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

@inproceedings{Bombn2007ExactTQ,
title={Exact topological quantum order in D=3 and beyond : Branyons and brane-net condensates},
author={H{\'e}ctor Bomb́ın and Miguel Angel Mart{\'i}n-Delgado},
year={2007}
}
• Published 2007
• Physics
• We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ 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 upon the homology of the 3-manifold. We generalize the system to $D\geq 4$, were different topological phases may occur. The… CONTINUE READING

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 69 CITATIONS

• Physics
• 2013

• Physics
• 2009

## A new Hamiltonian for the topological BF phase with spinor networks

• Physics, Mathematics
• 2012
VIEW 1 EXCERPT
CITES BACKGROUND

## Topological color codes and two-body quantum lattice Hamiltonians

• Physics
• 2010
VIEW 2 EXCERPTS
CITES BACKGROUND

• Physics
• 2011

• Physics
• 2018

## Gauging permutation symmetries as a route to non-Abelian fractons

• Physics
• 2019
VIEW 1 EXCERPT
CITES METHODS

## Quantum robustness and phase transitions of the 3D Toric Code in a field

• Physics
• 2019
VIEW 1 EXCERPT
CITES BACKGROUND

• Physics
• 2016

## Topological order in an exactly solvable 3D spin model

• Physics
• 2011
VIEW 1 EXCERPT
CITES BACKGROUND

2008
2019

### CITATION STATISTICS

• 6 Highly Influenced Citations

• Averaged 6 Citations per year from 2018 through 2020