Related papers: Series expansions from the corner transfer matrix …
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
We study how to compute the operator product expansion coefficients in the exact renormalization group formalism. After discussing possible strategies, we consider some examples explicitly, within the $\epsilon$-expansions, for the…
Modeling quantum many-body systems is enormously challenging due to the exponential scaling of Hilbert dimension with system size. Finding efficient compressions of the wavefunction is key to building scalable models. Here, we introduce…
The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained,…
Numerical approaches are an important tool to study strongly correlated quantum systems. However, their fragility with respect to rounding errors is not well studied and numerically verified enclosures of the results are not available. In…
Field theoretical renormalization group methods are applied to the Obukhov--Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<{\bf v}(t,{\bf x}){\bf v}(t',{\bf x})> - < v(t,{\bf x}){\bf…
The functional renormalization group method is used to take into account the vacuum polarization around localized bound states generated by external potential. The application to Atomic Physics leads to improved Hartree-Fock and Kohn-Sham…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
The perturbative renormalization group(RG) equation is applied to resum divergent series of perturbative wave functions of quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation…
Streamline-based quad meshing algorithms use smooth cross fields to partition surfaces into quadrilateral regions by tracing cross field separatrices. In practice, re-entrant corners and misalignment of singularities lead to small regions…
Extensions of real numbers in more than two dimensions, in particular quaternions and octonions are finding applications in physics due to the fact that they naturally capture certain symmetries of physical systems. Here it is shown that…
In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
In this study, we delve into the intricate mathematical frameworks essential for the renormalization of effective elastic models within complex physical systems. By integrating advanced tools such as Laurent series, residue theorem, winding…
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed…
We propose using the method of subtraction to renormalize quantum gauge theories with chiral fermions and with spontaneous symmetry breaking. The Ward-Takahashi identities derived from the BRST invariance in these theories are complex and…
We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum…