Crystalline structures in a one-dimensional two-component lattice gas with $1/r^{\alpha}$ interactions

TL;DR

This paper studies the ground states of a one-dimensional two-component lattice gas with power-law interactions, revealing phase configurations, transitions, and stability regions through analytical and numerical methods.

Contribution

It provides a detailed prescription for determining ground states based on filling fractions and explores phase transitions in a two-species lattice gas with variable interaction strengths.

Findings

Compatible and incompatible phases depend on filling fractions.

Strongly interacting species can be considered frozen, affecting the weak species.

Transitions between compatible and incompatible phases are characterized and stability regions identified.

Abstract

We investigate the ground state of a one-dimensional lattice system that hosts two different kinds of excitations (species) which interact with a power-law potential. Interactions are only present between excitations of the same kind and the interaction strength can be species-dependent. For the case in which only one excitation is permitted per site we derive a prescription for determining the ground state configuration as a function of the filling fractions of the two species. We show that depending on the filling fractions compatible or incompatible phases emerge. Furthermore, we discuss in detail the case in which one species is strongly and the other one weakly interacting. In this case the configuration of the strongly interacting (strong) species can be considered frozen and forms an effective inhomogeneous lattice for the other (weak) species. In this limit we work out in detail the microscopic ground state configuration and show that by varying the density of the weak species a series of compatible--incompatible transitions occurs. Finally we determine the stability regions of the weak species in the compatible phase and compare it with numerical simulations.