טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentIsrael Reichental
SubjectQuatum Spin-Orbital Liquids in Three Dimensions
DepartmentDepartment of Physics
Supervisor Professor Podolsky Daniel
Full Thesis textFull thesis text - English Version


Abstract

We conduct a theoretical study of a magnetic quantum insulator in three dimensions. Our goal is to determine the possibility to obtain a ground state with the unusual property that it does not break any symmetry of the system. This situation, in which the magnetic moments are not frozen even at zero temperature, is commonly referred to as a spin liquid. Spin liquids are common in one dimensional systems. By contrast, in higher dimensions the tendency to a spin liquid ground state is reduced, and additional mechanisms are necessary to compensate for their higher dimensionality. These include geometrical frustration and charge fluctuations. In this thesis, we study a system -- the SU(4) symmetric Kugel-Khomskii model -- that focuses on a different mechanism, enhanced quantum fluctuations. We study this model on the simple cubic and the diamond lattices. The model can't be solved analytically, and numerically it can only be solved for very small systems using exact diagonalization. Therefore, we resort to two different approaches which allow us to study larger systems. The first approach is to construct Ansatz spin liquid ground states. Notably, these states are constructed without any tunable parameters. We compare these wave functions to other candidate states, including symmetry breaking states, and find conditions under which their energy is favorable. In addition, we compute their correlations and verify that these states do not possess long range order. Finally, by a comparison to an exact diagonalization, we evaluate the proximity of these wave functions to the exact ground state for small systems, and place a lower bound on their overlap. We use Holstein-Primakoff representation of our model to show an indication for the absence of magnetic-orbital ordering in it. Our results may have implications for certain solid state systems with additional orbital degrees of freedom, and also for cold atom systems with enlarged symmetries.