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Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations.

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Summary
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This study introduces relaxation methods to efficiently map quantum phase transitions in condensed matter physics. These novel techniques accurately identify phase diagrams for quantum systems, advancing the study of quantum phase transitions.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Computational physics

Background:

  • Identifying quantum phase transitions is computationally demanding.
  • Existing methods struggle with scalability for large quantum systems.

Purpose of the Study:

  • To develop and demonstrate efficient relaxation methods for identifying quantum phase transitions.
  • To generate phase diagrams for one- and two-dimensional quantum systems.
  • To provide a scalable framework for studying quantum phase transitions.

Main Methods:

  • Formulating the ground-state problem as a solvable semidefinite program.
  • Utilizing a relaxed version of the ground-state problem.
  • Analyzing the vector of moments for different model parameters.
  • Employing cosine similarity to identify phase transitions.
  • Bounding observables to capture spontaneous symmetry breaking.

Main Results:

  • Successfully reproduced phase transitions for the 1D transverse field Ising model.
  • Generated phase diagrams for the 2D frustrated bilayer Heisenberg model.
  • Illustrated the impact of next-nearest-neighbor interactions on the 2D model's phase diagram.
  • Demonstrated the natural capture of spontaneous symmetry breaking.

Conclusions:

  • Relaxation methods offer a novel and efficient framework for studying quantum phase transitions.
  • The developed approach scales well with system size, overcoming limitations of previous methods.
  • This work provides a powerful new tool for condensed matter physics research.