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arXiv:2309.00749

Microscopic scale of quantum phase transitions: from doped semiconductors to spin chains, cold gases and moiré superlattices

Andrey Rogachev

Published Sep 1, 2023• 0 citations
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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, $τ_P$=$\hbar/k_BT$. 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 moiré 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.

DOI
10.48550/arxiv.2309.00749

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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, L0L_0L0​. 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, τPτ_PτP​=ℏ/kBT\hbar/k_BTℏ/kB​T. We have adapted this approach for QPTs in several systems and showed that L0L_0L0​ 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 moiré 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, L0L_0L0​ 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.
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Despite the fact that a complete theoretical description of critical phenomena in connection with phase transitions has been well established through the renormalization-group theory, the microscopic nature of the phase transitions remains to be understood in a satisfactory way. For example, how does the interaction between particle/spins drive the system across distinct phases as parameters vary, and how do these particle/spins respond to parameter variations during this transition process? In this work, we investigate these questions through the paradigmatic example of quantum phase transitions (QPT) in the one-dimensional transverse Ising model (TIM). We first introduce 2L collective structures, referred to as patterns, for the TIM with L ferromagnetically interacting spins, and then analyze the contributions of these patterns to the system's states, e.g., the ground state, the first excited state, and so on, from which the analog of the QPT process between the disordered phase in the weakly coupling regime and the ferromagnetic phase in the strongly coupling regime is clearly identified at the interaction strength J_{c}=1. We systematically explore this process for small lattice sizes of L=6,8,10,12, whose ground-state energies are identical to those obtained by directly numerical exact diagonalization. Increasing the system size up to L=128, the actual QPT point located at J_{c}=1 in the thermodynamical limit is gradually approached. Our results show that the pattern picture is not only able to provide a microscopic process of phase transitions, but also of practical interest in analyzing analogues of QPT in diverse quantum simulation platforms.
Metallic states near the Mott insulator show a variety of quantum phases, including various magnetic, charge-ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a variety of phases and their competitions are likely intimately associated with quantum transitions between the electron-correlation-driven Mott insulator and metals characterized by its criticality, and is related to many central questions of condensed matter. The quantum criticality is, however, not well understood when the transition is controlled by the bandwidth through physical parameters such as pressure. Here, we quantitatively estimate the universality class of the transition characterized by a comprehensive set of critical exponents by using a variational Monte Carlo method implemented as an open-source innovated quantum many-body solver, with the help of established scaling laws at a typical bandwidth-controlled Mott transition. The criticality indicates a weaker charge and density instability in contrast to the filling-controlled transition realized by carrier doping, implying a weaker instability to superconductivity as well. The present comprehensive clarification opens up a number of routes for quantitative experimental studies for complete understanding of elusive quantum Mott transition and nearby strange metal that cultivate future design of functionality.
This study has a look at investigates quantum phase transitions (QPTs) in low-dimensional substances, focusing at the outcomes of disorder, electron interactions, and outside fields. Theoretical frameworks, which includes the Hubbard and Ising models, have been employed to analyze essential behaviors, at the same time as renormalization organization strategies furnished insights into scaling near quantum critical points. Experimental observations of conductivity below varying magnetic fields and ultra-low temperatures showed segment transitions between steel, insulating, and superconducting states. These findings were in addition verified via computational simulations using Density Functional Theory (DFT) and Quantum Monte Carlo (QMC) methods, which correctly mapped phase diagrams and important temperatures. The effects underscore the transformative potential of QPTs in quantum technologies, in particular in the development of solid qubits and green nanoelectronics gadgets. Future research will awareness on refining theoretical fashions, enhancing experimental setups, and exploring new quantum levels to increase quantum and nano technology.