Related papers: Projector-based renormalization method (PRM) and i…
We present a quantum-number projection technique which enables us to exactly treat spin, momentum and other symmetries embedded in the Hubbard model. By combining this projection technique, we extend the path-integral renormalization group…
We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
The practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians is discussed as requiring an explicit reconstruction of the {\em ad hoc} Hilbert-space metrics which would render the time-evolution…
We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the hamiltonian…
We study the computational complexity of 2-local Hamiltonian problems generated by a positive-weight symmetric interaction term, encompassing many canonical problems in statistical mechanics and optimization. We show these problems belong…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
In this paper, we develop a wave function renormalization scheme for models of non-relativistic quantum particles interacting with a quantized relativistic field, in the Hamiltonian formalism of quantum field theory. We construct the…
A novel perturbative analysis for the 2+1 local supercritical field theory of pomerons is developed. It is based on the PT symmetry of the model which allows to study a similar Hamiltonian with the same real perturbative spectrum. In the…
Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…
In two lectures, we overview the renormalon and renormalon-related techniques and their phenomenological applications. We begin with a single renormalon chain which is a well defined and systematic way to specify the character of…
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
Characterizing quantum many-body systems is a fundamental problem across physics, chemistry, and materials science. While significant progress has been made, many existing Hamiltonian learning protocols demand digital quantum control over…
We propose PRM, a novel photometric stereo based large reconstruction model to reconstruct high-quality meshes with fine-grained local details. Unlike previous large reconstruction models that prepare images under fixed and simple lighting…
Nonlocal effective interactions are inherent to non-relativistic quantum many-body systems, but their systematic resummation poses a significant challenge known as the ``vertex problem" in many-body perturbation theory. We introduce a…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Schr\"odinger's equation serves as a fundamental component in characterizing quantum systems, wherein both quantum state tomography and Hamiltonian learning are instrumental in comprehending and interpreting quantum systems. While numerous…
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…