Inhomogeneous field theory inside the arctic circle

Understand

Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved.

• The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region.
• Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory.
• It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac field theory in curved space.