Programmable order by disorder effect and underlying phases through dipolar quantum simulators

In this work, we study two different quantum simulators through various theoretical and numerical tools. Our first result provides knowledge upon the quantum order by disorder effect of the S=1/2 system, which is programmable in a quantum simulator composed of circular Rydberg atoms. When the total magnetization is zero, a set of sub-extensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Among all possible configurations, we focus on the stripe (up and down spins aligning straightly) and kinked (up and down spins forming zigzag spin chains) patterns. Adopting the real space perturbation theory, we estimate the leading order energy correction when the nearest-neighbor spin exchange coupling, J, is considered, and the overall model becomes an effective XXZ model with a spatial anisotropy. Our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When J becomes larger, we adopt the infinite projected entangled-pair state and numerically check the effect of degeneracy lifting, showing that even when the spin exchange coupling term is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposals indicate realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases.