Emergent tilt order in Dirac polymer liquids

TL;DR

This paper investigates a 2D directed polymer liquid with bending rigidity, revealing a phase of tilted order through a quantum analogy, and analyzes the phase diagram and response functions considering fluctuations.

Contribution

It introduces a novel quantum many-fermion analogy to study the phase behavior of zigzagging directed polymers with bending rigidity.

Findings

Identification of a tilted ordered phase in the polymer liquid

Development of a phase diagram for the system

Analysis of fluctuation effects on the phase behavior

Abstract

We study a liquid of zigzagging two-dimensional directed polymers with bending rigidity, i.e., polymers whose conformations follow checkerboard paths. In the continuum limit the statistics of such polymers obey the Dirac equation for particles of imaginary mass. We exploit this observation to investigate a liquid of these polymers via a quantum many-fermion analogy. A self-consistent approximation predicts a phase of tilted order, in which the polymers may develop a preference to zig rather than zag. We compute the phase diagram and key response functions for the polymer liquid, and comment on the role played by fluctuations.