Abstract
It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin-\(\frac{1}{2}\) spin-1 ladder, a mixed spin-\(\frac{1}{2}\) spin-\({\frac{3}{2}}\) ladder and a spin-1 ladder with biquadratic interactions.
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REFERENCES
R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
V. Yu Popkov and A. A. Zvyagin, “Antichiral” exactly solvable effectively two-dimensional quantum spin model, Phys. Lett. A 175:295–298 (1993).
H. Frahm and C. Rödenbeck, Integrable models of coupled Heisenberg chains, Europhys. Lett. 33:47–52 (1996).
S. Albeverio, S.-M. Fei, and Y. Wang, An exactly solvable model of generalized spin ladder, Europhys. Lett. 47:364–370 (1999).
Y. Wang, Exact solution of a spin-ladder model, Phys. Rev. B 60:9236–9239 (1999).
N. Muramoto and M. Takahashi, Integrable magnetic model of two chains coupled by four-body interactions, J. Phys. Soc. Japan 68:2098–2104 (1999).
M. T. Batchelor and M. Maslen, Exactly solvable quantum spin tubes and ladders, J. Phys. A 32:L377–L380 (1999).
M. T. Batchelor and M. Maslen, Ground state energy and mass gap of a generalized quantum spin ladder, J. Phys. A 33:443–448 (2000).
H. Fan, The fermion-ladder models: extensions of the Hubbard model with η-pairing, J. Phys. A 32:L509–L514 (1999).
H. Frahm and A. Kundu, Phase diagram of an exactly solvable t-J ladder model, J. Phys. Condens. Matter 11:L557–L562 (1999).
M. T. Batchelor, J. de Gier, J. Links, and M. Maslen, Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras, J. Phys. A 33: L97–L101 (2000).
J. Links and A. Foerster, Solution of a two-leg spin ladder system, Phys. Rev. B 62:65–68 (2000).
A. K. Kolezhuk and H.-J. Mikeska, Finitely correlated generalized spin ladders, Int. J. Mod. Phys. B 12:2325–2348 (1998).
A. Honecker, F. Mila, and M. Troyer, Magnetization plateaux and jumps in a class of frustrated ladders: A simple route to a complex behaviour, Eur. Phys. J. B 15:227–234 (2000).
E. Dagotto and T. M. Rice, Surprises on the way from one-to two-dimensional quantum magnets: The ladder materials, Science 271:618–623 (1996).
E. Dagotto, Experiments on ladders reveal a complex interplay between a spin-gapped normal state and superconductivity, Rep. Prog. Phys. 62:1525–1572 (1999).
A. A. Nersesyan and A. M. Tsvelik, One-dimensional spin-liquid without magnon excitations, Phys. Rev. Lett. 78:3939–3942 (1997).
O. Legeza, G. Fáth, and J. Sólyom, Phase diagram of magnetic ladders constructed from a composite-spin model, Phys. Rev. B 55:291–298 (1997).
J. de Gier, M. T. Batchelor, and M. Maslen, Phase diagram of the su(8) quantum spin tube, Phys. Rev. B 61:15196–15202 (2000).
J. de Gier and M. T. Batchelor, Magnetization plateaus in a solvable 3–leg spin ladder, Phys. Rev. B 62:R3584–R3587 (2000).
M. Oshikawa, M. Yamanaka, and I. Affleck, Magnetization plateaus in spin chains: “Haldane gap” for half-integer spins, Phys. Rev. Lett. 78:1984–1987 (1997).
D. C. Cabra, A. Honecker, and P. Pujol, Magnetization plateaux in N-leg spin ladders, Phys. Rev. B 58:6241–6257 (1998).
B. Sutherland, Model for a multicomponent quantum system, Phys. Rev. B 12:3795–3805 (1975).
R. J. Baxter, Colorings of the hexagonal lattice, J. Math. Phys. 11:784–789 (1970).
G. V. Uimin, One-dimensional problem for S = 1 with modified antiferromagnetic Hamiltonian, JETP Lett. 12:225–228 (1970).
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Batchelor, M.T., de Gier, J. & Maslen, M. Exactly Solvable su(N) Mixed Spin Ladders. Journal of Statistical Physics 102, 559–566 (2001). https://doi.org/10.1023/A:1004886500083
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DOI: https://doi.org/10.1023/A:1004886500083