Simulating Quantum Field Theories with Boundaries in Curved Spacetimes Using Open Spin Systems

TL;DR

This paper presents a method to simulate quantum field theories with boundaries in curved spacetimes using open spin systems, extending previous work to include boundary conditions and demonstrating accurate reproduction of QFT dynamics.

Contribution

The authors extend the spin system to QFT mapping to include boundary conditions, enabling simulation of boundary effects in curved spacetime quantum fields.

Findings

Open spin systems can accurately reproduce boundary conditions of QFTs.

The framework successfully models spectra and mode functions in a flat spacetime example.

Boundary conditions are derived from inner product conservation in the spin system.

Abstract

We develop a framework to simulate quantum field theories (QFTs) with boundaries in $(1+1)$-dimenmsional curved spacetimes by employing open spin systems. Building upon our previous work that established a mapping from spin systems to QFTs in periodic geometries, we extend the correspondence to systems with boundaries, where boundary conditions play a crucial role in shaping the dynamics. Focusing on Majorana fermions, we derive the allowed boundary conditions from the requirement of inner product conservation and formulate their realization in spin systems. The corresponding spin model is shown to reproduce boundary conditions of QFT accurately when a free function in the spin model is appropriately chosen. As an explicit demonstration, we analyze a flat spacetime example, comparing spectra, mode functions, and linear responses between the continuum and lattice descriptions. Our findings confirm that open spin systems can successfully replicate QFT dynamics with boundaries.