The transverse field XY model on the diamond chain

Abstract: We consider the $s=1/2$ transverse field $XY$ model on the frustrated diamond chain, considering anisotropic exchange parameters between nearest-neighbor spins. To this end, we employ three different methodologies: mean-field approximations, and state-of-the-art exact diagonalizations (ED), and density matrix renormalization group (DMRG) simulations. Within a mean-field theory, the Hamiltonian is fermionized by introducing the Jordan-Wigner transformation, and the interacting (many-body) terms are approximated to single-particle ones by a Hartree-Fock approach. We analyze the behavior of the induced and spontaneous magnetization as functions of the external field, investigating the magnetic properties at the ground state, and at finite temperatures. Interestingly, the mean-field results are in reasonable agreement with the ED and DMRG ones, in particular for the distorted chain, or at an intermediate/large spin anisotropy parameter. As our key results, we present phase diagrams anisotropy $\times$ magnetic field at zero temperature, discussing the emergence of phases and their quantum critical points. Finally, our analysis at finite temperature provides a range of parameters in which an unusual behavior of the induced magnetization occurs -- with it increasing as a function of temperature. This work presents a \textit{global} picture of the XY model on the diamond chain, which may be useful to understand features of magnetism in more complex geometries.