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Reptation quantum Monte Carlo algorithm for lattice Hamiltonians with a directed-update scheme.
Giuseppe Carleo1, Federico Becca, Saverio Moroni
1Scuola Internazionale Superiore di Studi Avanzati and Democritos National Simulation Center, Istituto Officina dei Materiali del CNR, Via Bonomea 265, I-34136 Trieste, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
We extended the reptation quantum Monte Carlo algorithm for lattice systems, improving the fixed-node approximation for quantum systems. This method accurately estimates ground-state properties for models like the Heisenberg and Hubbard models.
Area of Science:
- Computational Physics
- Quantum Many-Body Systems
- Quantum Monte Carlo Methods
Background:
- The reptation quantum Monte Carlo (RQMC) algorithm is effective for continuous Hamiltonians.
- Lattice systems often face challenges like the sign problem, limiting accuracy.
- Accurate calculation of ground-state and excited-state properties is crucial in quantum mechanics.
Purpose of the Study:
- To extend the RQMC algorithm to lattice systems.
- To develop a systematic improvement over the fixed-node approximation for sign-problematic systems.
- To enable the study of diverse quantum systems and their properties.
Main Methods:
- Extension of the reptation quantum Monte Carlo algorithm to lattice systems.
- Implementation of a method to improve the fixed-node approximation.
- Utilization of a canonical worm algorithm for measuring off-diagonal observables.
Main Results:
- The generalized RQMC method is applicable to a wide range of quantum systems.
- Accurate ground-state energy estimates were obtained for the 2D fermionic Hubbard model.
- Quantum dynamics of the 1D Heisenberg model were investigated.
Conclusions:
- The developed method provides a powerful tool for studying quantum many-body systems.
- It offers a systematic way to improve upon approximations in quantum Monte Carlo simulations.
- The approach facilitates the investigation of both ground-state and excited-state properties.
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