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Relationship between Hirsch-Fye and weak-coupling diagrammatic quantum Monte Carlo methods
K Mikelsons1, A Macridin, M Jarrell
1Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA. mikelsk@email.uc.edu
Summary
Two continuous time quantum Monte Carlo (CTQMC) methods are equivalent for Hubbard interactions. The Hirsch-Fye quantum Monte Carlo (HFQMC) method is an approximation within CTQMC, becoming equivalent in the infinite time-slice limit.
Area of Science:
- Computational Physics
- Quantum Many-Body Theory
Background:
- Continuous Time Quantum Monte Carlo (CTQMC) methods are essential for simulating quantum many-body systems.
- Hubbard-type interactions are fundamental in condensed matter physics, describing correlated electron systems.
Purpose of the Study:
- To establish the equivalence between two weak-coupling CTQMC methods for Hubbard-type interactions.
- To clarify the relationship between CTQMC and the Hirsch-Fye Quantum Monte Carlo (HFQMC) method.
- To provide a diagrammatic interpretation of HFQMC within the CTQMC framework.
Main Methods:
- Weak-coupling continuous time quantum Monte Carlo (CTQMC) simulations.
- Establishment of analytical relationships between different quantum Monte Carlo algorithms.
- Diagrammatic analysis of quantum many-body methods.
Main Results:
- Demonstrated the equivalence of two specific weak-coupling CTQMC methods for Hubbard-type interactions.
- Identified the HFQMC method as an approximation within the broader CTQMC framework.
- Established that HFQMC and CTQMC become equivalent in the limit of infinite time slices.
Conclusions:
- The study provides a unified understanding of different quantum Monte Carlo approaches for correlated systems.
- The findings offer insights into the computational cost and limitations, including the fermion sign problem, associated with these methods.
- This work facilitates the selection and application of appropriate quantum Monte Carlo techniques for specific problems.
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