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Krylov-Projected Quantum Monte Carlo Method.

N S Blunt1, Ali Alavi1, George H Booth1

  • 1University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom; Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany; and Department of Physics, King's College London, The Strand, London WC2R 2LS, United Kingdom.

Physical Review Letters
|August 15, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a novel quantum Monte Carlo method for calculating spectral and thermal properties. The approach enables accurate computation of excited states and avoids complex analytic continuation for Hubbard models and ab initio systems.

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Area of Science:

  • Quantum many-body physics
  • Computational chemistry
  • Condensed matter physics

Background:

  • Full configuration interaction quantum Monte Carlo (FCIQMC) is a powerful method for electronic structure calculations.
  • Calculating real-frequency spectral and thermal properties often requires computationally expensive analytic continuation.
  • Accurate computation of excited states remains a challenge in quantum many-body methods.

Purpose of the Study:

  • To develop an unbiased approach for calculating arbitrary spectral, thermal, and excited state properties within the FCIQMC framework.
  • To enable the direct calculation of real-frequency properties, bypassing the need for analytic continuation.
  • To apply the new method to relevant systems like Hubbard models and ab initio calculations.

Main Methods:

  • Projection of the Hamiltonian eigenvalue problem into a space of stochastically sampled Krylov vectors.
  • Utilizing the full configuration interaction quantum Monte Carlo (FCIQMC) framework.
  • Direct calculation of spectral and thermal properties without analytic continuation.

Main Results:

  • Successfully calculated temperature-dependent properties and one- and two-body spectral functions for various Hubbard models.
  • Determined isolated excited states in ab initio systems.
  • Demonstrated the capability of the method for arbitrary spectral, thermal, and excited state property calculations.

Conclusions:

  • The presented approach offers an efficient and unbiased method for obtaining key properties in quantum many-body systems.
  • This method overcomes limitations of traditional techniques, particularly the need for analytic continuation.
  • The framework is versatile, applicable to both model Hamiltonians and real-world molecular systems.