How to discretize a quantum bath for real-time evolution

Abstract

Many numerical techniques for the description of quantum systems that are coupled to a continuous bath require the discretization of the latter. To this end, a wealth of methods has been developed in the literature, which we classify as (i) direct discretization, (ii) orthogonal polynomial, and (iii) numerical optimization strategies. We recapitulate strategies (i) and (ii) to clarify their relation. For quadratic Hamiltonians, we show that (ii) is the best strategy in the sense that it gives the numerically exact time evolution up to a maximum time $t_{\text{max}}$, for which we give a simple expression. For non-quadratic Hamiltonians, we show that no such best strategy exists. We present numerical examples relevant to open quantum systems and strongly correlated systems, as treated by dynamical mean-field theory (DMFT).

References in corpus (11)

• The numerical renormalization group method for quantum impurity systems
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Chebyshev expansion for Impurity Models using Matrix Product States
• Spectral functions and time evolution from the Chebyshev recursion
• Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems
• Dissipation due to two-level systems in nano-mechanical devices
• Quantum dynamics in photonic crystals
• Finite representations of continuum environments
• Lattice mapping for many-body open quantum systems and its application to atoms in photonic cystals

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