Thermodynamic limit of the Heisenberg–Ising chain

M. Fähnle

Frank Göhmann, Salvish Goomanee, Karol Kajetan Kozlowski +1 more

Bohdan Lisnyi

The exact solution of the distorted diamond Ising–Hubbard chain is analyzed in the special limit of infinite on-site electron-electron repulsion, where the two-electron Hubbard dimer becomes equivalent to the antiferromagnetic isotropic Heisenberg dimer. The special limit of infinite repulsion for the matrix of the cell Hamiltonian of this model is analytically calculated, and it is demonstrated that the exact solution of the distorted diamond Ising–Hubbard chain in this limit coincides with the exact solution of the spin-1/2 distorted diamond Ising–Heisenberg chain with antiferromagnetic isotropic Heisenberg interaction. The numerical calculation of the special limit of infinite repulsion for the ground-state phase diagram and thermodynamic characteristics of the distorted diamond Ising–Hubbard chain was performed in a way that provides a very fast convergence to the limit results for these characteristics.

Roya Radgohar, Afshin Montakhab

We provide a study of various quantum phase transitions occurring in the XY Heisenberg chain in a transverse magnetic field using the Meyer-Wallach (MW) measure of (global) entanglement. Such a measure, while being readily evaluated, is a multipartite measure of entanglement as opposed to more commonly used bipartite measures. Consequently, we obtain analytic expression of the measure for finite-size systems and show that it can be used to obtain critical exponents via finite-size scaling with great accuracy for the Ising universality class. We also calculate an analytic expression for the isotropic (XX) model and show that global entanglement can precisely identify the level-crossing points. The critical exponent for the isotropic transition is obtained exactly from an analytic expression for global entanglement in the thermodynamic limit. Next, the general behavior of the measure is calculated in the thermodynamic limit considering the important role of symmetries for this limit. The so-called oscillatory transition in the ferromagnetic regime can only be characterized by the thermodynamic limit where global entanglement is shown to be zero on the transition curve. Finally, the anisotropic transition is explored where it is shown that global entanglement exhibits an interesting behavior in the finite-size limit. In the thermodynamic limit, we show that global entanglement shows a cusp singularity across the Ising and anisotropic transition, while showing non-analytic behavior at the XX multicritical point. It is concluded that global entanglement, despite its relative simplicity, can be used to identify all the rich structure of the ground-state Heisenberg chain.

Zou Ha, F. D. M. Haldane

The exact and complete set of highest-weight eigenstates of the finite-size SU(n) Heisenberg chain with inverse-square exchange (ISE) are constructed using the occupation-number representation of the ``strings,'' which can be considered as the unbroken resonating-valence bonds. The string description, which is believed to be exact only in the thermodynamic limit for the Bethe ansatz solvable models, becomes exact for any size ISE model due to the squeezing effect of the strings in the ISE limit. This feature provides a basis for the realization of the Yangian symmetry in the ISE model.