Related papers: A systematic method for Schrieffer-Wolff transform…
Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of…
We derive recursive relations for the Schrieffer--Wolff (SW) transformation applied to the half-filled Hubbard dimer. While the standard SW transformation is set to block-diagonalize the transformed Hamiltonian solely at the first order of…
In quantum mechanics, the Schrieffer--Wolff (SW) transformation (also called quasi-degenerate perturbation theory) is known as an approximative method to reduce the dimension of the Hamiltonian. We present a geometric interpretation of the…
We present a formalized perturbation theory for Markovian open systems in the language of a generalized Schrieffer-Wolff (SW) transformation. A non-unitary rotation decouples the unper- turbed steady states from all fast degrees of freedom,…
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary…
We present a systematic method to implement a perturbative Hamiltonian diagonalization based on the time-dependent Schrieffer-Wolff transformation. Applying our method to strong parametric interactions we show how, even in the dispersive…
Full information about a many-body quantum system is usually out-of-reach due to the exponential growth -- with the size of the system -- of the number of parameters needed to encode its state. Nonetheless, in order to understand the…
We consider a general reducible gauge theory deformed by mass or/and interaction terms violating gauge invariance. It is shown that in the Abelian case, by using the Stueckelberg-type procedure, this theory with broken gauge symmetry can be…
We reexamine a unitary-transformation method of extracting a physical Hamiltonian from a gauge field theory after quantizing all degrees of freedom including redundant variables. We show that this {\it quantum Hamiltonian reduction} method…
The renormalization-group method is used to analyze the low-temperature behaviour of a two-dimentional, spin-$s$ quantum Heisenberg ferromagnet. A set of recursion equations is derived in an one-loop approximation. The low-temperature…
Renormalization group methods are well-established tools for the (numerical) investigation of the low-energy properties of correlated quantum many-body systems, allowing to capture their scale-dependent nature. The functional…
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an…
The Sommerfeld-Watson transformation is a powerful mathematical technique widely used in physics to simplify summations over discrete quantum numbers by converting them into contour integrals in the complex plane. This method has…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly-interacting pairs of…
With the help of computer algebra, I devise an exact unitary transformation for the Anderson impurity model which allows to kill the hybridization term in the slightly simplified case of zero chemical potential. Then I compute explicitly…
Exact unitary transformations play a central role in the analysis and simulation of many-body quantum systems, yet the conditions under which they can be carried out exactly and efficiently remain incompletely understood. We show that exact…
Here, we propose a new modified quantum mechanics and its new algorithms of atomic fine-structure,asymmetric variational method based on hydrogen-like atom orbit. In addition, as we all know, the ab initio calculation of atomic…
We introduce a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group. By a series of unitary transformations that successively decouples the high-frequency…