723 research outputs found
Commuting Pauli Hamiltonians as maps between free modules
We study unfrustrated spin Hamiltonians that consist of commuting tensor
products of Pauli matrices. Assuming translation-invariance, a family of Hamiltonians
that belong to the same phase of matter is described by a map between modules over
the translation-group algebra, so homological methods are applicable. In any dimension
every point-like charge appears as a vertex of a fractal operator, and can be isolated with
energy barrier at most logarithmic in the separation distance. For a topologically ordered
system in three dimensions, there must exist a point-like nontrivial charge. A connection
between the ground state degeneracy and the number of points on an algebraic set is
discussed. Tools to handle local Clifford unitary transformations are given
- ā¦