Renormalization group analysis of dipolar Heisenberg model on square lattice

Abstract

We present a detailed functional renormalization group analysis of spin-1/2 dipolar Heisenberg model on square lattice. This model is similar to the well known J1-J2 model and describes the pseudospin degrees of freedom of polar molecules confined in deep optical lattice with long-range anisotropic dipole-dipole interactions. Previous study of this model based on tensor network ansatz indicates a paramagnetic ground state for certain dipole tilting angles which can be tuned in experiments to control the exchange couplings. The tensor ansatz formulated on a small cluster unit cell is inadequate to describe the spiral order, and therefore the phase diagram at high azimuthal tilting angles remains undetermined. Here we obtain the full phase diagram of the model from numerical pseudofermion functional renormalization group calculations. We show that an extended quantum paramagnetic phase is realized between the Néel and stripe/spiral phase. In this region, the spin susceptibility flows smoothly down to the lowest numerical renormalization group scales with no sign of divergence or breakdown of the flow, in sharp contrast to the flow towards the long-range ordered phases. Our results provide further evidence that the dipolar Heisenberg model is a fertile ground for quantum spin liquids.

Higher-order topological quantum paramagnets

“…Previous works have studied the model using various approximations in the presence of anisotropy, but have found no sign of a QP in the zero-anisotropy limit [49,50]. Our DMRG results, however, show that the Néel order parameter vanishes in the ground state of the model.…”

“…Finally, we study the Heisenberg model with dipolar interactions and show that its ground state is also a HOTQP. The dipolar Heisenberg model has gained attention in the last years [49][50][51][52], since it naturally appears as an effective description of ultracold molecules trapped in optical lattices [53,54], and can also be simulated using trapped ions [55][56][57][58]. Ultracold molecules are particularly interesting for quantum simulation purposes due to their strong dipole interactions, and different schemes have been proposed to use them to simulate quantum magnetism [59][60][61][62] as well as topological phases [63][64][65][66].…”

Rise and fall of plaquette order in Shastry-Sutherland magnet revealed by pseudo-fermion functional renormalization group

“…To maintain sufficient momentum and frequency resolution, one must keep track of millions of running couplings at each FRG step. The calculation is made possible by migrating to the GPU platform which led to performance improvement by orders of magnitude [18,19]. Despite being a completely different approach, the phase boundaries predicted from our FRG are remarkably close to the state-of-the-art DMRG.…”

Frustrated Quantum Spins at finite Temperature: Pseudo-Majorana functional RG approach

“…To summarize, in our PMFRG scheme the flow equations for the free energy, self-energy (49) and the vertex functions (see Appendix A), are solved numerically starting from large but finite Λ J down to Λ 0, approximating the initial conditions with the Λ → ∞ values presented above. The flow of the free energy correction ( 48) is integrated along the way but does not feed back into the other flow equations.…”

“…Within the last decade the PFFRG has been successfully applied to a wide range of spin systems [22, and has constantly been extended and generalized. Today, the PFFRG is, hence, remarkably flexible with a scope of applicability comprising two [22, 24-35, 37, 38, 40, 41, 44-46, 48, 49, 51, 54, 55, 57, 59-61, 63] and three dimensional [36,39,42,43,47,50,52,53,55,56,58,62] quantum spin systems on arbitrary lattices, including complex frustrated and longer-range coupled networks [48,49] with general isotropic or anisotropic [54] two-body spin interactions. Further recent developments concern the generalization to arbitrary spin magnitudes S [41] or higher spin symmetry groups SU (N ) [44,45,60] and, on a more technical level, the implementation of multi-loop schemes [46,62,63].…”