase structure of XX0 spin chain and nonintersecting Brownian motion”, J. Stat. Mech. Theory Exp., 2018 (2018), 013104 | DOI | MR | Zbl

[5] M. Saeedian, A. Zahabi, “Exact solvability and asymptotic aspects of generalized XX0 spin chains”, Phys. A, 549 (2020), 124406 | DOI | MR | Zbl

[6] L. Santilli, M. Tierz, “Phase transition in complex-time Loschmidt echo of short and long range spin chain”, J. Stat. Mech. Theory Exp., 2020 (2020), 063102 | DOI | MR | Zbl

[7] N. M. Bogoliubov, “XX0 Heisenberg chain and random walks”, J. Math. Sci., 138 (2006), 5636–5643 | DOI | MR

[8] N. M. Bogoliubov, C. Malyshev, “Correlation functions of the $XX$ Heisenberg magnet and random walks of vicious walkers”, Theor. Math. Phys., 159 (2009), 563–574 | DOI | MR | Zbl

[9] N. M. Bogoliubov, A. G. Pronko, J. Timonen, “Multiple-grain dissipative sandpiles”, J. Math. Sci., 190 (2013), 411–418 | DOI | MR | Zbl

[10] N. M. Bogoliubov, C. Malyshev, “Correlation functions of $XX0$ Heisenberg chain, $q$-binomial determinants, and random walks”, Nucl. Phys. B, 879 (2014), 268–291 | DOI | MR | Zbl

[11] N. M. Bogoliubov, C. Malyshev, “The integrable models and combinatorics”, Russ. Math. Surveys, 70 (2015), 789–856 | DOI | MR | Zbl

[12] N. Bogoliubov, C. Malyshev, “How to Draw a Correlation Function”, SIGMA, 17 (2021), 106 | MR | Zbl

[13] N. M. Bogoliubov, C. L. Malyshev, “Heisenberg XX0 Chain and Random Walks on a Ring”, J Math Sci., 264 (2022), 232–243 | DOI | MR | Zbl

[14] C. Malyshev, N. Bogoliubov, “Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions”, J. Phys. A: Math. Theor., 55 (2022), 225002 | DOI | MR | Zbl

[15] C. Malyshev, “Condition of quasi-periodicity in imaginary time as a constraint at functional integration and the time-dependent ZZ-correlator of the XX Heisenberg magnet”, J. Math. Sci., 136 (2006), 3607–3624 | DOI | MR

[16] M. E. Fisher, “Walks, walls, wetting and melting”, J. Stat. Phys., 34 (1984), 667–729 | DOI | MR

[17] R. Gopakumar, D. Gross, “Mastering the master field”, Nucl. Phys. B, 451 (1995), 379–415 | DOI | MR | Zbl

[18] N. M. Bogoliubov, “Boxed plane partitions as an exactly solvable boson model”, J. Phys. A, 38 (2005), 9415–9430 | DOI | MR | Zbl

[19] V. Fock, “Konfigurationsraum und zwiete Quantelung”, Zs. f. Phys., 75 (1932), 622–647 | DOI | Zbl

[20] R. C. King, “Weight multiplicities for the classical groups”, Group Theoretical Methods in Physics, Springer, Berlin–Heidelberg, 1976 | MR

[21] C. Krattenthaler, A. J. Guttmann, X. G. Viennot, “Vicious walkers, friendly walkers and Young tableaux: II With a wall”, J. Phys. A: Math. Gen., 33 (2000), 8835–8866 | DOI | MR | Zbl

[22] R. A. Proctor, “New symmetric plane partitions identities from invariant theory work of De Concini and Procesi”, Europ. J. Combin., 11 (1990), 289–300 | DOI | MR | Zbl

[23] M. Fulmek, Ch. Krattenthaler, “Lattice path proofs for determinantal formulas for symplectic and orthogonal characters”, J. Combin. Theory, Ser. A, 77 (1997), 3–50 | DOI | MR | Zbl

[24] M. L. Mehta, Random Matrices, Academic, New York, 1991 | MR | Zbl

[25] I. G. Mcdonald, Symmetric functions and Hall polynomials, Clarendon Press, Oxford, 1995 | MR

[26] R. Stanley, Enumerative Combinatorics, v. 2, Cambridge University Press, Cambridge, 1999 | MR