Low-energy Effective Theory for One-dimensional Lattice Bosons near Integer Filling

TL;DR

This paper develops a low-energy effective theory for one-dimensional lattice bosons near integer filling, revealing the phase diagram, quantum phase transitions, and conditions for Pfaffian-like states.

Contribution

It introduces a novel effective theory with two bosonic phase fields to comprehensively describe phases and transitions in 1D lattice bosons near integer filling.

Findings

Identifies the complete phase diagram for 1D lattice bosons near integer filling.

Clarifies the nature of quantum phase transitions among different phases.

Derives conditions for the emergence of Pfaffian-like states from the effective action.

Abstract

A low-energy effective theory for interacting bosons on a one-dimensional lattice at and near integer fillings is proposed. It is found that two sets of bosonic phase fields are necessary in order to explain the complete phase diagram. Using the present effective theory, the nature of the quantum phase transitions among various phases can be identified. Moreover, the general condition for the appearance of the recently proposed Pfaffian-like state can be realized from our effective action.