One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization

TL;DR

This paper introduces a 1D pseudospin ladder model with alternating Ising interactions, revealing diverse phases including a nematic phase, and explores its rich phase diagram through exact diagonalization.

Contribution

The study presents a novel 1D ladder model interpolating between two compass models, analyzing its phase diagram and identifying a nematic phase with macroscopic degeneracy.

Findings

Identification of a nematic phase with macroscopic degeneracy.

Discovery of phases with broken translation symmetry, such as dimerized and trimerized states.

Reduction to a 1D compass model with spin-1 in certain parameter regimes.

Abstract

We introduce a one-dimensional (1D) pseudospin model on a ladder where the Ising interactions along the legs and along the rungs alternate between $X_{i}X_{i+1}$ and $Z_{i}Z_{i+1}$ for even/odd bond (rung). We include also the next nearest neighbor Ising interactions on plaquettes' diagonals that alternate in such a way that a model where only leg interactions are switched on is equivalent to the one when only the diagonal ones are present. Thus in the absence of rung interactions the model can interpolate between two 1D compass models. The model posses local symmetries which are the parities within each $2\times 2$ cell (plaquette) of the ladder. We find that for different values of the interaction it can realize ground states that differ by the patterns formed by these local parities. By exact diagonalization we derive detailed phase diagrams for small systems of $L=4$, 6 and 8 plaquettes, and use next $L=12$ to identify generic phases that appear in larger systems as well. Among them we find a nematic phase with macroscopic degeneracy when the leg and diagonal interactions are equal and the rung interactions are larger than a critical value. The nematic phase is similar to the one found in the two-dimensional compass model. For particular parameters the low-energy sector of the present plaquette model reduces to a 1D compass model with spins $S=1$ which suggests that it realizes peculiar crossovers within the class of compass models. Finally, we show that the model can realize phases with broken translation invariance which can be either dimerized, trimerized, \textit{etcetera}, or completely disordered and highly entangled in a~well identified window of the phase diagram.