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Published on: February 15, 2016
Numerical linked-cluster algorithms. I. Spin systems on square, triangular, and kagomé lattices
Marcos Rigol1, Tyler Bryant, Rajiv R P Singh
1Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA.
Summary
Numerical linked-cluster (NLC) algorithms accurately determine quantum lattice model properties. These advanced methods provide more precise thermodynamic data than traditional techniques for various spin models.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
- Computational Physics
Background:
- Accurately calculating temperature-dependent properties of quantum lattice models in the thermodynamic limit is computationally challenging.
- Traditional methods like high-temperature expansions (HTE) and exact diagonalization (ED) of finite systems have limitations in accuracy and applicability.
- There is a need for robust numerical techniques to study complex quantum systems.
Purpose of the Study:
- Introduce and evaluate recently developed numerical linked-cluster (NLC) algorithms.
- Assess the capability of NLC algorithms to compute thermodynamic observables for spin models on various lattices.
- Compare the accuracy of NLC results against established analytical and numerical methods.
Main Methods:
- Employed numerical linked-cluster (NLC) algorithms utilizing exact diagonalization of finite clusters.
- Studied thermodynamic observables for spin models on square, triangular, and kagomé lattices.
- Utilized cluster extrapolation methods to accelerate NLC convergence and compared results with HTE, ED, and quantum Monte Carlo simulations.
Main Results:
- NLC algorithms successfully obtained temperature-dependent properties for quantum lattice models.
- Demonstrated the application of NLCs to diverse spin models on different lattice geometries.
- NLC results showed substantially higher accuracy compared to HTE and ED for many models and properties.
Conclusions:
- Numerical linked-cluster algorithms represent a significant advancement for studying quantum lattice models.
- NLCs offer a more accurate and reliable approach for calculating thermodynamic properties than previously available methods.
- These findings pave the way for more precise investigations of complex quantum materials and phenomena.
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