Discrete quantum systems from topological field theory

2025/06/05 by Daniel S. Freed, Michael J. Hopkins, Freed, Daniel S. +3
Computer Science · Physics and Astronomy · #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.2506.05131

openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We introduce a technique to construct gapped lattice models using defects in topological field theory. We illustrate with 2+1 dimensional models, for example Chern-Simons theories. These models are local, though the state space is not necessarily a tensor product of vector spaces over the complex numbers. The Hamiltonian is a sum of commuting projections. We also give a topological field theory construction of Levin-Wen models.

Citations

• Topological symmetry in quantum field theory
• Wick rotation and the positivity of energy in quantum field theory
• Models for Gapped Boundaries and Domain Walls
• String-net condensation: A physical mechanism for topological phases
• On fusion categories
• Fault-tolerant quantum computation by anyons
• Invariants of 3-manifolds via link polynomials and quantum groups

Related

• Topological Quantum Computation with Gapped Boundaries and Boundary Defects
• Topological Defects on the Lattice: Dualities and Degeneracies
• Topological Quantum Field Theory: A Progress Report
• Topological Quantum Computation with Gapped Boundaries
• Topological quantum field theories