### Speaker

Andrzej M. Oles
(Jagiellonian University)

### Description

Exchange interactions in orbital models are frustrated even on a
square lattice, where two $T=1/2$ pseudospin components
$T_i^{\gamma}(\theta)$ parameterized by angle $\theta\in(0,\pi/2]$ interact by terms $JT_i^{\gamma}(\theta)T_j^{\gamma}(\theta)$.
Maximal frustration in the quantum compass model with
$T_i^{\gamma}(\pi/2)\equiv\frac12\sigma_i^{\gamma}$, where
$\sigma_i^{\gamma}$ is the Pauli matrix, is reduced to moderate
frustration for the $e_g$ orbital model at $\theta=\pi/3$ [1].
We investigate thermodynamic phase transitions at temperature $T_c$
on an infinite square lattice by variational tensor network renormalization (VTNR) in imaginary time. From the linear susceptibility (order parameter) in the symmetric (symmetry-broken) phase the onset of nematic order in the quantum compass model is estimated at $T_c/J=0.0606(4)$ [2], in good agreement with Quantum Monte Carlo (QMC). For the 2D $e_g$ orbital model one finds: ($i$) a very accurate VTNR estimate of $T_c/J=0.3566\pm 0.0001$ while QMC fails due to the sign problem, and ($ii$) that the critical exponents are within the Ising universality class. Remarkably large difference in frustration and entanglement results in so distinct $T_c$.
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[1] L. Cincio, J. Dziarmaga, and A. M. Oleś, Phys. Rev. B **82**, 104416 (2010).
[2] P. Czarnik, J. Dziarmaga, and A. M. Oleś, Phys. Rev. B **93**, 184410 (2016).

### Primary author

Andrzej M. Oles
(Jagiellonian University)

### Co-authors

Jacek Dziarmaga
(Jagiellonian University)
Piotr Czarnik
(Jagiellonian University)