Simulation of state evolutions in Gross-Neveu model by matrix product state representation

TL;DR

This paper presents a classical simulation method using matrix product states to model real-time dynamics of the Gross-Neveu model, revealing how fermion mass and coupling influence state evolution and bound state formation.

Contribution

It introduces a matrix product state-based quantum simulation approach for the Gross-Neveu model on classical computers, capturing complex fermion dynamics.

Findings

Fermion and bound state evolutions depend on mass and coupling constants.

Simultaneous fermion evolution occurs under specific mass and coupling conditions.

Bound states form automatically under certain parameter regimes.

Abstract

A quantum algorithm to simulate the real time dynamics of two-flavor massive Gross-Neveu model is presented in Schrodinger picture. We implement the simulation on a classic computer by applying the matrix product state representation. The real time evolutions of up to four particles on a site in initial state are figured out in space-time coordinate. The state evolutions are effectively affected by fermion mass and coupling constant of the model. Especially when the mass of fermion is small enough and the coupling is strong enough, the fundamental fermions evolve synchronistically in space from the two-fermion and four-fermion initial states. These are also the conditions on which the bound states made up of fundamental fermion pairs were found to arise automatically in the literatures.