Phase diagram in the quantum XY model with long-range interactions

F. G. Ribeiro, J.P. de Lima, L.L. Gonçalves

Antonio S. T. Pires

David Cecil Smith, Spencer Leeper, Christopher N. Varney

Guido Giachetti, Nicolò Defenu, Stefano Ruffo +1 more

Abstract The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor XY model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional XY has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, σ, in which there are a magnetized, a disordered and a critical phase [1]. Here we address the issue of whether the critical behavior of the two-dimensional XY model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range XY model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for σ < 2 the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with 1/r2 interactions.

Antonio S. T. Pires

Ferenc Iglói, Benjamin Blaß, Gergő Roósz +1 more

We consider the quantum XX model in the presence of competing nearest-neighbor and global-range interactions, which is equivalent to a Bose-Hubbard model with cavity mediated global-range interactions in the hard-core boson limit. Using fermionic techniques the problem is solved exactly in one dimension in the thermodynamic limit. The ground state phase diagram consists of two ordered phases: ferromagnetic (F) and antiferromagnetic (AF), as well as an XY phase having quasi-long-range order. We have also studied quantum relaxation after sudden quenches. Quenching from the AF phase to the XY region remanent AF order is observed below a dynamical transition line. In the opposite quench, from the XY region to the AF phase beyond a static metastability line AF order arises on top of remanent XY quasi-long-range order, which corresponds to dynamically generated supersolid state in the equivalent Bose-Hubbard model with hard-core bosons.