Holographic State Complexity from Group Cohomology
High Energy Physics - Theory
2022-01-10 v2
Abstract
Topological phases of matter are often described using auxiliary systems in one extra dimension. I review the one-dimensional cluster state--the simplest quantum state with Symmetry-Protected Topological (SPT) order--as a toy model of holographic duality, and inspect it for clues about defining holographic complexity. Group cohomology, which classifies SPT orders, is a viable candidate for a robust definition of complexity in gauge/gravity duality.
Keywords
Cite
@article{arxiv.2201.01303,
title = {Holographic State Complexity from Group Cohomology},
author = {Bartlomiej Czech},
journal= {arXiv preprint arXiv:2201.01303},
year = {2022}
}
Comments
5 pages plus references, 4 figures; contribution to Proceedings of the 2021 Nankai Symposium on Mathematical Dialogues. v2: one typo, which persists in two equations, fixed