Phase Transitions in Models for Coupled Charge-Density Waves

TL;DR

This paper investigates phase transitions in coupled charge-density wave models using analytical and numerical methods, revealing how commensurability and frustration influence the nature and boundaries of different ordered states.

Contribution

It maps the zero-temperature effective action onto ext{XY} models and analyzes the impact of commensurability and frustration on phase transition behavior.

Findings

Single transition between clock order and disorder in 3D and 4D systems.

Transition nature depends on the commensurability factor M.

Hysteresis occurs due to frustration in charge-density waves.

Abstract

Various phase transitions in models for coupled charge-density waves are investigated by means of the $\epsilon$-expansion, mean-field theory, and Monte Carlo simulations. At zero temperature the effective action for the system with appropriate commensurability effects is mapped onto the three- or four-dimensional \XY model, depending on spatiotemporal fluctuations, under the corresponding symmetry-breaking fields. It is revealed that the three- and four-dimensional systems display a single transition between the clock order (with broken Z$_M$ symmetry) and disorder. The nature of the phase transition depends crucially on the commensurability factor $M$: For $M \ge 4$, in particular, the transition belongs to the same university class as the \XY model. On the other hand, in the presence of misfit causing frustration in the charge-density wave, the inter-chain coupling is observed to favor either the commensurate state or the incommensurate state depending on the initial configuration; this gives rise to hysteresis around the commensurate-incommensurate transition. Boundaries separating such phases with different symmetries are obtained in the parameter space consisting of the temperature, symmetry-breaking field, fluctuation strength, inter-chain coupling, and misfit.