Ground State Fidelity from Tensor Network Representations

2007/09/30 by Huan-Qiang Zhou, Román Orús, Roman Orus +2 · 5 citations
Mathematics · Physics and Astronomy · #Model Reduction and Neural Networks #Quantum many-body systems #Tensor decomposition and applications #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.100.080601

published as Physical Review Letters 100, 080601 (2008) · 4 pages, 2 figures. Published version in Physical Review Letters

openalex publication_date 2008/02/28 · arxiv created 2008/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields.

Citations

• Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective
• Diverging Entanglement Length in Gapped Quantum Spin Systems

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