Theory of d-density wave viewed from a vertex model and its implications

TL;DR

This paper models the thermal disordering of the d-density wave in high-temperature superconductors using a 6-vertex model, revealing a transition with no specific heat anomaly and exploring quantum effects and generalizations.

Contribution

It establishes a classical vertex model framework for the d-density wave transition and extends it to quantum and lattice generalizations, linking to broader condensed matter phenomena.

Findings

Disordered phase exhibits power-law correlations without a specific heat anomaly.

Transition involves a collapse of the order parameter magnitude at higher temperature.

Quantum and lattice generalizations provide insights into quantum criticality and metal-insulator transitions.

Abstract

The thermal disordering of the $d$-density wave, proposed to be the origin of the pseudogap state of high temperature superconductors, is suggested to be the same as that of the statistical mechanical model known as the 6-vertex model. The low temperature phase consists of a staggered order parameter of circulating currents, while the disordered high temperature phase is a power-law phase with no order. A special feature of this transition is the complete lack of an observable specific heat anomaly at the transition. There is also a transition at a even higher temperature at which the magnitude of the order parameter collapses. These results are due to classical thermal fluctuations and are entirely unrelated to a quantum critical point in the ground state. The quantum mechanical ground state can be explored by incorporating processes that causes transitions between the vertices, allowing us to discuss quantum phase transition in the ground state as well as the effect of quantum criticality at a finite temperature as distinct from the power-law fluctuations in the classical regime. A generalization of the model on a triangular lattice that leads to a 20-vertex model may shed light on the Wigner glass picture of the metal-insulator transition in two-dimensional electron gas. The power-law ordered high temperature phase may be generic to a class of constrained systems and its relation to recent advances in the quantum dimer models is noted.