We analyze a one-dimensional system of particles evolving from a domain-wall initial state. This 'quantum quench' problem is well-known in real-time; here we analyze in imaginary time. The main interest of this model is that it exhibits the 'arctic-circle phenomenon' originally discovered in dimer models by [Propp, Jokusch, Shor], 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) massless Dirac theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac theory in curved two-dimensional space. The technique used to solve the toy-model can be extended to deal with the transfer matrices of other models: dimers on the honeycomb lattice, on the square lattice, and the six-vertex model at the free fermion point ($\Delta=0$). In all cases, explicit expressions are given for the long-range correlations in the critical region, and for the underlying Dirac action.

Nicolas Allegra (UCSB)Tue, Mar 8

We analyze a one-dimensional system of particles evolving from a domain-wall initial state. This 'quantum quench' problem is well-known in real-time; here we analyze in imaginary time. The main interest of this model is that it exhibits the 'arctic-circle phenomenon' originally discovered in dimer models by [Propp, Jokusch, Shor], 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) massless Dirac theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac theory in curved two-dimensional space. The technique used to solve the toy-model can be extended to deal with the transfer matrices of other models: dimers on the honeycomb lattice, on the square lattice, and the six-vertex model at the free fermion point ($\Delta=0$). In all cases, explicit expressions are given for the long-range correlations in the critical region, and for the underlying Dirac action.