Abstract
The Haldane-Shastry model is one of the most studied interacting spin systems. The Yangian symmetry makes it exactly solvable, and the model has semionic excitations. We introduce disorder into the Haldane-Shastry model by allowing the spins to sit at random positions on the unit circle and study the properties of the eigenstates. At weak disorder, the spectrum is similar to the spectrum of the clean Haldane-Shastry model. At strong disorder, the long-range interactions in the model do not decay as a simple power law. The eigenstates in the middle of the spectrum follow a volume law, but the coefficient is small, and the entropy is hence much less than for an ergodic system. In addition, the energy level spacing statistics is neither Poissonian nor of the Wigner-Dyson type. The behavior at strong disorder hence serves as an example of a non-ergodic phase, which is not of the many-body localized kind, in a model with long-range interactions and SU(2) symmetry.
Highlights
The typical behavior of interacting quantum many-body systems is to display ergodic physics. This is encoded in the eigenstate thermalization hypothesis, which says that local observables computed for an individual eigenstate of the Hamiltonian is described by the thermal microcanonical ensemble [1,2,3,4,5,6]
We investigated the role of disorder on the Haldane-Shastry model, which has long-range interactions and SU(2) symmetry
The disorder-averaged entanglement entropy for a state close to the middle of the energy spectrum showed a transition into a nonergodic phase at strong disorder
Summary
The typical behavior of interacting quantum many-body systems is to display ergodic physics. An investigation of the antiferromagnetic Heisenberg chain with SU(2) symmetry and nearest-neighbor exchange interactions of random strengths showed that a different type of nonergodic phase appears in a broad regime at strong disorder [16,17]. We study the effects of disorder on the excited states of the Haldane-Shastry model. The model possesses an approximate Yangian symmetry due to the proximity to the clean model, which is integrable, and the disorder-averaged entanglement entropy follows a volume law. Entanglement entropy follows a volume law, but the coefficient is much smaller than for weak disorder, and the entanglement is much less than for an ergodic system To further confirm this nonergodic phase, we study the level spacing statistics at strong disorder, which turns out to be neither Poissonian nor of the Wigner-Dyson type.
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