# 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

### Interfaces and droplets in quantum lattice models

- Physics
- 2000

This paper is a short review of recent results on interface states in the Falicov-Kimball model and the ferromagnetic XXZ Heisenberg model. More specifically, we discuss the following topics: 1) The…

### Instability of Interfaces in the Antiferromagnetic XXZ Chain at Zero Temperature

- Physics
- 2003

Abstract: For the antiferromagnetic, highly anisotropic XZ and XXZ quantum spin chains, we impose periodic boundary conditions on chains with an odd number of sites to force an interface (or kink)…

### Asymmetric Diffusion and the Energy Gap Above¶the 111 Ground State of the Quantum XXZ Model

- Mathematics
- 2002

Abstract: We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an…

### The spectral gap for the ferromagnetic spin-J XXZ chain

- Mathematics
- 2001

We investigate the spectrum above the kink ground states of the spin J ferromagnetic XXZ chain. Our main theorem is that there is a non-vanishing gap above all ground states of this model for all…

## 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