Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model

We introduce a one-dimensional plaquette orbital model with a topology of a ladder and alternating interactions between $x$ and $z$ pseudospin components along both the ladder legs and on the rungs. We show that it is equivalent to an effective spin model in a magnetic field, with spin dimers that replace plaquettes and are coupled along the chain by three-spin interactions. Using perturbative treatment and mean field approaches with dimer correlations we study the ground state spin configuration and its defects in the lowest excited states. By the exact diagonalization approach we find that the quantum effects in the model are purely short-range and we get estimated values of the ground state energy and the gap in the thermodynamic limit from the system sizes up to $L=12$ dimers. Finally, we study a class of excited states with classical-like defects accumulated in the central region of the chain to find that in this region the quantum entanglement measured by the mutual information of neighboring dimers is locally increased and coincides with disorder and frustration. Such islands of entanglement in otherwise rather classical system may be of interest in the context of quantum computing devices.Comment: 12 pages, 12 figure

Symmetry properties and spectra of the two-dimensional quantum compass model

We use exact symmetry properties of the two-dimensional quantum compass model to derive nonequivalent invariant subspaces in the energy spectra of $L\times L$ clusters up to L=6. The symmetry allows one to reduce the original $L\times L$ compass cluster to the $(L-1)\times (L-1)$ one with modified interactions. This step is crucial and enables: (i) exact diagonalization of the $6\times 6$ quantum compass cluster, and (ii) finding the specific heat for clusters up to L=6, with two characteristic energy scales. We investigate the properties of the ground state and the first excited states and present extrapolation of the excitation energy with increasing system size. Our analysis provides physical insights into the nature of nematic order realized in the quantum compass model at finite temperature. We suggest that the quantum phase transition at the isotropic interaction point is second order with some admixture of the discontinuous transition, as indicated by the entropy, the overlap between two types of nematic order (on horizontal and vertical bonds) and the existence of the critical exponent. Extrapolation of the specific heat to the $L\to\infty$ limit suggests the classical nature of the quantum compass model and high degeneracy of the ground state with nematic order.Comment: 15 pages, 12 figures; accepted for publication in Physical Review

One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization

We introduce a one-dimensional (1D) pseudospin model on a ladder where the Ising interactions along the legs and along the rungs alternate between $X_{i}X_{i+1}$ and $Z_{i}Z_{i+1}$ for even/odd bond (rung). We include also the next nearest neighbor Ising interactions on plaquettes' diagonals that alternate in such a way that a model where only leg interactions are switched on is equivalent to the one when only the diagonal ones are present. Thus in the absence of rung interactions the model can interpolate between two 1D compass models. The model posses local symmetries which are the parities within each $2\times 2$ cell (plaquette) of the ladder. We find that for different values of the interaction it can realize ground states that differ by the patterns formed by these local parities. By exact diagonalization we derive detailed phase diagrams for small systems of $L=4$, 6 and 8 plaquettes, and use next $L=12$ to identify generic phases that appear in larger systems as well. Among them we find a nematic phase with macroscopic degeneracy when the leg and diagonal interactions are equal and the rung interactions are larger than a critical value. The nematic phase is similar to the one found in the two-dimensional compass model. For particular parameters the low-energy sector of the present plaquette model reduces to a 1D compass model with spins $S=1$ which suggests that it realizes peculiar crossovers within the class of compass models. Finally, we show that the model can realize phases with broken translation invariance which can be either dimerized, trimerized, \textit{etcetera}, or completely disordered and highly entangled in a~well identified window of the phase diagram.Comment: 18 pages, 14 figures, accepted by Physical Review

Entangled Spin-Orbital Phases in the d9^9 Model

We investigate the phase diagrams of the spin-orbital $d^9$ Kugel-Khomskii model for a bilayer and a monolayer square lattice using Bethe-Peierls-Weiss method. For a bilayer we obtain valence bond phases with interlayer singlets, with alternating planar singlets, and two entangled spin-orbital (ESO) phases, in addition to the antiferromagnetic and ferromagnetic order. Possibility of such entangled phases in a monolayer is under investigation at present.Comment: 3 pages, 2 figures, presented at Euroconference Physics of Magnetism 201

Noncollinear Magnetic Order Stabilized by Entangled Spin-Orbital Fluctuations

Quantum phase transitions in the two-dimensional Kugel-Khomski model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization ansatz. When $3z^2-r^2$ orbitals are favored by the crystal field and Hund's exchange is finite, both methods give a noncollinear exotic magnetic order which consists of four sublattices with mutually orthogonal nearest neighbor and antiferromagnetic second neighbor spins. We derive effective frustrated spin model with second and third neighbor spin interactions which stabilize this phase and follow from spin-orbital quantum fluctuations involving spin singlets entangled with orbital excitations.Comment: 5 pages, 5 figures and supplemental material (4 pages, 3 figures); accepted for publication in Phys. Rev. Let

Driving Topological Phases by Spatially Inhomogeneous Pairing Centers

We investigate the effect of periodic and disordered distributions of pairing centers in a one-dimensional itinerant system to obtain the microscopic conditions required to achieve an end Majorana mode and the topological phase diagram. Remarkably, the topological invariant can be generally expressed in terms of the physical parameters for any pairing center configuration. Such a fundamental relation allows us to unveil hidden local symmetries and to identify trajectories in the parameter space that preserve the non-trivial topological character of the ground state. We identify the phase diagram with topologically non-trivial domains where Majorana modes are completely unaffected by the spatial distribution of the pairing centers. These results are general and apply to several systems where inhomogeneous perturbations generate stable Majorana modes.Comment: 9 pages, 5 figure