# Renormalization group analysis of dipolar Heisenberg model on square lattice

## TL;DR

This paper uses functional renormalization group analysis to map out the phase diagram of a dipolar Heisenberg model on a square lattice, revealing an extended quantum paramagnetic phase suggestive of quantum spin liquids.

## Contribution

It provides the full phase diagram of the dipolar Heisenberg model using pseudofermion functional renormalization group, including the identification of an extended quantum paramagnetic phase.

## Key findings

- Extended quantum paramagnetic phase between Néel and stripe/spiral phases
- Smooth flow of spin susceptibility indicating absence of long-range order in the paramagnetic region
- Confirmation of the model as a candidate for quantum spin liquids

## 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 $J_1$-$J_2$ 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 N\'{e}el 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.