Effects of energy extensivity on the quantum phases of long-range interacting systems

TL;DR

This study explores how energy extensivity affects quantum phases in long-range interacting one-dimensional systems, revealing a transition from insulating to novel metallic phases when applying Kac's rescaling.

Contribution

It demonstrates that applying Kac's rescaling to long-range interactions fundamentally alters the quantum phase diagram in one-dimensional systems.

Findings

Without Kac's rescaling, the system exhibits an insulating phase.

With Kac's rescaling, a new metallic phase emerges.

The metallic phase does not conform to the traditional Luttinger liquid theory.

Abstract

We investigate the ground state properties of one-dimensional hard-core bosons interacting via a variable long-range potential using the density matrix renormalization group. We demonstrate that restoring energy extensivity in the system, which is done by rescaling the interaction potential with a suitable size-dependent factor known as Kac's prescription, has a profound influence on the low-energy properties in the thermodynamic limit. While an insulating phase is found in the absence of Kac's rescaling, the latter leads to a new metallic phase that does not fall into the conventional Luttinger liquid paradigm. Our results in one dimension illustrate the subtlety of determining the thermodynamic properties of generic long-range quantum systems.