We present a renormalization group (RG) analysis of the problem of Anderson localization on a random regular graph (RRG) which generalizes the RG of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The RG equations necessarily involve two parameters (one being the changing connectivity of subtrees), but we show that the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables. We also explain the nonmonotonic behavior of dynamical and spectral quantities as a function of the system size for values of disorder close to the transition, by identifying two terms in the beta function of the running fractal dimension of different signs and functional dependence. Our theory provides a simple and coherent explanation for the unusual scaling behavior observed in numerical data of the Anderson model on RRG and of many-body localization.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11260133 | PMC |
| http://dx.doi.org/10.1073/pnas.2401955121 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Pair approximating the action for molecular rotations in path integral Monte Carlo.
J Chem Phys
January 2025
Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair discrete variable representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed helium, is naturally well-suited for systems interacting with a pairwise potential.
View Article and Find Full Text PDFHybridization effects on the magnetic ground state of ruthenium in double perovskite LaZnRuTiO.
J Phys Condens Matter
January 2025
School of Materials Science, Indian Association for the Cultivation of Science, Calcutta 700 032, Kolkata, West Bengal, 700032, INDIA.
An exotic quantum mechanical ground state, i.e. the nonmagnetic= 0 state, has been predicted for higher transition metal tsystems, due to the influence of strong spin-orbit coupling (SOC) or in other words, due to unquenched orbital moment contribution.
View Article and Find Full Text PDFPhase Diagram, d-Wave Superconductivity, and Pseudogap of the t-t^{'}-J Model at Finite Temperature.
Phys Rev Lett
December 2024
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China.
Recently, robust d-wave superconductive (SC) order has been unveiled in the ground state of the 2D t-t^{'}-J model-with both nearest-neighbor (t) and next-nearest-neighbor (t^{'}) hoppings-by density matrix renormalization group studies. However, there is currently a debate on whether the d-wave SC holds up strong on both t^{'}/t>0 and t^{'}/t<0 cases for the t-t^{'}-J model, which correspond to the electron- and hole-doped sides of the cuprate phase diagram, respectively. Here, we exploit state-of-the-art thermal tensor network approach to accurately obtain the phase diagram of the t-t^{'}-J model on cylinders with widths up to W=6 and down to low temperature as T/J≃0.
View Article and Find Full Text PDFSpin-Polarized Scanning Tunneling Microscopy Measurements of an Anderson Impurity.
Phys Rev Lett
December 2024
II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, 50937 Cologne, Germany.
We report spin-polarized scanning tunneling microscopy measurements of an Anderson impurity system in MoS_{2} mirror-twin boundaries, where both the quantum-confined impurity state and the Kondo resonance resulting from the interaction with the substrate are accessible. Using a spin-polarized tip, we observe magnetic-field-induced changes in the peak heights of the Anderson impurity states as well as in the magnetic-field-split Kondo resonance. Quantitative comparison with numerical renormalization group calculations provides evidence of the notable spin polarization of the spin-resolved impurity spectral function under the influence of a magnetic field.
View Article and Find Full Text PDFPath integral Monte Carlo in a discrete variable representation with Gibbs sampling: Dipolar planar rotor chain.
J Chem Phys
January 2025
Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
In this work, we propose a path integral Monte Carlo approach based on discretized continuous degrees of freedom and rejection-free Gibbs sampling. The ground state properties of a chain of planar rotors with dipole-dipole interactions are used to illustrate the approach. Energetic and structural properties are computed and compared to exact diagonalization and numerical matrix multiplication for N ≤ 3 to assess the systematic Trotter factorization error convergence.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!