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Symmetry-projected cluster mean-field theory applied to spin systems
Athanasios Papastathopoulos-Katsaros1, Thomas M Henderson1,2, Gustavo E Scuseria1,2
1Department of Chemistry, Rice University, Houston, Texas 77005, USA.
The Journal of Chemical Physics
|August 23, 2023
Summary
We developed new methods, generalized cluster mean-field (GcMF) and Sz spin-projected generalized cluster mean-field (SzGcMF), to better describe strongly correlated spin systems. These approaches improve the understanding of inter-cluster correlations in Heisenberg models.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Theory
- Computational Physics
Background:
- Cluster mean-field theory approximates ground states using factorized cluster wavefunctions.
- Previous unrestricted cluster mean-field methods maintained Sz symmetry within each cluster.
- Strongly correlated spin systems present significant challenges for accurate theoretical description.
Purpose of the Study:
- Introduce generalized cluster mean-field (GcMF) theory, relaxing Sz symmetry constraints per cluster.
- Develop Sz spin-projected generalized cluster mean-field (SzGcMF) by restoring global Sz symmetry.
- Improve the accounting for inter-cluster correlations in strongly correlated spin systems.
Main Methods:
- Developed generalized cluster mean-field (GcMF) theory, allowing clusters access to all Sz sectors.
- Implemented Sz spin-projection to restore global Sz symmetry, forming SzGcMF.
- Applied GcMF and SzGcMF to benchmark 1D, quasi-2D, and 2D J1-J2 and XXZ Heisenberg models.
Main Results:
- GcMF and SzGcMF methods provide qualitative and semi-quantitative descriptions of Heisenberg lattices.
- The new methods successfully account for inter-cluster correlations.
- Demonstrated improved accuracy compared to previous cluster mean-field approaches.
Conclusions:
- GcMF and SzGcMF are valuable tools for studying strongly correlated spin systems.
- These methods offer improved insights into inter-cluster correlations.
- The developed theories serve as useful references for future research in the field.
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