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Published on: November 15, 2013
Universal stochastic series expansion algorithm for Heisenberg model and Bose-Hubbard model with interaction
1Moscow Engineering Physics Institute, Moscow 115409, Russia. mikhail_zyubin@yahoo.com
Summary
We developed a universal stochastic series expansion (SSE) method for simulating quantum models like the Heisenberg and Bose-Hubbard models. This efficient algorithm overcomes critical slowing down, enabling accurate simulations of interacting bosons.
Area of Science:
- Quantum many-body physics
- Computational condensed matter physics
Background:
- Simulating quantum many-body systems is computationally challenging.
- Existing methods struggle with large systems or strong interactions.
- The Heisenberg and Bose-Hubbard models are fundamental to understanding magnetism and cold atoms.
Purpose of the Study:
- To introduce a universal stochastic series expansion (SSE) method.
- To apply the SSE method to simulate the Heisenberg model with arbitrary spin.
- To simulate the Bose-Hubbard model with soft-core bosons and interactions.
Main Methods:
- Developed a universal stochastic series expansion (SSE) algorithm.
- Implemented an efficient procedure to enhance the SSE algorithm's performance.
- Calculated integrated autocorrelation times to assess efficiency.
Main Results:
- Successfully simulated the Heisenberg and Bose-Hubbard models using the SSE method.
- Demonstrated the algorithm's efficiency for soft-core bosons with interactions.
- The SSE method effectively eliminates the critical slowing down problem.
Conclusions:
- The universal SSE method is efficient for simulating quantum models.
- The developed algorithm overcomes limitations of previous simulation techniques.
- This approach provides a powerful tool for studying quantum many-body systems.
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