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We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan et al., and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states. 相似文献
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We study the antiferromagnetic spin-1/2 Heisenberg model on the highly frustrated, three-dimensional, hyperkagome lattice of Na(4)Ir(3)O(8) using a series expansion method. We propose a valence bond crystal with a 72 site unit cell as a ground state that supports many, very low lying, singlet excitations. Low energy spinons and triplons are confined to emergent lower-dimensional motifs. Here, and for analogous kagome and pyrochlore states, we suggest finite temperature signatures, including an Ising transition, in the magnetic specific heat due to a multistep breaking of discrete symmetries. 相似文献
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BłAŻEJ JAN WRÓBEL 《Proceedings Mathematical Sciences》2011,121(1):45-75
We examine weighted L
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boundedness of g-functions based on semigroups related to multi-dimensional Laguerre function expansions of Hermite type. A technique of vector-valued
Calderón–Zygmund operators is used. 相似文献
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