Detecting topological order in a ground state wave function.
By Michael Levin, X. Wen. Physical Review Letters, 2005
1,681 citations recorded by the source corpus.
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).
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/1740360b10784fc3937a19c2ae55c0b6cec4edbc
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
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- Entanglement entropy and nonabelian gauge symmetry (2014, background): “In condensed matter theory, the entanglement entropy has been shown to contain useful universal information characterizing topological phases of matter [7, 8].”
- Fracton Models on General Three-Dimensional Manifolds (2017, background): “The subleading linear correction to entanglement entropy for the X-cube model, thus, corresponds to a combination of the constant topological corrections present in toric code ground states [34,35].”
- Quantum coherence and geometric quantum discord (2017, background): “Additionally, the topological entanglement entropy and entanglement spectrum are studied based on the theory of entanglement (Hamma et al., 2005; Kitaev and Preskill, 2006; Levin and Wen, 2006; Li and Haldane, 2008).”
- Neural-Network Quantum States, String-Bond States, and Chiral Topological States (2017, background): “The topological entanglement entropy is then defined as[85, 86]”
- On the architecture of spacetime geometry (2012, background): “Entanglement entropy has emerged as a useful measure of entanglement which can be used to characterize the correlations in a quantum system [6].”
- Exact results for the entanglement entropy and the energy radiated by a quark (2013, methodology): “Here T = 0 and the entanglement entropy is just given by the Wilson loop expectation value [2, 3].”
- Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids (2008, methodology): “Since S0 = 1/D, we recover the known result [13, 14] for the topological entropy for a simply connected region of a sphere S2 (or a disk) in terms of”
- Holographic entanglement entropy: an overview (2009, background): “Thus, our holographic approach which can be applied to strongly coupled theories will provide a powerful complementary method.”
- Provably efficient machine learning for quantum many-body problems (2021, background): “This includes local order parameters for classifying symmetry-breaking phases and topological entanglement entropy in a sufficiently large local region for partially classifying topological phases (57, 58).”
- A covariant holographic entanglement entropy proposal (2007, background): “Recently, entanglement entropies of various 1+1 and 2+1 dimensional condensed matter systems have been actively investigated in order to understand zero temperature quantum phase transitions [11, 4, 12, 13, 14].”
- Quantum Information Meets Quantum Matter (2015, background): “The word ‘entanglement’ was first mentioned by Schrödinger in 1935 [15], where he described a famous cat that is unfortunately”
- Black holes and the butterfly effect (2013, methodology): “Entropy of entanglement of the ground state can be used as a diagnostic of topological order in gapped quantum systems [1, 2].”