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- W4386499056 abstract "In the vicinity of continuous quantum phase transitions (QPTs), quantum systems become scale-invariant and can be grouped into universality classes characterized by sets of critical exponents. We have found that despite scale-invariance and universality, the experimental data still contain information related to the microscopic processes and scales governing QPTs. We conjecture that near QPTs, various physical quantities follow the generic exponential dependence predicted by the scaling theory of localization; this dependence includes as a parameter a microscopic seeding scale of the renormalization group, $L_0$. We also conjecture that for interacting systems, the temperature cuts the renormalization group flow at the length travelled by a system-specific elementary excitation over the life-time set by the Planckian time, $tau_P$=$hbar/k_BT$. We have adapted this approach for QPTs in several systems and showed that $L_0$ extracted from experiment is comparable to physically-expected minimal length scales, namely (i) the mean free path for metal-insulator transition in doped semiconductors, (ii) the distance between spins in Heisenberg and Ising chains, (iii) the period of an optical lattice for cold atom boson gases, and (iv) the period of a moir'e superlattice for the Mott QPT in dichalcogenide bilayers. In the first companion paper, we show that in superconducting films and nanowires, as well as in the high temperature superconductor La$_{1.92}$Sr$_{0.08}$CuO$_4$, $L_0$ is comparable to superconducting coherence length. In the second companion paper, we show that in quantum Hall systems, $L_0$ is comparable to the magnetic length. The developed theoretical approach quantitatively explains and unifies a large body of experimental data and can be expanded to other complex systems" @default.
- W4386499056 created "2023-09-07" @default.
- W4386499056 creator A5080506498 @default.
- W4386499056 date "2023-09-01" @default.
- W4386499056 modified "2023-10-16" @default.
- W4386499056 title "Microscopic scale of quantum phase transitions: from doped semiconductors to spin chains, cold gases and moir'e superlattices" @default.
- W4386499056 doi "https://doi.org/10.48550/arxiv.2309.00749" @default.
- W4386499056 hasPublicationYear "2023" @default.
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