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Résumé : For more than thirty years, experimental analysis of quantum phase transitions (QPTs) has been largely focused on finding critical exponents and universality classes of studied systems. This approach emphasizes scale-invariance of QPTs and ignores the fact that system response also depends on two non-universal length scales: microscopic “seeding” scale of the correlation length and the dephasing length. Correcting this deficiency, we have developed a phenomenological model of QPTs based on conjecture that the dephasing length is set by a distance travelled by a system-specific semi-classical elementary excitation over the Planckian time, and that the scaling function assumes the generic exponential form predicted by the scaling theory of localization (the figure shows some examples). Using this model, we have quantitatively explained QPTs in eighteen systems including: magnetic-field-driven QPT in superconducting films, nanowires, La1.92Sr0.08CuO4 and Josephson junction chains; QPT in Ising and Heisenberg spin chains, the Mott transition in 2d cold atomic gases and moiré superlattices; and QPT between the states of quantum Hall and other topological insulators. The model illuminates the universal microscopic nature of many-body gapless state of matter emerging near QPTs. Surprisingly, the only system deviating from the trend is doped Si : P, where metal-insulator transition is explained by the non-interaction version of the model. We anticipate that shifting emphasis from critical exponents to the microscopic parameters of a phase transition will be a fruitful approach for many systems beyond equilibrium condensed matter physics. Ref. : 1 A. Rogachev, Microscopic scale of quantum phase transition: from doped semiconductors to spin chains, cold gases and moiré superlattices, arXiv:2309.00749. 2 A. Rogachev and K. Davenport, Microscopic scale of pair-breaking quantum phase transitions in superconducting films, nanowires and La1.92Sr0.08CuO4, arXiv:2309.00747. 3 A. Rogachev, Quantum phase transitions in quantum Hall and other topological systems: role of the Planckian time, arXiv:2309.00747.
