Spectroscopy using tensor renormalization group method

TL;DR

This paper introduces a tensor network-based spectroscopy method that computes energy spectra, quantum numbers, momenta, and scattering phase shifts of lattice models, demonstrated on the (1+1)d Ising model.

Contribution

The paper develops a novel tensor network approach combining transfer matrix and impurity tensors for spectral analysis of lattice models.

Findings

Successfully computed energy spectra and quantum numbers.

Classified momenta of one- and two-particle states.

Calculated scattering phase shifts using Lüscher's formula.

Abstract

We present a spectroscopy scheme using transfer matrix and tensor network. With this method, the energy spectrum is obtained from the eigenvalues of the transfer matrix which is estimated by coarse grained tensor network of a lattice model, and the quantum number is classified from the matrix elements of a proper operator that can be represented as an impurity tensor network. Additionally, the momentum of one-particle state and two-particle state whose total momentum is zero are classified using matrix elements of proper momentum operators. Furthermore, using L\"uscher's formula, the scattering phase shift is also computed from the energy of two-particle state. As a demonstration, the method is applied to (1+1)d Ising model.