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Bulletin of the American Physical Society

Dynamical simulations of strongly correlated electron materials

Joel D. Kress, Kipton M. Barros, Cristian D. Batista, Gia-Wei Chern, Gabriel Kotliar

Published Mar 18, 2016• 0 citations
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Numerical simulation of strongly correlated electron systems

R. D. Sedgewick

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Lectures on the physics of strongly correlated systems XIV : fourteenth training course in the physics of strongly correlated systems, Vietri sul Mare (Salerno), Italy, 5-16 October 2009

Adolfo Avella, Ferdinando Mancini

This volume contains the lectures delivered at the XIV Training Course in the Physics of Strongly Correlated Systems, held in Vietri sul Mare (Salerno) Italy, in October 2009. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographs of relevant subjects in the field of Condensed Matter Physics. Contributions include: Electronic Structure of Strongly Correlated Materials (Electronic structure calculations in one-electron approximation; Hubbard model in Dynamical Mean-Field Theory (DMFT); Electronic structure calculations for real materials by LDA+DMFT method); and, Computational Studies of Quantum Spin Systems (Quantum spin models, their ground states and quantum phase transitions; Classical phase transitions, Monte Carlo simulations, and finite-size scaling; Exact diagonalization methods; Quantum Monte Carlo simulations and the Stochastic Series Expansion method; and, Survey of related computational methods). Contributions also include: Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials (Mean-field theories for many-body systems; Lattice fermions in the limit of high dimensions; Dynamical mean-field theory for correlated lattice fermions; The Mott-Hubbard Metal-Insulator Transition; Electronic correlations and disorder; Theory of electronic correlations in materials; and, Kinks in the dispersion of strongly correlated electron systems).

AIP eBooks•Jan 1, 2010•1 citation

Numerical study of strongly correlated electron systems

Tôru Sakai

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Simulating Materials with Strong Correlations on BlueGene/L.

Andreas Dolfen, Yuan Lung Luo, Erik Koch

Understanding the physics of strongly correlated materials is one of the grand-challenges in condensed-matter physics.Simple approximations such as the local density approximation fail, due to the importance of the Coulomb repulsion between localized electrons.Instead we have to resort to non-perturbative many-body techniques.Such calculations are, however, only feasible for quite small model systems.This means that the full Hamiltonian of a real material has to be approximated by a model Hamiltonian comprising only the most important electronic degrees of freedom, while the effect of all other electrons can merely be included in an average way.Realistic calculations of strongly correlated materials need to include as many of the electronic degrees of freedom as possible.We use the Lanczos method for calculating ground state and dynamical properties of such model Hamiltonians.In the method we have to handle the full many-body state of the correlated system.The method is thus limited by the available main memory.The principal problem for a distributed-memory implementation is that the central routine of the code, the application of the Hamiltonian to the many-body state, leads, due to the kinetic energy term, to very non-local memory access.We describe a solution for this problem and show that the new algorithm scales very efficiently on BlueGene/L.Moreover, our approach is not restricted to correlated electrons but can also be used to simulate quantum spin systems relevant for quantum computing.

•Jan 1, 2007•0 citations

The Dynamical Cluster Approximation: A New Technique for Simulations of Strongly Correlated Electron Systems

S. Moukouri, Carey Huscroft, Mark Jarrell

arXiv:cond-mat/0004279•Springer proceedings in physics•Jan 1, 2001•0 citations

Dynamic Simulations of Strongly Coupled Spin Ensembles for Inferring Nature of Electronic Correlations from Nuclear Magnetic Resonance

Charles Snider, Stephen Carr, D. E. Feldman +2 more

We develop an efficient package for the simulation of nuclear magnetic resonance spin echo experiments to study the effects of strong electronic spin correlations on the dynamics of the nuclear spin ensemble. A mean-field model is used to study correlated electronic phases through their hyperfine interaction with nuclear spins. We explore the dynamics of the interacting nuclear ensemble and discuss the key behaviors of the system. In particular, we classify the types of temporal asymmetry that the interaction induces in the system as well as a pulse-dependent shift in the spectral domain. Using these results, we discuss how careful measurement of the pulse-dependent shift can be used to extract information about the anisotropy of the electronic interaction and how these results represent a novel tool for the examination of exotic NMR signatures in strongly correlated materials. Finally, we review specific aspects of the simulation package developed for our exploration and give explicit examples where package can be used to infer range and anisotropy of electronic correlations. In particular, we discuss its structure, accuracy, and the technical merits of the various approximations used to model the nuclear spin ensemble.

cond-mat.str-elCross-listedarXiv:2602.02732•Feb 4, 2026
This volume contains the lectures delivered at the XIV Training Course in the Physics of Strongly Correlated Systems, held in Vietri sul Mare (Salerno) Italy, in October 2009. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographs of relevant subjects in the field of Condensed Matter Physics. Contributions include: Electronic Structure of Strongly Correlated Materials (Electronic structure calculations in one-electron approximation; Hubbard model in Dynamical Mean-Field Theory (DMFT); Electronic structure calculations for real materials by LDA+DMFT method); and, Computational Studies of Quantum Spin Systems (Quantum spin models, their ground states and quantum phase transitions; Classical phase transitions, Monte Carlo simulations, and finite-size scaling; Exact diagonalization methods; Quantum Monte Carlo simulations and the Stochastic Series Expansion method; and, Survey of related computational methods). Contributions also include: Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials (Mean-field theories for many-body systems; Lattice fermions in the limit of high dimensions; Dynamical mean-field theory for correlated lattice fermions; The Mott-Hubbard Metal-Insulator Transition; Electronic correlations and disorder; Theory of electronic correlations in materials; and, Kinks in the dispersion of strongly correlated electron systems).
Understanding the physics of strongly correlated materials is one of the grand-challenges in condensed-matter physics.Simple approximations such as the local density approximation fail, due to the importance of the Coulomb repulsion between localized electrons.Instead we have to resort to non-perturbative many-body techniques.Such calculations are, however, only feasible for quite small model systems.This means that the full Hamiltonian of a real material has to be approximated by a model Hamiltonian comprising only the most important electronic degrees of freedom, while the effect of all other electrons can merely be included in an average way.Realistic calculations of strongly correlated materials need to include as many of the electronic degrees of freedom as possible.We use the Lanczos method for calculating ground state and dynamical properties of such model Hamiltonians.In the method we have to handle the full many-body state of the correlated system.The method is thus limited by the available main memory.The principal problem for a distributed-memory implementation is that the central routine of the code, the application of the Hamiltonian to the many-body state, leads, due to the kinetic energy term, to very non-local memory access.We describe a solution for this problem and show that the new algorithm scales very efficiently on BlueGene/L.Moreover, our approach is not restricted to correlated electrons but can also be used to simulate quantum spin systems relevant for quantum computing.
We develop an efficient package for the simulation of nuclear magnetic resonance spin echo experiments to study the effects of strong electronic spin correlations on the dynamics of the nuclear spin ensemble. A mean-field model is used to study correlated electronic phases through their hyperfine interaction with nuclear spins. We explore the dynamics of the interacting nuclear ensemble and discuss the key behaviors of the system. In particular, we classify the types of temporal asymmetry that the interaction induces in the system as well as a pulse-dependent shift in the spectral domain. Using these results, we discuss how careful measurement of the pulse-dependent shift can be used to extract information about the anisotropy of the electronic interaction and how these results represent a novel tool for the examination of exotic NMR signatures in strongly correlated materials. Finally, we review specific aspects of the simulation package developed for our exploration and give explicit examples where package can be used to infer range and anisotropy of electronic correlations. In particular, we discuss its structure, accuracy, and the technical merits of the various approximations used to model the nuclear spin ensemble.