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Full-Text Articles in Physical Sciences and Mathematics
A Short Introduction To Numerical Linked-Cluster Expansions, Baoming Tang, Ehsan Khatami, Marcos Rigol
A Short Introduction To Numerical Linked-Cluster Expansions, Baoming Tang, Ehsan Khatami, Marcos Rigol
Faculty Publications
We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact diagonalization. We discuss how to reduce the computational cost of the NLCE calculations by taking into account symmetries and topologies of the linked clusters. Finally, we generalize the algorithm to the thermodynamic limit, and discuss several numerical resummation techniques …
Cluster Solver For Dynamical Mean-Field Theory With Linear Scaling In Inverse Temperature, Ehsan Khatami, C. Lee, Z. Bai, R. Scalettar, M. Jarrell
Cluster Solver For Dynamical Mean-Field Theory With Linear Scaling In Inverse Temperature, Ehsan Khatami, C. Lee, Z. Bai, R. Scalettar, M. Jarrell
Faculty Publications
Dynamical mean-field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians and, in combination with electronic structure theory, constitute powerful methods to treat strongly correlated materials. The key advantage to the technique is that, unlike competing real-space methods, the sign problem is well controlled in the Hirsch-Fye (HF) quantum Monte Carlo used as an exact cluster solver. However, an important computational bottleneck remains; the HF method scales as the cube of the inverse temperature, β. This often makes simulations at low temperatures extremely challenging. We present here a method based on determinant …
Using Genetic Algorithms To Map First-Principles Results To Model Hamiltonians: Application To The Generalized Ising Model For Alloys, Gus L. W. Hart, Volker Blum, Michael J. Walorski, Alex Zunger
Using Genetic Algorithms To Map First-Principles Results To Model Hamiltonians: Application To The Generalized Ising Model For Alloys, Gus L. W. Hart, Volker Blum, Michael J. Walorski, Alex Zunger
Faculty Publications
The cluster expansion method provides a standard framework to map first-principles generated energies for a few selected configurations of a binary alloy onto a finite set of pair and many-body interactions between the alloyed elements. These interactions describe the energetics of all possible configurations of the same alloy, which can hence be readily used to identify ground state structures and, through statistical mechanics solutions, find finite-temperature properties. In practice, the biggest challenge is to identify the types of interactions which are most important for a given alloy out of the many possibilities. We describe a genetic algorithm which automates this …