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This article is cited in 3 scientific papers (total in 3 papers)
Eigenvectors of the Baxter–Bazhanov–Stroganov $\tau^{(2)}(t_q)$
model with fixed-spin boundary conditions
N. Z. Iorgov, V. N. Shadura, Yu. V. Tykhyy N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine
Abstract:
We give explicit formulas for the eigenvectors of the transfer matrix of
the Baxter–Bazhanov–Stroganov {(}BBS{\rm)} model {\rm(}$N$-state spin
model{)} with fixed-spin boundary conditions. We obtain these formulas
from the formulas for the eigenvectors of the periodic BBS model by
a limit procedure. The latter formulas were derived in the framework of
Sklyanin's method of separation of variables. In the case of fixed-spin
boundaries, we solve the corresponding $T$–$Q$ Baxter equations for
the functions of separated variables explicitly. As a particular case, we obtain
the eigenvectors of the Hamiltonian of the Ising-like $\mathbb{Z}_N$ quantum
chain model.
Keywords:
integrable quantum chain, fixed boundary conditions, method of separation of variables.
Received: 31.03.2008
Citation:
N. Z. Iorgov, V. N. Shadura, Yu. V. Tykhyy, “Eigenvectors of the Baxter–Bazhanov–Stroganov $\tau^{(2)}(t_q)$
model with fixed-spin boundary conditions”, TMF, 155:1 (2008), 94–108; Theoret. and Math. Phys., 155:1 (2008), 585–597
Linking options:
https://www.mathnet.ru/eng/tmf6195https://doi.org/10.4213/tmf6195 https://www.mathnet.ru/eng/tmf/v155/i1/p94
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