The XYZ chain with Dzyaloshinsky-Moriya interaction and the magnetic properties of spin-orbit-coupled lattice bosons

(1) Department of Physics, University of California, San Diego, La Jolla, CA 92093,USA(2) NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa,Italy(3) Dipartimento di Fisica dellUniversita di Pisa and INFN, Largo Pontecorvo 3,I-56127 Pisa, Italy(4) NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa(5) Center for Quantum Technologies, National University of Singapore, SingaporeAbstract. Using the density-matrix renormalization-group algorithm (DMRG)and nite-size-scaling, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. Themodel shows a rich phase diagram: depending on the value of the coupling constants,the system can display di erent kinds of ferromagnetic order and Luttinger-liquidbehavior. Transitions from ferromagnetic to Luttinger-liquid phases are rst order.We thoroughly discuss the transition between di erent ferromagnetic phases, which,in the absence of DM interactions, belongs to the XX universality class; we provideevidence that in presence of DM it is split into two Ising-like transitions. In between,an interesting disordered phase appears. Our study sheds light on the general problemof strongly-interacting spin-orbit-coupled systems and is particularly useful to guidefuture experimental work on cold bosons loaded in optical lattices.