Detecting Topological Order in a Ground State Wave Function

2005/10/31 by Michael Levin, Xiao-Gang Wen · 74 citations
Mathematics · Physics and Astronomy · #Combinatorics #Function (biology) #Ground state #Mathematics #Model Reduction and Neural Networks #Order (exchange) #Physics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Statistical physics #Topology (electrical circuits) #Wave function #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.96.110405

published as Phys. Rev. Lett., 96, 110405 (2006) · 4 pages, 5 figures, homepage http://dao.mit.edu/~wen

openalex publication_date 2006/03/24 · arxiv created 2007/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, di, F(lmn)(ijk), delta(ijk). We describe a way to detect this kind of topological order using only the ground state wave function. The method involves computing a quantity called the "topological entropy" which directly measures the total quantum dimension D= Sum(id2i).

Citations

• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
• Bipartite entanglement and entropic boundary law in lattice spin systems
• String-net condensation: A physical mechanism for topological phases
• Fault-tolerant quantum computation by anyons

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• Topological order [wikipedia]