Related papers: Higher-Order Structure of Hamiltonian Truncation E…
We apply the wavelet formalism of quantum field theory to investigate nonperturbative dynamics within the Hamiltonian framework. In particular, we employ Daubechies wavelets in momentum space, whose basis functions are labeled by resolution…
The $\lambda$-superposition calculus is a successful approach to proving higher-order formulas. However, some parts of the calculus are extremely explosive, notably due to the higher-order unifier enumeration and the functional…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
We have proposed a method in the context of BFFT approach that leads to truncation of the infinite series regarded to constraints in the extended phase space, as well as other physical quantities (such as Hamiltonian). This has been done…
Exploiting inherent symmetries is a common and effective approach to speed up the simulation of quantum systems. However, efficiently accounting for non-Abelian symmetries, such as the $SU(2)$ total-spin symmetry, remains a major challenge.…
We search for short-range Hamiltonians of finite spin-1 kagome systems, maximizing the overlaps with lattice Moore-Read states. Our starting point is an exact, long-range parent Hamiltonian for such a state on a finite plane, obtained from…
We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict…
We take advantage of the fact that in lambda phi ^4 problems a large field cutoff phi_max makes perturbative series converge toward values exponentially close to the exact values, to make optimal choices of phi_max. For perturbative series…
We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as…
We discuss structure-preserving model order reduction for port-Hamiltonian systems based on an approximation of the full-order state by a linear combination of ansatz functions which depend themselves on the state of the reduced-order…
We extend the study of the two-dimensional euclidean $\phi^4$ theory initiated in ref. [1] to the $\mathbb Z_2$ broken phase. In particular, we compute in perturbation theory up to N$^4$LO in the quartic coupling the vacuum energy, the…
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
We use functional methods to match the Two-Higgs Doublet Model with heavy scalars in the nondecoupling regime to the appropriate nonlinear effective field theory, which takes the form of an electroweak chiral Lagrangian (HEFT). The…
We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $\Phi: \mathbb{R}^d \rightarrow \mathbb{R}$ that is convex and twice…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
The calculation of higher twist (or dimension) corrections to physical quantities using operator product expansions is delicate. If dimensional regularization is used to regulate the ultra-violet divergences then there are ambiguities in…
We consider a general class of large $N$ vector-like theories in $d=2+1$ in a Hamiltonian approach. We show that by using lightcone quantization and the $N\to\infty$ limit, we can diagonalize the Hamiltonian exactly and construct the…
In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for…
In this paper, we present an adaptive framework for constructing a pseudo-optimal reduced model for the frequency-limited H2-optimal model order reduction problem. We show that the frequency-limited pseudo-optimal reduced-order model has an…