# Regensburg 2016 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 35: Correlated Electrons: Quantum-Critical Phenomena - Theory

### TT 35.6: Vortrag

### Dienstag, 8. März 2016, 15:15–15:30, H21

**Dimensionless ratios: characteristics of quantum liquids and their phase transitions** — Yi-Cong Yu^{1}, Yang-Yang Chen^{1}, Hai-Qing Lin^{2}, •Rudolf A. Römer^{3}, and Xi-Wen Guan^{1,4,5} — ^{1}Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China — ^{2}Beijing Computational Science Research Center, Beijing 100094, China — ^{3}University of Warwick, Coventry, CV4 7AL, UK — ^{4}Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China — ^{5}Australian National University, Canberra ACT 0200, Australia

Dimensionless ratios of physical properties can be constant in low-temperatures 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 can be described by WRs based on the compressibility, susceptibility and specific heat associated with each component. These WRs arise due to surprisingly simple additivity rules within subsystems reminiscent of the rules for multi-resistor networks in series and parallel. Using experimentally realized multi-species cold atomic gases as examples, we prove that the Wilson ratios uniquely identify phases of Tomonaga-Luttinger liquids, while providing universal scaling relations at the boundaries between phases. Their values within a phase identify the internal degrees of freedom of said phase such as its spin-degeneracy.