We study the antiferromagnetic XXZ chain with longitudinal boundary magnetic fields using numerical diagonalization and the exact Bethe ansatz solution. We identify a phase transition at $h_w=-\mathrm{\Delta }+1$ (with $\mathrm{\Delta }>1$) as a continuous wetting transition, in which the domain wall delocalizes from the boundary at the transition point. From the exact solution, we obtain both the energy gap and the boundary magnetization. We then propose a perturbation approximation, whose predictions for the energy gap and boundary magnetization closely match the exact results. The universal magnetization profile at the critical point is obtained. Using this approximation, we also compute the correlation function and, in turn, determine the correlation length and the thickness of the wetting layer. The correlation length, the wetting layer thickness, and the dynamical critical exponents are $\nu =1, {\beta }_s=1$, and $z=2$, respectively, together with the universal magnetization profile at the critical point, indicating that the transition belongs to the Ising universality class.

Close

PrevNext

View figure in article

• Quantum criticality
• Quantum phase transitions
• 1-dimensional spin chains
• Bethe ansatz
• Perturbation theory
• Quantum spin chains
• XYZ model