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Projection-Based Density Matrix Renormalization Group in Density Functional Theory Embedding
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Electron-momentum dependence of electron-phonon coupling underlies dramatic phonon renormalization in YNi 2 B 2 C
Electron-phonon coupling, i.e., the scattering of lattice vibrations by electrons and vice versa, is ubiquitous in solids and can lead to emergent ground states such as superconductivity and charge-density wave order. A broad spectral phonon line shape is often interpreted as a marker of strong electron-phonon coupling associated with Fermi surface nesting, i.e., parallel sections of the Fermi surface connected by the phonon momentum. Alternatively broad phonons are known to arise from strong atomic lattice anharmonicity. Here, we show that strong phonon broadening can occur in the absence of both Fermi surface nesting and lattice anharmonicity, if electron-phonon coupling is strongly enhanced for specific values of electron-momentum, k. We use inelastic neutron scattering, soft x-ray angle-resolved photoemission spectroscopy measurements and ab-initio lattice dynamical and electronic band structure calculations to demonstrate this scenario in the highly anisotropic tetragonal electron-phonon superconductor YNi 2 B 2 C. This new scenario likely applies to a wide range of compounds.
Stochastic exciton-scattering theory of optical line shapes: Renormalized many-body contributions
Spectral line shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by broad-band pulsed laser stimulation, as distinguished from those for stationary phonon bath. In particular, we consider the contribution of pair-fluctuations arising from the full bosonic many-body Hamiltonian within a mean-field approximation, treating the coupling to the system as a stochastic noise term. Herein, using the Itô transformation, we consider two limiting cases for our model, which lead to a connection between the observed spectral fluctuations and the spectral density of the environment. In the first case, we consider a Brownian environment and show that this produces spectral dynamics that relax to form dressed excitonic states and recover an Anderson–Kubo-like form for the spectral correlations. In the second case, we assume that the spectrum is Anderson–Kubo like and invert to determine the corresponding background. Using the Jensen inequality, we obtain an upper limit for the spectral density for the background. The results presented here provide the technical tools for applying the stochastic model to a broad range of problems.
Machine learning approach for vibronically renormalized electronic band structures
Here, we present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the nonperturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming ab initio calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT). We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.
Frustrated quantum spins at finite temperature: Pseudo-Majorana functional renormalization group approach
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Ground-state order in magic-angle graphene at filling ν = - 3 : A full-scale density matrix renormalization group study
Here we investigate twisted bilayer graphene (TBG) at filling ν = -3 in the presence of realistic heterostrain. Strain amplifies the band dispersion and drives the system beyond the strong-coupling regime of previous theoretical studies. We use DMRG to conduct an unbiased, large-scale numerical calculations that include all spin and valley degrees of freedom, up to bond dimension χ = 24576. We establish a global phase diagram that unifies a number of theoretical and experimental results. Near zero strain we find an intervalley-coherent quantized anomalous Hall (QAH-IVC) state, a competitive strong-coupling order that evaded past numerical studies. A tiny strain around 0.05% drives a transition into an incommensurate Kekulé spiral (IKS) phase, supporting the mean-field prediction in [Kwan, Phys. Rev. X 11, 041063 (2021)2160-330810.1103/PhysRevX.11.041063]. Even higher strains above 0.2% favor a flavor-symmetric metallic order, which may explain metals found at ν = -3 in many experiments.
Quantum impurity with 2 3 local moment in one-dimensional quantum wires: A numerical renormalization group study
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Two-dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
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Renormalized density matrix downfolding: A rigorous framework in learning emergent models from ab initio many-body calculations
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In-medium similarity renormalization group at finite temperature
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Unpolarized isovector quark distribution function from lattice QCD: A systematic analysis of renormalization and matching
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Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD
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