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.

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

References in corpus (5)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Variational cluster approach to spontaneous symmetry breaking: The itinerant antiferromagnet in two dimensions
• Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
• Phase diagram and single-particle spectrum of CuO${}_2$ layers within a variational cluster approach to the 3-band Hubbard model
• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase