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Related Experiment Videos

Ground state fidelity from tensor network representations.

Huan-Qiang Zhou1, Roman Orús, Guifre Vidal

  • 1Department of Physics, Chongqing University, Chongqing 400044, The People's Republic of China.

Physical Review Letters
|March 21, 2008
PubMed
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Quantum system fidelity is mapped to classical statistical models. This allows characterizing quantum phase diagrams using fidelity per site calculations with tensor network algorithms, demonstrated on the 2D quantum Ising model.

Area of Science:

  • Quantum many-body physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Fidelity quantifies the distinguishability between quantum states.
  • Ground state properties are crucial for understanding quantum phases.
  • Classical statistical models provide a framework for analyzing phase transitions.

Purpose of the Study:

  • To establish a mapping between quantum system fidelity and classical statistical models.
  • To introduce fidelity per site as a tool for quantum phase diagram characterization.
  • To demonstrate the computational feasibility using tensor network algorithms.

Main Methods:

  • Mapping the fidelity of D-dimensional quantum lattice ground states to D-dimensional classical statistical vertex lattice models.

Related Experiment Videos

  • Utilizing tensor network algorithms for computing fidelity per site.
  • Analyzing the two-dimensional quantum Ising model as a test case.

    • Main Results:

    • A direct correspondence is established between quantum fidelity and classical partition functions.
    • Fidelity per site is shown to be a well-defined thermodynamic quantity.
    • The phase diagram of the 2D quantum Ising model was analyzed using this fidelity-based approach.

    Conclusions:

    • The fidelity-based mapping provides a powerful new method for studying quantum phase transitions.
    • Tensor network algorithms are effective for calculating fidelity per site.
    • This approach offers insights into the relationship between quantum and classical statistical mechanics.