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

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.

Figures (8)

• Figure 1: Spectra of QFT (blue dots) and spin systems (orange dots) for $p = 1, 0.5, 0.1,$ and $0$. The parameters are set to $L = 128$, $\ell = \pi$, and $m = 1$. The spectrum of the spin system typically begins to deviate from that of the QFT at the doubler mass scale given by $2p/\varepsilon - m$.
• Figure 2: Mode functions of QFT and spin systems for $p = 1, 0.5, 0.1,$ and $0$. The parameters are set to $L = 128$, $\ell = \pi$, and $m = 1$.
• Figure 3: Linear response of QFT and spin systems under a Gaussian source for $p = 1, 0.5, 0.1,$ and $0$. The parameters are set to $L = 128$, $\ell = \pi$, and $m = 1$.
• Figure 4: Profiles of the function $p(x)$ for $\eta = 0, 0.5, 0.9, 1,$ and $2$ from top to bottom.
• Figure 5: Spectra of the QFT (blue dots) and spin systems (orange dots) for $\eta = 0, 0.5, 0.9, 1,$ and $2$. The parameters are set to $L = 128$, $\ell = \pi$, and $m = 1$.