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A new Polynomially Filtered Exact Diagonalization (POLFED) method offers improved memory efficiency for large quantum systems. This approach aids in studying the many-body localization transition in quantum spin chains.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • Exact diagonalization is a powerful method for studying quantum systems.
  • Large system sizes pose significant computational challenges, particularly in memory requirements.
  • Existing methods like shift-invert face limitations with increasing system size.

Purpose of the Study:

  • Introduce a novel Polynomially Filtered Exact Diagonalization (POLFED) method.
  • Develop an algorithm with improved memory scaling for large sparse matrices.
  • Apply POLFED to investigate the many-body localization transition in quantum systems.

Main Methods:

  • Developed POLFED, an algorithm utilizing spectral transformation with high-order matrix polynomials.
  • Analyzed memory requirements, demonstrating better scaling with system size compared to shift-invert.
  • Applied POLFED to 1D interacting quantum spin-1/2 chains to study many-body localization.

Main Results:

  • POLFED exhibits superior memory efficiency for large sparse matrices.
  • Investigated the scaling of Thouless time with disorder strength and system size.
  • Observed significant finite-size effects on bipartite entanglement entropy and gap ratio.

Conclusions:

  • POLFED is a promising computational tool for large quantum systems.
  • Finite-size effects are crucial for understanding the many-body localization transition.
  • Estimates for critical disorder strength in 1D spin chains were obtained.