Related papers: Numerical Renormalization Group for Quantum Impuri…
The real-space renormalization group technique is introduced to evaluate the effective diffusion constant for diffusion in inhomogeneous media, which has been obtained by singular perturbation methods. Our method is formulated on a…
We introduce a numerical method of the adaptive time-dependent density-matrix renormalization-group to compute one-dimensional quantum spin systems with periodic boundary condition. We check our algorithm to study the dynamic correlation in…
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov…
A new numerical method for the solution of the Dynamical Mean Field Theory's self-consistent equations is introduced. The method uses the Density Matrix Renormalization Group technique to solve the associated impurity problem. The new…
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero temperature or ground-state properties of one dimensional strongly correlated quantum systems. The development of the…
We extend the spin-boson model of open quantum systems to the regime of quantum $1/f^\eta$ noise characterized by negative exponents of its spectral distribution. Using the numerically exact time-evolving matrix product operator, we find…
We present a comprehensive theory for a novel method to discretize the spectral density of a bosonic heat bath, as introduced in [H. Takahashi and R. Borrelli, J. Chem. Phys. \textbf{161}, 151101 (2024)]. The approach leverages a low-rank…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
Study of dissipative quantum phase transitions in the Ohmic spin-boson model is numerically challenging in a dense limit of environmental modes. In this work, large-scale numerical simulations are carried out based on the variational…
The treatment of quantum thermodynamic systems beyond weak coupling is of increasing relevance, yet extremely challenging. The evaluation of thermodynamic quantities in strong-coupling regimes requires a nonperturbative knowledge of the…
In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix…
By means of time-dependent density-matrix renormalization-group (TDMRG) we are able to follow the real-time dynamics of a single impurity embedded in a one-dimensional bath of interacting bosons. We focus on the impurity breathing mode,…
We study the spin--boson model with a sub--Ohmic bath using infinitesimal unitary transformations. Contrary to some results reported in the literature we find a zero temperature transition from an untrapped state for small coupling to a…
We discuss the ground state properties of a one-dimensional bosonic system doped with an impurity (the so-called Bose polaron problem). We introduce a formalism that allows us to calculate analytically the thermodynamic zero-temperature…
We analyze the static and dynamical properties of two Ising-coupled quantum spins embedded in a common bosonic bath as an archetype of dissipative quantum mechanics. First, we elucidate the ground state phase diagram for an ohmic and a…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
The spin-boson model, describing a two-level system coupled to a bath of harmonic oscillators, is a generic model for quantum dissipation, with manifold applications. It has also been studied as a simple example for an impurity quantum…
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This…
We present a perturbative treatment of the subohmic spin-boson model which remedies a crucial flaw in previous treatments. The problem is traced back to the incorrect application of a Markov type approximation to specific terms in the…