Spin quantum number in the ground state of the Mattis-Heisenberg model

We suggest a general rule for the shift quantum numbers k of the relative ground states of antiferromagnetic Heisenberg spin rings. This rule generalizes the well-known results of Marshall, Peierls, Lieb, Schultz, and Mattis for even rings. Our rule is confirmed by numerical investigations and rigorous proofs for special cases, including systems with a Haldane gap for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}.$ Implications for the total spin quantum number S of relative ground states are discussed as well as generalizations to the XXZ model.We suggest a general rule for the shift quantum numbers k of the relative ground states of antiferromagnetic Heisenberg spin rings. This rule generalizes the well-known results of Marshall, Peierls, Lieb, Schultz, and Mattis for even rings. Our rule is confirmed by numerical investigations and rigorous proofs for special cases, including systems with a Haldane gap for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}.$ Implications for the total spin quantum number S of relative ground states are discussed as well as generalizations to the XXZ model.

arXiv:cond-mat/0303386Physical review. B, Condensed matterAug 26, 200353 citations

Ground States of the Heisenberg Model

Assa Auerbach

Graduate texts in contemporary physicsJan 1, 19942 citations

Ground States in the Spin Boson Model

David Hasler, Ira Herbst

arXiv:1003.5923Annales Henri PoincaréMar 9, 201146 citations

Ground-State Phase Diagram of the Two-Dimensional Quantum Heisenberg Mattis Model

Yoshihiko Nonomura

The two-dimensional $S=1/2$ asymmetric Heisenberg Mattis model is investigated with the exact diagonalization of finite clusters. The Néel order parameter and the spin glass order parameter can be smoothly extrapolated to the thermodynamic limit in the antiferromagnetic region, as in the pure Heisenberg antiferromagnet. The critical concentration of the Néel phase is consistent with that of the two-dimensional Ising Mattis model, and the spin glass order parameter increases monotonously as the ferro-bond concentration increases. These facts suggest that quantum fluctuation does not play an essential role in two-dimensional non-frustrated random spin systems. KEYWORDS: quantum spin system, ground state, randomness, Mattis model, Néel order, spin glass orderThe two-dimensional $S=1/2$ asymmetric Heisenberg Mattis model is investigated with the exact diagonalization of finite clusters. The Néel order parameter and the spin glass order parameter can be smoothly extrapolated to the thermodynamic limit in the antiferromagnetic region, as in the pure Heisenberg antiferromagnet. The critical concentration of the Néel phase is consistent with that of the two-dimensional Ising Mattis model, and the spin glass order parameter increases monotonously as the ferro-bond concentration increases. These facts suggest that quantum fluctuation does not play an essential role in two-dimensional non-frustrated random spin systems. KEYWORDS: quantum spin system, ground state, randomness, Mattis model, Néel order, spin glass order

arXiv:cond-mat/9512144Journal of the Physical Society of JapanFeb 15, 19962 citations

The two-dimensional

S=1/2

asymmetric Heisenberg Mattis model is investigated with the exact diagonalization of finite clusters. The Néel order parameter and the spin glass order parameter can be smoothly extrapolated to the thermodynamic limit in the antiferromagnetic region, as in the pure Heisenberg antiferromagnet. The critical concentration of the Néel phase is consistent with that of the two-dimensional Ising Mattis model, and the spin glass order parameter increases monotonously as the ferro-bond concentration increases. These facts suggest that quantum fluctuation does not play an essential role in two-dimensional non-frustrated random spin systems. KEYWORDS: quantum spin system, ground state, randomness, Mattis model, Néel order, spin glass order