Valence Bond Ground States in Isotropic Quantum Antiferromagnets
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TLDR
The first rigorous example of an isotropic model in such a phase is presented in this paper, where the Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but the model has a unique ground state and exponential decay of the correlation functions in the ground state.Abstract:
Haldane predicted that the isotropic quantum Heisenberg spin chain is in a “massive” phase if the spin is integral. The first rigorous example of an isotropic model in such a phase is presented. The Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but we prove the model has a unique ground state, a gap in the spectrum of the Hamiltonian immediately above the ground state and exponential decay of the correlation functions in the ground state. Models in two and higher dimension which are expected to have the same properties are also presented. For these models we construct an exact ground state, and for some of them we prove that the two-point function decays exponentially in this ground state. In all these models exact ground states are constructed by using valence bonds.read more
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References
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The resonating valence bond state in La2CuO4 and superconductivity
TL;DR: The oxide superconductors, particularly those recently discovered that are based on La2CuO4, have a set of peculiarities that suggest a common, unique mechanism: they tend in every case to occur near a metal-insulator transition into an odd-electron insulator with peculiar magnetic properties.