Variational Cluster Approximation to the Thermodynamics of Quantum Spin Systems

Abstract

We derive a variational cluster approximation for Heisenberg spin systems at finite temperature based on the ideas of the self-energy functional theory by Potthoff for fermionic and bosonic systems with local interactions. Partitioning the real system into a set of clusters, we find an analytical expression for the auxiliary free energy, depending on a set of variational parameters defined on the cluster, whose stationary points provide approximate solutions from which the thermodynamics of spin models can be obtained. We explicitly describe the technical details of how to evaluate the free energy for finite clusters and remark on specific problems and possible limitations of the method. To test the approximation we apply it to the antiferromagnetic spin 1/2 chain and compare the results for varying cluster sizes and choices of variational parameters with the exact Bethe ansatz solution.

arXiv comment25 pages; 5 figures; to be published in New Journal of Physics

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Cited by in corpus (4)

• A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer
• Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling
• Variational cluster approach to superconductivity and magnetism in the Kondo lattice model
• Two-particle Correlation Functions in Cluster Perturbation Theory: Hubbard Spin Susceptibilities