Quantum simulation of the Schwinger model in deformed space: quantum gravitational effects

In this article, we study the real-time chiral phase transitions in the (1 + 1)-dimensional massive Schwinger model with a θ-term in the presence of a minimal length. The minimal length, which induces quantum gravitational effects, is implemented through deformed operators. First, we study the real-time chiral condensate for a time-independent and time-dependent Hamiltonian with a vanishing θ-term in the presence of minimal length. Finally, we study chiral phase transitions in the presence of minimal length by gradually changing the θ-term angle from 0 to 2π. We find that quantum gravitational effects cause long-range interactions, and these effects induce remarkable changes in the time-dependent chiral condensate. However, the perturbative GUP corrections to the time-dependent chiral condensate, which corresponds to energy beyond the LHC energy scale, are small.