Order in Quantum Compass and Orbital $e_g$ Models

TL;DR

This study uses tensor network methods to analyze phase transitions in quantum compass and $e_g$ orbital models, accurately estimating critical temperatures and confirming Ising universality class behavior.

Contribution

The paper provides precise estimates of critical temperatures and exponents for the compass and $e_g$ orbital models using variational tensor network renormalization.

Findings

Critical temperature for compass model: ${ m T}_c/J=0.0606(4)$.

Critical temperature for $e_g$ orbital model: ${ m T}_c/J=0.3566 ext{±}0.0001$.

Critical exponents match Ising universality class.

Abstract

We investigate thermodynamic phase transitions in the compass model and in $e_g$ orbital model on an infinite square lattice by variational tensor network renormalization (VTNR) in imaginary time. The onset of nematic order in the quantum compass model is estimated at ${\cal T}_c/J=0.0606(4)$. For~the $e_g$ orbital model one finds: ($i$) a very accurate estimate of ${\cal T}_c/J=0.3566\pm 0.0001$ and ($ii$)~the~critical exponents in the Ising universality class. Remarkably large difference in frustration results in so distinct values of ${\cal T}_c$, while entanglement influences the quality of ${\cal T}_c$ estimation.