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Generating Generalized Ground-State Ansätze from Few-Body Examples.

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We developed a new method using symbolic language and evolutionary algorithms to create accurate and analytically solvable quantum many-body ground-state Ansätze. This approach ensures scalability and captures essential system properties for diverse models.

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Area of Science:

  • Quantum physics
  • Computational physics
  • Condensed matter theory

Background:

  • Accurate ground-state Ansätze are crucial for understanding quantum many-body systems.
  • Existing methods often struggle with analytical tractability or scalability.
  • Developing versatile and efficient Ansätze remains a key challenge.

Purpose of the Study:

  • To introduce a novel method for generating ground-state Ansätze for quantum many-body systems.
  • To ensure these Ansätze are both analytically tractable and accurate across wide parameter ranges.
  • To develop Ansätze that automatically scale with system size.

Main Methods:

  • Utilizing a custom symbolic language to construct tensor network states.
  • Employing an evolutionary algorithm to generate and optimize Ansätze.
  • Evaluating Ansatz fitness on small systems to predict performance for larger systems.
  • Demonstrating the method on the Lipkin-Meshkov-Glick and quantum transverse-field Ising models.

Main Results:

  • Generated analytically tractable Ansätze with universal properties.
  • Ansätze successfully encode correlations and capture finite-size effects.
  • Accurate prediction of ground-state energies and description of critical phenomena.
  • Identified a single Ansatz applicable to both tested models.
  • Obtained exact expressions for expectation values and correlation functions.

Conclusions:

  • The developed method provides a systematic way to generate accurate and scalable ground-state Ansätze.
  • The generated Ansätze exhibit universality and offer insights into quantum system behavior.
  • Restoring broken symmetries offers a pathway for systematically improving Ansatz accuracy.