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The European Physical Journal B

Quantum correlations in the dimerized spin chain at zero and finite temperatures

Jianjun Jiang, Y. -J. Liu, F. Tang, Cuihong Yang

Published Jun 1, 2011• 3 citations
Publisher
DOI
10.1140/epjb/e2011-20280-1

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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.
We use the density matrix renormalization group method to compute the frequency and momentum-resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features strongly depend on the regime of the magnetic field. For increasing magnetic fields, the transitions from a gapped spin liquid phase to a Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be identified in the spectra. Compared to the zero-temperature case, the finite-temperature excitations give rise to additional spectral features that we compute numerically and identify analytically as transitions from thermally excited states. We compute quantitatively the broadening of the dispersion of a single spin-flip excitation due to the temperature and find a strong asymmetric broadening. We discuss the consequences of these findings for neutron experiments on dimerized one-dimensional quantum chains.
We describe a Peierls dimerization which occurs in ferromagnetic spin chains at finite temperature, within the modified spin-wave theory. Usual spin-wave theory is modified by introducing a Lagrange multiplier which enforces a nonmagnetic state at finite temperature. It is shown that this method gives results in excellent agreement with the density–matrix renormalization group applied to transfer matrices for dimerized ferromagnetic chains. We study bond correlation functions ( S i · S i+1 ) and explore the characteristic features of dimerization in the specific heat.