Dimensionless ratios: characteristics of quantum liquids and their phase transitions

TL;DR

This paper introduces Wilson ratios based on thermodynamic properties to characterize phases of multi-component quantum liquids in one dimension, providing universal criteria for phase identification and insights into experimental observations.

Contribution

It demonstrates that Wilson ratios can uniquely identify phases of 1D quantum liquids and are governed by additivity rules, independent of microscopic details.

Findings

Wilson ratios characterize phases of 1D quantum liquids.

Universal scaling relations at phase boundaries are established.

Wilson ratios depend on subsystem stiffnesses and sound velocities.

Abstract

Dimensionless ratios of physical properties can characterize low-temperature phases in a wide variety of materials. As such, the Wilson ratio (WR), the Kadowaki-Woods ratio and the Wiedemann\--Franz law capture essential features of Fermi liquids in metals, heavy fermions, etc. Here we prove that the phases of many-body interacting multi-component quantum liquids in one dimension (1D) can be described by WRs based on the compressibility, susceptibility and specific heat associated with each component. These WRs arise due to additivity rules within subsystems reminiscent of the rules for multi-resistor networks in series and parallel --- a novel and useful characteristic of multi-component Tomonaga-Luttinger liquids (TLL) independent of microscopic details of the systems. Using experimentally realised multi-species cold atomic gases as examples, we prove that the Wilson ratios uniquely identify phases of TLL, while providing universal scaling relations at the boundaries between phases. Their values within a phase are solely determined by the stiffnesses and sound velocities of subsystems and identify the internal degrees of freedom of said phase such as its spin-degeneracy. This finding can be directly applied to a wide range of 1D many-body systems and reveals deep physical insights into recent experimental measurements of the universal thermodynamics in ultracold atoms and spins.