Orbital order driven quantum criticality

Abstract

Charge, spin, and orbital degrees of freedom underlie the physics of transition metal compounds. Much work has revealed quantum critical points associated with spin and charge degrees of freedom in many of these systems. Here we illustrate that the simplest models that embody the orbital degrees of freedom - the two- and three-dimensional quantum orbital compass models - exhibit an exact quantum critical behavior on diluted square and cubic lattices (with a doping fraction of 1/4 and 1/2 respectively). This raises the possibility of quantum critical points triggered by the degradation of orbital order upon doping (or applying pressure to) such transition metal systems. We prove the existence of an orbital spin glass in several related systems in which the orbital couplings are made non-uniform. Moreover, a new orbital Larmor precession (i.e., a periodic change in the orbital state) is predicted when uniaxial pressure is applied.

6 pages, 1 figure (to appear in Europhysics Letters)

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• Effective and exact holographies from symmetries and dualities
• Spin-orbital physics for p orbitals in alkali RO_2 hyperoxides --- generalization of the Goodenough-Kanamori rules
• Transverse fields to tune an Ising-nematic quantum critical transition
• Entangled spin-orbital phases in the bilayer Kugel-Khomskii model
• Exact solution for a quantum compass ladder
• Absence of Finite Temperature Phase Transitions in the X-Cube Model and its ${\mathbb{Z}}_p$ Generalization
• Valence Bond Crystal and possible orbital pinball liquid in a t2g model
• Dilution effect in correlated electron system with orbital degeneracy
• Robust Topological Degeneracy of Classical Theories
• A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets