Abstract
One-dimensional quantum spin systems with short-range interaction are strongly fluctuating many-body systems under most circumstances. Any spontaneous magnetic long-range order (LRO) that might exist in the ground state is destabilized by thermal fluctuations at all nonzero temperatures no matter how small. Even at T=0 the order parameter is, in general, considerably reduced by correlated quantum fluctuations. It is not unusual that the zero-point motion prevents the onset of magnetic ordering entirely and gives rise to a ground state that is either critical or magnetically disordered.
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References
These relationships have been described, for example, in the work of Coleman [1975], Luther [1976], Bergknoff and Thacker [1979], Dashen, Hasslacher, and Neuveu [1975].
Bethe [1931] proposed a representation for the eigenfunctions of the s=1/2 Heisenberg model (|△|=1) which enabled him to classify all 2N eigenstates in terms of a discrete set of quantum numbers, and to give a prescription for calculating the eigenfunctions, energies, and wave numbers in terms of the solutions of a set of coupled nonlinear equations. Bethe’s ansatz was later generalized by Orbach [1958], Des Cloizeaux and Gaudin [1966], and Yang and Yang [1966] to the XXZ model in its entire parameter range.
For △<0, a pole below the 2-particle continuum leads to the prediction of a spurious branch of bound states in the Hartree-Fock approximation. This shortcoming was pointed out by Schneider, Stoll, and Glaus [1982].
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© 1994 Springer-Verlag Berlin Heidelberg
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(1994). Quantum Spin Dynamics at Zero Temperature. In: The Recursion Method. Lecture Notes in Physics Monographs, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48651-0_11
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DOI: https://doi.org/10.1007/978-3-540-48651-0_11
Publisher Name: Springer, Berlin, Heidelberg
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