Inhomogeneous field theory inside the arctic circle

• Published in: Journal of Statistical Mechanics: Theory and Experiment
• Main Authors: Allegra, Nicolas, Dubail, Jerome, Stéphan, Jean-Marie, Viti, Jacopo
• Other Authors: Institut Jean Lamour (IJL), Institut de Chimie - CNRS Chimie (INC-CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Max Planck Institute for the Physics of Complex Systems (MPI-PKS), Max-Planck-Gesellschaft
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2016
• Subjects: [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]; [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el]; [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]; Arctic
• Online Access: https://hal.science/hal-01586415; https://doi.org/10.1088/1742-5468/2016/05/053108

International audience 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. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and 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, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix.