Non-Interacting Motzkin Chain - Periodic Boundary Conditions

Abstract

The Motzkin spin chain is a spin-1 model introduced in \cite{shor} as an example of a system exhibiting a high degree of quantum fluctuations whose ground state can be mapped to Motzkin paths that are generated with local equivalence moves. This model is difficult to solve in general but keeping just the height preserving local equivalence moves we show that the model becomes integrable which when projected to certain subspaces of the full Hilbert space is isomorphic to the spin-$\frac{1}{2}$ XXX chain. In fact in the full Hilbert space the system is akin to two non-interacting spin-$\frac{1}{2}$ XXX chains making the spectrum the same as the latter with the change coming in the degeneracy of the states. We then show that including the height-changing local-equivalence move is the same as introducing interactions in the above system.

arXiv comment18 pages, 5 figures

References in corpus (14)

• Area laws for the entanglement entropy - a review
• An Area Law for One Dimensional Quantum Systems
• Entanglement in XY Spin Chain
• Power law violation of the area law in quantum spin chains
• On an algebraic approach to higher dimensional statistical mechanics
• Criticality without frustration for quantum spin-1 chains
• Stochastic Error Cancellation in Analog Quantum Simulation
• The two-boundary Temperley-Lieb algebra
• Deformed Fredkin Spin Chain with Extensive Entanglement
• Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains
• Ground State Entanglement in One Dimensional Translationally Invariant Quantum Systems
• The Temperley-Lieb algebra and its generalizations in the Potts and XXZ models
• Algebraic Bethe ansatz
• The pair-flip model: a very entangled translationally invariant spin chain