# Hard-core magnons in the S=1/2 Heisenberg model on the square lattice

## Abstract

We propose a versatile approach to treat commonly arising constraints. It is illustrated for interacting magnons of the Heisenberg antiferromagnet on a square lattice. For systems of LxL sites a nonperturbative continuous unitary transformation (CUT) is used to derive an effective Hamiltonian conserving the number of magnons. They are bosonic particles with a hard-core constraint which is captured by a local, repulsive interaction U. The limits U{yields}{infinity} and L{yields}{infinity} are achieved by extrapolation. The residual spin gap {delta}{sub 1} is smaller than 0.01J reflecting the gapless nature of the magnons. The one-magnon dispersion displays all known characteristics.

- Authors:

- Institute of Theoretical Physics, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne (Switzerland)
- (Germany)

- Publication Date:

- OSTI Identifier:
- 20788152

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 17; Other Information: DOI: 10.1103/PhysRevB.73.172407; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; ANTIFERROMAGNETISM; BOSONS; EXTRAPOLATION; HAMILTONIANS; HEISENBERG MODEL; MAGNONS; SPIN; TRANSFORMATIONS

### Citation Formats

```
Schmidt, K. P., Uhrig, G. S., and Theoretische Physik, FR 7.1, Geb. E2.6, Universitaet des Saarlandes, D-66123 Saarbruecken.
```*Hard-core magnons in the S=1/2 Heisenberg model on the square lattice*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVB.73.1.

```
Schmidt, K. P., Uhrig, G. S., & Theoretische Physik, FR 7.1, Geb. E2.6, Universitaet des Saarlandes, D-66123 Saarbruecken.
```*Hard-core magnons in the S=1/2 Heisenberg model on the square lattice*. United States. doi:10.1103/PHYSREVB.73.1.

```
Schmidt, K. P., Uhrig, G. S., and Theoretische Physik, FR 7.1, Geb. E2.6, Universitaet des Saarlandes, D-66123 Saarbruecken. Mon .
"Hard-core magnons in the S=1/2 Heisenberg model on the square lattice". United States.
doi:10.1103/PHYSREVB.73.1.
```

```
@article{osti_20788152,
```

title = {Hard-core magnons in the S=1/2 Heisenberg model on the square lattice},

author = {Schmidt, K. P. and Uhrig, G. S. and Theoretische Physik, FR 7.1, Geb. E2.6, Universitaet des Saarlandes, D-66123 Saarbruecken},

abstractNote = {We propose a versatile approach to treat commonly arising constraints. It is illustrated for interacting magnons of the Heisenberg antiferromagnet on a square lattice. For systems of LxL sites a nonperturbative continuous unitary transformation (CUT) is used to derive an effective Hamiltonian conserving the number of magnons. They are bosonic particles with a hard-core constraint which is captured by a local, repulsive interaction U. The limits U{yields}{infinity} and L{yields}{infinity} are achieved by extrapolation. The residual spin gap {delta}{sub 1} is smaller than 0.01J reflecting the gapless nature of the magnons. The one-magnon dispersion displays all known characteristics.},

doi = {10.1103/PHYSREVB.73.1},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 17,

volume = 73,

place = {United States},

year = {Mon May 01 00:00:00 EDT 2006},

month = {Mon May 01 00:00:00 EDT 2006}

}

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