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Bulletin of the American Physical Society

Exact Diagonalization of a Quantum XXZ Model with Long-Range Interactions

Justin A. Williams, David A. Smith, C.C.-Joseph Wang, Christopher N. Varney

Published Mar 14, 2016• 0 citations
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Ground-state properties of ferrimagnetic XXZ chains with alternating spins S A and S B with nearest-neighbor exchange interaction are discussed based upon the results for finite-size systems obtained mainly by the exact diagonalization method and partly by the density matrix renormalization group method. For -1<Δ<1, where Δ is the parameter of anisotropy of the interactions, the ground state is unique or doubly degenerate and gapless. When Δ=1, the ground state of 2 N sites is the state with total spin N | S A - S B |, and has nonvanishing Néel long-range order parameter. For Δ>1, the ground state is doubly degenerate Néel long-range ordered state with a finite energy gap.
Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many metastable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional (1D) model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization and quasi-exact numerical techniques (density-matrix renormalization group and infinite time-evolving block decimation). We find that the complete devil's staircase—an infinite sequence of crystal states existing at vanishing tunneling—spreads to a succession of lobes similar to the Mott lobes found in Bose–Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar 2D models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long-range (algebraic) correlations, as opposed to models with nearest-neighbor tunneling, that show exponential decay of correlations.