On the phase diagram of the anisotropic XY chain in transverse magnetic field

• Extensive study of the ground energy of the XY chain in transverse magnetic field.
• Explicit proof of the ground energy smoothness on the oscillatory–ferromagnetic line.
• Ground state energy expansions around all singular points are calculated.
• Detailed numerical analysis of the gap energy of the open chain.

We investigate an explicit formula for ground state energy of the anisotropic XY chain in transverse magnetic field. In particular, we examine the smoothness properties of this expression. We explicitly demonstrate that the ground-state energy is infinitely differentiable on the boundary between ferromagnetic and oscillatory phases. We also confirm known 2d-Ising type behaviour in the neighbourhood of certain lines of phase diagram and give more detailed information there, calculating a few next-to-leading exponents as well as the corresponding amplitudes.