Narrow Results

In the present paper, by applying the reflection positivity method due to Dyson, Lieb, and Simon, we rigorously establish the sufficient condition for existence of the Néel long-range order (NLRO) in two-dimensional spin-1/2 XXZ. Our result shows that if the anisotropic coupling Δ satisfies 0 ≤ Δ ≤ 0.30 or Δ ≥ 1.52, the existence of the NLRO along easy axis is proved.

In this paper, we study quantum phase transitions in both the one- (1D) and two-dimensional (2D) spin 1/2 XXZ models by a two-site correlation entropy. We show that the behavior of the correlation entropy is related to the ground-state symmetries and low-lying excitations of these systems. Therefore, the anomalies and minimum behaviors of the correlation entropy can signal the quantum phase transition points in the ground state of both models.

The four-level entangled quantum refrigerator (QR) is studied in the XXZ Heisenberg model for the two-qubits. The Hamiltonian of the problem includes the exchange parameters J_x = J_y = J and J_z = αJ along the x-, y- and z-directions, respectively, and constant external magnetic field B in the z-direction. The parameter α is introduced into the model which controls the strength of the exchange parameter J_z in comparison to J_x and J_y, thus, our investigation of QR includes the XX (α = 0.0), XXX (α = 1.0) and XXZ (for other α's) Heisenberg models. The two-qubits are assumed to be in contact with two heat reservoirs at different temperatures. The concurrences for a two-qubit are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency are derived. The contour, i.e., the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are illustrated.

We show how defects in a spin chain described by the XXZ model may be used to generate entangled states, such as Bell and W states, and how to maintain them with high fidelity. We also discuss, in the presence of several excitations, how the anisotropy of the system may be combined with defects to effectively assist in the creation of the desired states.

The four-level entangled quantum heat engine (QHE) is analyzed in the various Heisenberg models for a two-qubit. The QHE is examined for the XX, XXX and XXZ Heisenberg models by introducing a parameter x which controls the strength of the exchange parameter J_z = xJ along the z-axis with respect to the ones along the x- and y-axes, i.e. J_x = J_y = J, respectively. It is assumed that the two-qubit is entangled and in contact with two heat reservoirs at different temperatures and under the effect of a constant magnetic field. The concurrences (C) are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency of the QHE are derived. The contour, i.e. the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are calculated and some interesting features are found.

Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin ½, the phase model on a finite chain, etc.) is reviewed. Some additional information on this issue is also presented.

For the integrable 6 vertex model, the expectation values of local operators are known to be given by complicated multiple integrals. We show that there exists a basis of (quasi) local operators for which the expectation values simplify drastically. Such a basis is constructed out of a simple ‘tail’ operator (analogous to the disorder field in the Ising model) by acting with integrals of motion and a newly introduced set of fermions. The expectation values for their generating functions are given by determinants with explicit entries. This fermionic structure is present at a generic coupling, away from the usual ‘free fermion point’.

Taking the continuum limit to CFT and the sine-Gordon model, we formulate conjectural explicit formulas for the one-point functions of all descendant fields in both cases, generalizing the remarkable formulas due to Lukyanov, Zamolodchikov and others. We argue also that at the level of form factors our fermions coincide with yet another fermions which have been introduced some time ago by Babelon, Bernard and Smirnov.

This talk is based on a series of joint works with H. Boos, T. Miwa, F. Smirnov and T. Takeyama.

Note from Publisher: This article contains the abstract only.