Order in Quantum Compass and Orbital e_{g} Models |

P. Czarnik
^{a,b}, J. Dziarmaga^{a} and A.M. Oleś^{a,c}^{a}M. Smoluchowski Institute of Physics, Jagiellonian University, prof. S. Łojasiewicza 11, PL-30348 Kraków, Poland
^{b}Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, PL-31342 Kraków, Poland
^{c}Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany |

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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 𝓣_{c}/J=0.0606(4). For the e_{g} orbital model one finds: (i) a very accurate estimate of 𝓣_{c}/J=0.3566± 0.0001 and (ii) the critical exponents in the Ising universality class. Remarkably large difference in frustration results in so distinct values of 𝓣_{c}, while entanglement influences the quality of 𝓣_{c} estimation. |

DOI: 10.12693/APhysPolA.133.359 PACS numbers: 75.10.Jm, 05.10.Cc, 05.70.Fh, 75.25.Dk |