A continuum approximation for the excitations of the (1,1,...,1) interface in the quantum Heisenberg model
@inproceedings{Bolina1999ACA,
title={A continuum approximation for the excitations of the (1,1,...,1) interface in the quantum Heisenberg model},
author={Oscar Bolina and Pierluigi Contucci and Bruno Nachtergaele and Shannon Starr},
year={1999}
}It is shown that, with an appropriate scaling, the energy of low-lying excitations of the (1;1;:::;1) interface in the d-dimensional quantum Heisenberg model are given by the spectrum of the (d 1)-dimensional Laplacian on a suitable domain.
4 Citations
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References
SHOWING 1-6 OF 6 REFERENCES
On the Spectra of the Kink for Ferromagnetic XXZ Models
- Mathematics
- 1997
We consider the kink (infinite volume nontranslationally invariant ground states) of the ferromagnetic XXZ models on the multi-dimensional lattices. We obtained the following results: (i) The pure…
Finite-Volume Excitations of the¶111 Interface in the Quantum XXZ Model
- Physics
- 2000
Abstract: We show that the ground states of the three-dimensional XXZ Heisenberg ferromagnet with a 111 interface have excitations localized in a subvolume of linear size R with energies bounded by…
Ground states of the infinite q-deformed Heisenberg ferromagnet
- Mathematics, Physics
- 1995
We set up a general structure for the analysis of ``frustration-free ground states'', or ``zero-energy states'', i.e., states minimizing each term in a lattice interaction individually. The nesting…
Low-lying spectrum of quantum interfaces
- Abstracts of the AMS,
- 1996
Low-lying spectrum of quantum interfaces, Abstracts of the AMS
- Low-lying spectrum of quantum interfaces, Abstracts of the AMS
- 1996