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arXiv:1605.08178 · Physical review. B./Physical review. B

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

Wojciech Brzezicki, Andrzej M. Oleś

Published Jun 1, 2016• 2 citations
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Abstract

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 possesses local symmetries which are the parities within each $2\ifmmode\times\else\texttimes\fi{}2$ 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. By performing a perturbative expansion around this phase we find indeed a very complex competition around the nematic phase which has to do with releasing frustration in this range of parameters. 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, etc., or completely disordered and highly entangled in a well identified window of the phase diagram.

DOI
10.1103/physrevb.93.214402

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We introduce a one-dimensional (1D) pseudospin model on a ladder where the Ising interactions along the legs and along the rungs alternate between XiXi+1{X}_{i}{X}_{i+1}Xi​Xi+1​ and ZiZi+1{Z}_{i}{Z}_{i+1}Zi​Zi+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 possesses local symmetries which are the parities within each 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 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=4L=4L=4, 6, and 8 plaquettes, and use next L=12L=12L=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. By performing a perturbative expansion around this phase we find indeed a very complex competition around the nematic phase which has to do with releasing frustration in this range of parameters. 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=1S=1S=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, etc., or completely disordered and highly entangled in a well identified window of the phase diagram.
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We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions σizσi+1zσ_i^zσ_{i+1}^zσiz​σi+1z​ and σixσi+1xσ_i^xσ_{i+1}^xσix​σi+1x​, alternating between even/odd bonds, and present its exact solution by mapping to quantum Ising models. We show that the nearest neighbor pseudospin correlations change discontinuosly and indicate divergent correlation length at the first order quantum phase transition. At this transition one finds the disordered ground state of the compass model with high degeneracy 2×2N/22\times 2^{N/2}2×2N/2 in the limit of N→∞N\to\inftyN→∞.
We introduce a one-dimensional plaquette orbital model with a topology of a ladder and alternating interactions between xxx and zzz pseudospin components both along the ladder legs and on the rungs. We show by an exact transformation 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 in the Hilbert space reduced by a factor of 2. 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 establish that the quantum effects are of purely short-range nature in the model and we find estimated values of the ground state energy and the gap in the thermodynamic limit from the system sizes up to L=12L=12L=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 an otherwise rather classical system may be of interest in the context of quantum computing devices.
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