Green's function theory for spin-1/2 ferromagnets with an easy-plane exchange anisotropy

TL;DR

This paper develops an improved Green's function approach for easy-plane spin-1/2 ferromagnets under in-plane magnetic fields, resolving inconsistencies in traditional methods and aligning well with quantum Monte Carlo results.

Contribution

It introduces a self-consistent method considering all relevant Green's functions, enhancing the accuracy of theoretical predictions for anisotropic ferromagnets.

Findings

Traditional Green's function approach yields unreasonable results.

Including additional Green's functions resolves contradictions.

Results agree well with quantum Monte Carlo simulations.

Abstract

The many-body Green's function theory with the random-phase approximation is applied to the study of easy-plane spin-1/2 ferromagnets in an in-plane magnetic field. We demonstrate that the usual procedure, in which only the three Green's functions $<< S_i^\mu;S_j^->>$ ($\mu=+,-,z$) are used, yields unreasonable results in this case. Then the problem is discussed in more detail by considering all combinations of Green's functions. We can derive one more equation, which cannot be obtained by using only the set of the above three Green's functions, and point out that the two equations contradict each other if one demands that the identities of the spin operators are exactly satisfied. We discuss the cause of the contradiction and attempt to improve the method in a self consistent way. In our procedure, the effect of the anisotropy can be appropriately taken into account, and the results are in good agreement with the quantum Monte Carlo calculations.