# Exact topological quantum order in D=3 and beyond: Branyons and brane-net condensates

## Abstract

We construct an exactly solvable Hamiltonian acting on a three-dimensional lattice of spin-(1/2) systems that exhibits topological quantum order. The ground state is a string net and a membrane-net condensate. Excitations appear in the form of quasiparticles and fluxes, as the boundaries of strings and membranes, respectively. The degeneracy of the ground state depends on the homology of the 3-manifold. We generalize the system to D{>=}4, where different topological phases may occur. The whole construction is based on certain special complexes that we call colexes.

- Authors:

- Departamento de Fisica Teorica I, Universidad Complutense, 28040 Madrid (Spain)

- Publication Date:

- OSTI Identifier:
- 20976696

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevB.75.075103; (c) 2007 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; BRANES; CONDENSATES; EXACT SOLUTIONS; EXCITATION; GROUND STATES; HAMILTONIANS; LATTICE FIELD THEORY; MEMBRANES; QUASI PARTICLES; SPIN; STRING MODELS; STRING THEORY; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY

### Citation Formats

```
Bombin, H., and Martin-Delgado, M. A.
```*Exact topological quantum order in D=3 and beyond: Branyons and brane-net condensates*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVB.75.075103.

```
Bombin, H., & Martin-Delgado, M. A.
```*Exact topological quantum order in D=3 and beyond: Branyons and brane-net condensates*. United States. doi:10.1103/PHYSREVB.75.075103.

```
Bombin, H., and Martin-Delgado, M. A. Thu .
"Exact topological quantum order in D=3 and beyond: Branyons and brane-net condensates". United States.
doi:10.1103/PHYSREVB.75.075103.
```

```
@article{osti_20976696,
```

title = {Exact topological quantum order in D=3 and beyond: Branyons and brane-net condensates},

author = {Bombin, H. and Martin-Delgado, M. A.},

abstractNote = {We construct an exactly solvable Hamiltonian acting on a three-dimensional lattice of spin-(1/2) systems that exhibits topological quantum order. The ground state is a string net and a membrane-net condensate. Excitations appear in the form of quasiparticles and fluxes, as the boundaries of strings and membranes, respectively. The degeneracy of the ground state depends on the homology of the 3-manifold. We generalize the system to D{>=}4, where different topological phases may occur. The whole construction is based on certain special complexes that we call colexes.},

doi = {10.1103/PHYSREVB.75.075103},

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

number = 7,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

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