Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

Inhomogeneous field theory inside the arctic circle


Stéphan,  Jean-Marie
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;


Viti,  Jacopo
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available

Allegra, N., Dubail, J., Stéphan, J.-M., & Viti, J. (2016). Inhomogeneous field theory inside the arctic circle. Journal of Statistical Mechanics: Theory and Experiment, 2016: 053108. doi:10.1088/1742-5468/2016/05/053108.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-E9D1-0
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 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.