Effective theory of quantum phases in the dipolar planar rotor chain

TL;DR

This paper develops a theoretical framework for understanding quantum phases in a system of interacting dipolar planar rotors, using perturbation theory and quadratic approximations, validated by numerical benchmarks.

Contribution

It introduces a combined analytical approach for ordered and disordered phases of dipolar rotors, emphasizing the importance of quartic terms for accurate energy spectra.

Findings

Perturbation theory effectively describes the disordered phase.

Quadratic approximation captures ordered phase configurations.

Quartic terms are crucial for correcting energy spectrum shifts.

Abstract

In this work, we develop a theoretical description of the collective behavior of interacting dipolar planar rotors by using time independent perturbation theory and a small angle quadratic approximation. The ground state properties for both the ordered and disordered quantum phases of the system are directly calculated and analyzed. Time-independent perturbation theory is shown to be appropriate for the disordered phase. For the ordered phase, we construct a quadratic approximation based on the stable equilibrium configurations of the dipolar ordering; we show that the inclusion of the quartic terms from the expansion of the potential energy are essential to correct the shift in the energy spectrum due to quantization ambiguities. Numerical techniques such as Exact Diagonalization and Density Matrix Renormalization Group are used for the benchmark the quality of both approximations.