An Exactly Solvable Model of Randomly Pinned Charge Density Waves in Two Dimensions

TL;DR

This paper introduces an exactly solvable two-dimensional model for charge density waves with random pinning, revealing how disorder and fluctuations influence phase transitions and order in such systems.

Contribution

It presents a novel exactly solvable model for 2D charge density waves with quenched disorder, using large-N techniques to analyze phase behavior and correlations.

Findings

Captures Berezinskii-Kosterlitz-Thouless transition physics at large N.

Identifies a crossover between weak and strong disorder regimes.

Shows disorder and thermal fluctuations suppress long-range order.

Abstract

The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-$N$ technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii-Kosterlitz-Thouless phase transition in the clean limit at large $N$. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.