arXiv:0809.4068 · Physical Review Letters

First Order Phase Transition in the Anisotropic Quantum Orbital Compass Model

Román Orús, Andrew C. Doherty, Guifré Vidal

Published Feb 19, 2009• 92 citations

Abstract

We investigate the anisotropic quantum orbital compass model on an infinite square lattice by means of the infinite projected entangled-pair state algorithm. For varying values of the Jx and Jz coupling constants of the model, we approximate the ground state and evaluate quantities such as its expected energy and local order parameters. We also compute adiabatic continuations of the ground state, and show that several ground states with different local properties coexist at Jx=Jz. All our calculations are fully consistent with a first order quantum phase transition at this point, thus corroborating previous numerical evidence. Our results also suggest that tensor network algorithms are particularly fitted to characterize first order quantum phase transitions.

DOI: 10.1103/physrevlett.102.077203

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arXiv:0809.4068 · Physical Review Letters

First Order Phase Transition in the Anisotropic Quantum Orbital Compass Model

Román Orús, Andrew C. Doherty, Guifré Vidal

Published Feb 19, 2009• 92 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.102.077203

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Motivated by the recent discovery of ferromagnetic quantum criticality in the heavy fermion compound

{\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}

, we develop a numerical algorithm of infinite projected entangled pair states for the anisotropic ferromagnetic Kondo-Heisenberg model in two dimensions and study the ferromagnetic quantum phase transitions with varying magnetic and hopping anisotropy. Our calculations reveal a continuous ferromagnetic quantum phase transition in the large anisotropic region and first-order quantum phase transitions for smaller anisotropy. Our results highlight the importance of magnetic anisotropy on ferromagnetic quantum criticality in Kondo lattice systems and provide a possible explanation for the experimental observation in

{\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}

with a quasi-one-dimensional magnetic structure. Our work opens the avenue for future studies of the rich Kondo lattice physics using state-of-the-art tensor network approaches.

We investigate the ground state of the

\mathrm{SU}(4)

Heisenberg model on a square lattice with spatial anisotropy on each plaquette bond using the tensor-network method based on infinite projected entangled pair states. We find that the

\mathrm{SU}(4)

singlet ground state appears in the strongly anisotropic limit, whereas N\'eel and valence-bond crystal orders coexist in the nearly isotropic limit. By examining the intermediate parameter region, we identify a phase transition between these phases. The nature of the phase transition is likely to be of first order, and the transition point is estimated to be around ${J}^{\ensuremath{'}}/J\ensuremath{\approx}0.85(5)$, where

J

and ${J}^{\ensuremath{'}}$ are the interaction strengths of intra- and interplaquette bonds, respectively. We also calculate the anisotropy dependence of singlet correlations on a plaquette bond, which will be useful for future experiments of ultracold atoms in optical lattices.