Momentum-resolved time evolution with matrix product states

TL;DR

This paper presents a matrix product state method for calculating spectral functions of one-dimensional spin chains directly in momentum space, enabling more efficient and accurate simulations of their time evolution and spectral properties.

Contribution

The authors develop a momentum-space MPS approach for spectral functions, reducing entanglement growth and improving accuracy in simulating one-dimensional quantum spin systems.

Findings

Smaller entanglement growth in momentum space improves simulation efficiency.

Accurate spectral functions achieved with small bond dimension.

Method successfully applied to various spin chain models.

Abstract

We introduce a method based on matrix product states (MPS) for computing spectral functions of (quasi) one-dimensional spin chains, working directly in momentum space in the thermodynamic limit. We simulate the time evolution after applying a momentum operator to an MPS ground state by working with the momentum superposition of a window MPS. We show explicitly for the spin-1 Heisenberg chain that the growth of entanglement is smaller in momentum space, even inside a two-particle continuum, such that we can attain very accurate spectral functions with relatively small bond dimension. We apply our method to compute spectral lineshapes of the gapless XXZ chain and the square-lattice J1-J2 Heisenberg model on a six-leg cylinder.