A couple of weeks ago we uploaded to the arXive our latest paper: Non-transverse factorizing fields and entanglement in finite spin systems.

Let me explain what this paper is about.

The ground state of strongly interacting spin systems immersed in a magnetic field can exhibit, under certain conditions, the remarkable phenomenon of factorization, i.e., of becoming a product of single spin states. Thus, all entanglement in the system vanishes to zero.

This particular phenomenon was first discovered by J. Kurmann, H. Thomas, and G. Müller in 1982. In their paper they showed that antiferromagnetic 1/2-spin chains with Heisenberg first neighbor XYZ couplings possess a separable Néel-type ground state if the field vector lies on the surface of an ellipsoid determined by the couplings. Factorization was then investigated in other models with transverse fields, in particular, it was shown in [2, 3] (papers by my workgroup) that in finite ferromagnetic XYZ chains, the factorizing field points along a principal axis (thus called transverse factorizing field).

Factorizing fields were largely studied, but most of the research was done either for antiferromagnetic spin chain with first neighbor interactions or for ferromagnetic spin systems with transverse field. Thus, we decided to study the most general case possible, i.e. the conditions for the existence of non-transverse factorizing fields in spin systems of arbitrary spins in any dimension interacting through Heisenberg XYZ coupling of arbitrary range in the presence of non-uniform magnetic fields.

If you are interested in finding out what our results where, I invite you to check out the paper at http://arxiv.org/pdf/1507.07166

[1] J. Kurmann, H. Thomas, and G. Müller, Physica A 112, 235 (1982).
[2] R. Rossignoli, N. Canosa, and J.M. Matera, Phys. Rev. A 77, 052322 (2008); Phys. Rev. A 80, 062325 (2009).
[3] N. Canosa, R. Rossignoli, and J.M. Matera, Phys. Rev. B 81, 054415 (2010); L. Ciliberti, R. Rossignoli, and N. Canosa, Phys. Rev. A 82, 042316 (2010).