Renormalization and Short Distance Singular Structure

Renormalization for singular-potential scattering

In the calculation of quantum-mechanical singular-potential scattering, one encounters divergence. We suggest three renormalization schemes, dimensional renormalization, analytic continuation approach, and minimal-subtraction scheme to remove the divergence.

Entanglement under the renormalization-group transformations on quantum states and in quantum phase transitions

We consider quantum states under the renormalization-group (RG) transformations introduced by Verstraete et al. [Phys. Rev. Lett. 94, 140601 (2005)] and propose a quantification of entanglement under such RG (via the geometric measure of entanglement). We examine the resulting entanglement under RG for the ground states of "matrix-product-state" (MPS) Hamiltonians constructed by Wolf et al. [Phys. Rev. Lett. 97, 110403 (2006)] that possess quantum phase transitions. We find that near critical points, the ground-state entanglement exhibits singular behavior. The singular behavior within finite …

Coarse-graining renormalization by higher-order singular value decomposition

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 lattice models in two- or three-dimensions. We have demonstrated this method using the Ising model on the square and cubic lattices. By keeping up to 16 bond basis states, we obtain by far the most accurate numerical renormalization group results for the 3D Ising model. We have also applied the method to study the ground state as well as finite temperature prop…

On the Inequivalence of Renormalization and Self-Adjoint Extensions for Quantum Singular Interactions

A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian.

Renormalization of Singular Potentials and Power Counting

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analys…

由奇异形状因子介导的自旋–玻色子相互作用的重整化

Renormalization of spin$\unicode{x2013}$boson interactions mediated by singular form factors

本文将旋转波自旋–玻色子及同类系统–场耦合模型推广到奇异不可归一化形状因子，并借助 Fock 空间尺度上的湮灭、产生算符构造与严格重整化程序加以定义。