Year: 2019
Type: preprint
Abstract: We formalize and generalize the concept of a topological state-sum construction using the language of tensor networks. We give examples for constructions that are possibly more general than all state-sum constructions in the literature that we are aware of. In particular we propose a state-sum construction that is universal in the sense that it can emulate every other state-sum construction. Physically, state-sum models in $n$ dimensions correspond to fixed point models for topological phases of matter in $n$ space-time dimensions. We conjecture that our universal state-sum construction contains fixed point models for topological phases that are not captured by known constructions. In particular we demonstrate that, unlike common state-sum constructions, the construction is compatible with the absence of gapped boundaries and commuting-projector Hamiltonians in $2+1$-dimensional chiral topological phases.
Source: arXiv (Cornell University)
Author: Bauer, Andreas
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2971757005