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

TL;DR

This paper analyzes the ground state energy of the anisotropic XY chain in a transverse magnetic field, revealing phase transition behaviors and smoothness properties using elliptic integrals, with detailed calculations near critical lines.

Contribution

It provides an explicit formula for the ground state energy and detailed analysis of its smoothness and critical behavior near phase boundaries.

Findings

Confirmed 2D-Ising type behavior near phase boundaries

Demonstrated infinite differentiability of energy on phase boundary

Calculated next-to-leading exponents and amplitudes

Abstract

We investigate an explicite formula for ground state energy of the anisotropic XY chain in transverse magnetic field. In particular, we examine the smoothness properties of the expression, given in terms of elliptic integrals. We 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 corresponding amplitudes. We also explicitly demonstrate that the ground-state energy is infinitely differentiable on the boundary between ferromagnetic and oscillatory phases.