Speaker
Description
The study of two- and three-particle states interaction is important for hadron physics. Lattice QCD provides a non-perturbative framework for investigating strongly interacting quantum field theories and can be used to study the two- and three-particle states numerically, where Monte Carlo (MC) method is the standard approach employed for the simulations. Despite of its success, MC method has several practical limitations, one of which is the large statistical noise encountered during the extraction of the two- and three-particle states. Motivated by this issue, we propose a deterministic scheme based on transfer matrix and tensor network approach to investigate the two- and three-particle states and demonstrate its application to the (1+1)d Ising model. The first step of the scheme is to coarse grain the tensor network of a given lattice model using higher order tensor renormalization group (HOTRG). From the coarse-grained tensor, an approximation of the transfer matrix is constructed, and the energy spectrum is extracted from its eigenvalues. The quantum numbers of the resulting states are not known a priori, so we identify them by using selection rules derived from the symmetries of the system. The matrix elements of a proper operator are the important quantities of this identification process and are estimated using impurity tensor network method. Furthermore, by analyzing the volume dependence of the energy spectrum, the two- and three-particle states are identified. Focusing on the two-particle state sector, we investigate its dynamics by computing the two-particle scattering phase shift in rest and moving frames using Lüscher’s formula and compare the result with theoretical prediction. In the three-particle state sector, we show that the numerical finite volume energy agrees with the three-particle dispersion relation computed under the assumption that no three-body forces and only pairwise interactions are present.