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NMR-Based Fragment Screening in a Minimum Sample but Maximum Automation Mode

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Importance-sampling FCIQMC: Solving weak sign-problem systems.

Niklas Liebermann¹, Khaldoon Ghanem¹, Ali Alavi¹

¹Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.

The Journal of Chemical Physics

|October 1, 2022

Summary

This summary is machine-generated.

We reduced the computational cost of quantum Monte Carlo simulations for fermionic systems with a weak sign problem. This was achieved by optimizing the representation and using importance sampling, enabling exact energy calculations for larger systems.

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Area of Science:

Computational Physics
Quantum Many-Body Systems
Quantum Monte Carlo Methods

Background:

The sign problem in quantum Monte Carlo (QMC) simulations hinders exact calculations for many fermionic systems.
Weak sign-problem systems, characterized by a small energy gap to a stoquastic state, are prime candidates for QMC advancements.

Purpose of the Study:

To investigate the exact full configuration interaction quantum Monte Carlo algorithm for weak sign-problem fermionic systems.
To explore methods for reducing the computational resources required to overcome the sign problem.
To calculate and compare the fundamental charge gap in Hubbard ladders and 1D chains.

Main Methods:

Application of the exact full configuration interaction quantum Monte Carlo algorithm without the initiator approximation.
Utilizing importance-sampling similarity transformations to reduce the number of walkers.
Comparing real-space (site) and momentum space representations for the Hubbard model.
Employing a Gutzwiller-like guiding wavefunction for importance sampling in Hubbard ladders.

Main Results:

A significant reduction in the minimum number of walkers is achievable via importance-sampling similarity transformations.
The real-space representation exhibits a weaker sign problem than the momentum space representation for the off-half-filling Hubbard model.
Exact energies for sizable 2 × ℓ Hubbard ladders were obtained by reducing walker requirements.
Hubbard ladder systems show a reduced fundamental charge gap compared to strictly one-dimensional Hubbard chains.

Conclusions:

The developed methods effectively mitigate the sign problem in weak sign-problem fermionic systems.
Importance sampling and appropriate representation choices are crucial for efficient QMC simulations.
Ladder geometries exhibit distinct electronic properties, such as a reduced fundamental charge gap, compared to 1D chains.