Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states

TL;DR

This study uses tensor network methods to explore how interactions in quantum field theories affect particle production and entanglement in curved spacetime, revealing that interactions suppress particle creation and influence entanglement dynamics.

Contribution

First numerical investigation of interacting quantum field theories in curved spacetime using tensor networks, demonstrating interaction effects on particle production and entanglement.

Findings

Interactions suppress gravitational particle production compared to free theories.

Entanglement growth is suppressed in the $bb\u03bb ext{phi}^4$ theory.

Complex entanglement behavior arises from interplay between particle production and correlations.

Abstract

Understanding real-time dynamics of interacting quantum fields in curved spacetime remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar $\lambda\phi^4$ theory and the Schwinger model, i.e. a Dirac fermion coupled to a $U(1)$ gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the $\lambda\phi^4$ theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.