Microscopic scale of quantum phase transitions: from doped semiconductors to spin chains, cold gases and moir\'e superlattices

TL;DR

This paper introduces a new method to analyze quantum phase transitions, revealing that experimental data contain microscopic information and that the scaled data can be approximated by a universal exponential dependence involving a microscopic length scale.

Contribution

The paper demonstrates that microscopic length scales can be extracted from experimental data near QPTs, linking them to physical parameters across various systems.

Findings

Extracted microscopic length scales match physical expectations in different systems.

Scaled data near QPTs follow a universal exponential dependence.

The method unifies analysis of diverse quantum systems.

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 have found that for many systems, the scaled data near QPTs can be approximated by the generic exponential dependence introduced in the scaling theory of localization; this dependence includes as a parameter a microscopic seeding scale of the renormalization group, $L_0$. We have also conjectured 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 semiconductor Si:B, (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. The metal-insulator transition in Si:P has been explained using a non-interacting version of the model. In two companion papers, we show that in superconducting systems, $L_0$ is comparable to superconducting coherence length, and in quantum Hall systems, to the magnetic length. The developed new method of data analysis identifies microscopic processes leading to QPTs and quantitatively explains and unifies a large body of experimental data.