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Chaos Solitons & Fractals

Emptiness formation probability of XX-chain in diffusion process

Yoshiko Ogata

Published Aug 7, 2003• 0 citations
Publisher
DOI
10.1016/s0960-0779(03)00262-5

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The emptiness formation probability (EFP) that the first n spins of the chain are all aligned downwards is studied for the one-dimensional spin-1 2 XX chain system with both critical and non-critical regimes with three spin and uniform long-range interactions.By using the emptiness formation probability P (n), the block-block entanglement Sn and the magnetization M z , the properties of the system are also studied.It is worthy of note that when the quantum phase transition from the phase III to the phase II occurs, the Emptiness Formation Probability P (n) of the system decreases, but the block-block entanglement Sn increases.
The emptiness formation probability (EFP) that the first n spins of the chain are all aligned downwards is studied for the one-dimensional spin- 1/2 XX chain system with both critical and non-critical regimes with three spin and uniform long-range interactions. By using the emptiness formation probability P(n), the block-block entanglement Sn and the magnetization Mz, the properties of the system are also studied. It is worthy of note \nthat when the quantum phase transition from the phase III to the phase II occurs, the Emptiness Formation Probability P(n) of the system decreases, but the block-block entanglement Sn increases.
We review some known properties of the "emptiness formation probability" correlation which we have calculated numerically for spin-1/2 XX chains with constant (homogeneous) or alternating (dimerized) nearestneighbor coupling and an external field (in z direction) for arbitrary temperature.The long-distance asymptotic behavior of this correlation is known to be Gaussian at zero temperature and exponential at finite temperature for the homogeneous chain.By simple analytical arguments the exponential behavior at finite temperature extends to the dimerized system.Numerical results for the dimerized chain confirm the exponential decay at finite temperature and show Gaussian decay at zero temperature.