Static non-linear Schr\"{o}dinger equations for the achiral-chiral transitions of polar chiral molecules

TL;DR

This paper derives static non-linear Schrödinger equations from a many-body Hamiltonian to analyze achiral-chiral phase transitions in polar chiral molecules, revealing different transition types and phase diagrams.

Contribution

It introduces a parameter-free mean-field approach based on many-body Hamiltonians to classify and analyze achiral-chiral transitions in polar molecules.

Findings

Polar chiral molecules are classified into two categories based on transition behavior.

The phase transition can be continuous or discontinuous depending on the molecule category.

A mean-field phase diagram for achiral-chiral transitions is provided.

Abstract

In the mean-field theory, the stabilization of polar chiral molecules is understood as a quantum phase transition where the mean-field ground state of molecules changes from the achiral eigenstate of the molecular Hamiltonian to one of the degenerated chiral states as the increase of the intermolecular interaction. Starting from the many-body Hamiltonian of the molecular gases with electric dipole-dipole interactions, we give the static non-linear Schr\"{o}dinger equations without free parameters to explore the achiral-chiral transitions of polar chiral molecules. We find that the polar chiral molecules of different species can be classified into two categories: At the critical point for the achiral-chiral transition, the mean-field ground state changes continuously in one category, and changes discontinuously in the other category. We further give the mean-field phase diagram of the achiral-chiral transitions for both two categories.