# Quantum symmetries of quantum spin systems

> **NSF 01002627DB NSF RESEARCH & RELATED ACTIVIT** · OHIO STATE UNIVERSITY, THE (OH) · $300,000

## Abstract

Symmetry is a fundamental tool to understand physical and mathematical systems. Classically, symmetries of a system are captured by a collection of invertible self-maps called a group. Collections of certain quantum mathematical objects naturally form higher categories, and thus they admit richer collections of non-invertible or quantum symmetries. Examples of such quantum mathematical objects include algebras of quantum observables and quantum spin systems, which are mathematical models of pieces of matter, where atomic degrees of freedom are represented by local Hilbert spaces. Topologically ordered quantum spin systems give local quantum error correction codes for quantum computation. The main goal of this project is to use techniques from operator algebras and higher category theory to study the quantum symmetries of topologically ordered quantum spin systems. This project also funds research training for both graduate and undergraduate students.

This project has three main focuses. First, the PI will develop the operator algebra approach to topologically ordered quantum spin systems, using nets of von Neumann algebras to study superselection sectors. The PI will also make connections between superselection theory for topological order and the quantum information theoretic boundary algebra approach to topological order. Second, the PI will make rigorous connections between higher category theory and topologically ordered quantum spin systems by both developing new high

## Key facts

- **NSF award ID:** 2554723
- **Awardee organization:** OHIO STATE UNIVERSITY, THE (OH)
- **SAM.gov UEI:** DLWBSLWAJWR1
- **PI:** David S Penneys
- **Primary program:** 01002627DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** QUANTUM INFORMATION SCIENCE
- **Estimated total:** $300,000
- **Funds obligated:** $300,000
- **Transaction type:** Standard Grant
- **Period:** 06/15/2026 → 05/31/2029

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2554723

## Citation

> US National Science Foundation, Award 2554723, Quantum symmetries of quantum spin systems. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2554723. Licensed CC0.

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