Hierarchical equations of motion for impurity solver in dynamical mean-field theory

Abstract

A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate evaluation of physical properties of strongly correlated electronic systems, in the framework of dynamical mean-field theory (DMFT). The HEOM method is also numerically convenient to achieve the same level of accuracy as that using the state-of-the-art numerical renormalization group impurity solver at finite temperatures. The practicality of the novel HEOM+DMFT method is demonstrated by its applications to the Hubbard models with Bethe and hypercubic lattice structures. We investigate the metal-insulator transition phenomena, and address the effects of temperature on the properties of strongly correlated lattice systems.

14 pages, 11 figures, updated version accepted to be published in PRB

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Cited by in corpus (12)

• Real time evolution of Anderson impurity models via tensor network influence functionals
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Local temperatures of strongly-correlated quantum dots out of equilibrium
• Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
• Quantum Monte Carlo in the steady-state
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
• The thermodynamic meaning of local temperature of nonequilibrium open quantum systems
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• A Standard Basis Operator Equation of Motion Impurity Solver for Dynamical Mean Field Theory
• Natural Orbital-Based Lanczos Method for Anderson Impurity Models
• Thermopower of few-electron quantum dots with Kondo correlations
• Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions