Dimensionless ratios: characteristics of quantum liquids and their phase transitions

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.

12 pages (main paper), (6 figures)

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• FFLO correlation and free fluids in the one-dimensional attractive Hubbard model
• Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field
• Universality and quantum criticality of the one-dimensional spinor Bose gas
• Phase determination with and without deep learning
• Machine learning of phases and structures for model systems in physics
• Grüneisen parameters for Lieb-Liniger and Yang-Gaudin models
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• Universal thermodynamics of the one-dimensional attractive Hubbard model
• One-dimensional model of chiral fermions with Feshbach resonant interactions
• Excitation Spectra of one-dimensional spin-1/2 Fermi gas with an attraction
• A unified approach to the thermodynamics and quantum scaling functions of one-dimensional strongly attractive $SU(w)$ Fermi Gases