Tensor-product representations for string-net condensed states
By Z. Gu, Michael Levin, Brian Swingle, X. Wen. 2008
133 citations recorded by the source corpus.
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPSs). These TPSs are built from local tensors. They can describe both states with short-range entanglement (such as the symmetry-breaking states) and states with long-range entanglement (such as string-net condensed states with topological/quantum order). The tensor product representation provides a kind of ``mean-field'' description for topologically ordered states and could be a powerful way to study quantum phase transitions between such states. As an attempt in this direction, we show that the constructed TPSs are fixed points under a certain wave-function renormalization-group transformation for quantum states.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Hardware and Architecture
View Paper: https://www.semanticscholar.org/paper/0e66abf33b20e1629baff7efa07f865cbcde89d1
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Efficient representation of quantum many-body states with deep neural networks (2017, unknown): “For the toric code, the correlation function g(v1, v2, v3, v4) = (v1 + v2 + v3 + v4 mod 2) on each vertex and the wave function is a product of these functions over all vertices [31].”
- Measurement as a Shortcut to Long-Range Entangled Quantum Matter (2022, methodology): “|DS〉 admits an exact tensor-network representations [35, 36] (see Fig.”
- Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “The Tensor Trace operator performs the summation of all inner indices of the tensor (Gu et al., 2009).”