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We propose a new concept for the dynamics of a quantum bath, the Chebyshev space, and a new method based on this concept, the Chebyshev space method. The Chebyshev space is an abstract vector space that exactly represents the fermionic or bosonic bath degrees of freedom, without a discretization of the bath density of states. Relying on Chebyshev expansions the Chebyshev space representation of a bath has very favorable properties with respect to extremely precise and efficient calculations of groundstate properties, static and dynamical correlations, and time-evolution for a great variety of quantum systems. The aim of the present work is to introduce the Chebyshev space in detail and to demonstrate the capabilities of the Chebyshev space method. Although the central idea is derived in full generality the focus is on model systems coupled to fermionic baths. In particular we address quantum impurity problems, such as an impurity in a host or a bosonic impurity with a static barrier, and the motion of a wave packet on a chain coupled to leads. For the bosonic impurity, the phase transition from a delocalized electron to a localized polaron in arbitrary dimension is detected. For the wave packet on a chain, we show how the Chebyshev space method implements different boundary conditions, including transparent boundary conditions replacing infinite leads. Furthermore the self-consistent solution of the Holstein model in infinite dimension is calculated. With the examples we demonstrate how highly accurate results for system energies, correlation and spectral functions, and time-dependence of observables are obtained with modest computational effort.
We study a model of a quantum dot coupled to a quantum Hall edge of the Laughlin state, taking into account short-range interactions between the dot and the edge. This system has been studied experimentally in electron quantum optics in the context o
We propose a highly efficient numerical method to describe inhomogeneous superconductivity by using the kernel polynomial method in order to calculate the Greens functions of a superconductor. Broken translational invariance of any type (impurities,
The Sachdev-Ye-Kitaev (SYK) model describes interacting fermionic zero modes in zero spatial dimensions, e.g. quantum dot, with interactions strong enough to completely washout quasiparticle excitations in the infrared. In this note, we consider the
The theory of probability shows that, as the fraction $X_n/Yto 0$, the conditional probability for $X_n$, given $X_n+Y in h_{delta}:=[h, h+delta]$, has a limit law $f_{X_n}(x)e^{-psi_n(h_delta)x}$, where $psi_n(h_delta) $ equals to $[partial ln P(Y i
We investigate the impact of an Ohmic-class environment on the conduction and correlation properties of one-dimensional interacting systems. Interestingly, we reveal that inter-particle interactions can be engineered by the environments noise statist