Tensor-product representations for string-net condensed states

2008/09/16 by Zheng‐Cheng Gu, Zheng-Cheng Gu, Michael Levin +2 · 1 voice · 1 citation
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Parallel Computing and Optimization Techniques #Quantum many-body systems #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.79.085118

published as Phys. Rev. B 79, 085118 (2009) · 11 pages. RevTeX4

arxiv created 2008/09/16 · arxiv published 2008/09/16 · openalex publication_date 2009/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's 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 TPS's are fixed-points under a certain wave-function renormalization group transformation for quantum states.

Citations

• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topologically protected quantum bits using Josephson junction arrays
• Criticality, the area law, and the computational power of PEPS
• Ground States of Quantum Antiferromagnets in Two Dimensions
• String-net condensation: A physical mechanism for topological phases
• Deconfined Quantum Critical Points
• Fault-tolerant quantum computation by anyons

Cited by

• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to p-String Condensation

Discussions

• It's a matter of convention. Typically though, it's conventional to use upper indices for the physical degrees of freedom, and lower indices for the virtual (see for example section II of this paper h [stackexchange, 3 points]

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