Variational matrix product state approach to quantum impurity models

Abstract

We present a unified framework for renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows improvements over Wilson's NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially \emph{linear} scaling of complexity for $n$-channel problems.

revised version with application to Kondo model at large magnetic field (5 pages, 2 figures)

References in corpus (28)

• The density-matrix renormalization group
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Matrix product states represent ground states faithfully
• DMRG and periodic boundary conditions: a quantum information perspective
• Transport Coefficients of the Anderson Model via the Numerical Renormalization Group
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Dynamical density-matrix renormalization-group method
• Numerical Renormalization Group Calculations for the Self-energy of the impurity Anderson model
• Dynamical Correlation Functions using the Density Matrix Renormalization Group
• Energy resolution and discretization artefacts in the numerical renormalization group
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Generalized Numerical Renormalization Group for Dynamical Quantities
• Density matrix algorithm for the calculation of dynamical properties of low dimensional systems
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• Fixed Point of the Finite System DMRG
• Spectral function of the Kondo model in high magnetic fields
• Matrix product state comparison of the numerical renormalization group and the variational formulation of the density matrix renormalization group
• Density-matrix renormalisation group approach to quantum impurity problems
• High Energy Dynamics of the Single Impurity Anderson Model
• Energy-resolved inelastic electron scattering off a magnetic impurity
• Spectral Densities from Dynamic Density-Matrix Renormalization
• Optimal broadening of finite energy spectra in the numerical renormalization group: application to dissipative dynamics in two-level systems
• Density matrix renormalization group study of a quantum impurity model with Landau-Zener time-dependent Hamiltonian

Cited by in corpus (108)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Unifying time evolution and optimization with matrix product states
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• Quantum Hamiltonian Complexity
• DMFT+NRG study of spin-orbital separation in a three-band Hund's metal
• Chebyshev matrix product state approach for spectral functions
• Critical and strong-coupling phases in one- and two-bath spin-boson models
• Comparative study of theoretical methods for nonequilibrium quantum transport
• Spin-1/2 Kondo effect in an InAs nanowire quantum dot: the Unitary limit, conductance scaling and Zeeman splitting
• Nonequilibrium and nonperturbative dynamics of ultrastrong coupling in open lines
• Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution
• Computation of extreme eigenvalues in higher dimensions using block tensor train format
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• How to discretize a quantum bath for real-time evolution
• Chebyshev expansion for Impurity Models using Matrix Product States
• Geometry of variational methods: dynamics of closed quantum systems
• Tensor networks and the numerical renormalization group
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Kondo screening cloud in the single-impurity Anderson model: A density matrix renormalization group study
• Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit
• Tensor-network method to simulate strongly interacting quantum thermal machines
• Interplay between Kondo and Majorana interactions in quantum dots
• Driven dissipative dynamics and topology of quantum impurity systems
• Solving quantum impurity problems in and out of equilibrium with variational approach
• Dynamical polaron ansatz: a theoretical tool for the ultra-strong coupling regime of circuit QED
• Multigrid Renormalization
• Emergent Bloch Excitations in Mott Matter
• Matrix product state formulation of frequency-space dynamics at finite temperatures
• Numerical evaluation of Greens functions based on the Chebyshev expansion
• Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems
• Tensor Network simulation of polaron-polaritons in organic microcavities
• Adaptive broadening to improve spectral resolution in the numerical renormalization group
• Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group
• Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
• At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model
• Variational principle for quantum impurity systems in and out of equilibrium: application to Kondo problems
• Entanglement Renormalization for Weakly Interacting Fields
• Anatomy of quantum critical wave functions in dissipative impurity problems
• Two-bath spin-boson model: Phase diagram and critical properties
• S matrix from matrix product states
• Variational methods for contracting projected entangled-pair states
• Spectral functions for single- and multi-Impurity models using DMRG
• Renormalization Group Circuits for Weakly Interacting Continuum Field Theories
• SU(3) Anderson impurity model: A numerical renormalization group approach exploiting non-Abelian symmetries
• Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• Tensor renormalization group study of the 3d $O(2)$ model
• Real time evolution at finite temperatures with operator space matrix product states
• Dissipative spin dynamics near a quantum critical point: Numerical Renormalization Group and Majorana diagrammatics
• Manipulation of organic polyradicals in a single-molecule transistor
• Quantitative determination of the discretization and truncation errors in the numerical renormalization-group calculations of spectral functions
• Variational Numerical Renormalization Group: Bridging the gap between NRG and Density Matrix Renormalization Group
• Matrix product state approach for a two-lead, multi-level Anderson impurity model
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
• Ground and Excited States from Ensemble Variational Principles
• Efficient evaluation of high-order moments and cumulants in tensor network states
• Scale free property and edge state of Wilson's numerical renormalization group
• Anderson Orthogonality and the Numerical Renormalization Group
• Automatic Differentiable Numerical Renormalization Group
• Complex Time Evolution in Tensor Networks
• Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action
• Discarded weight and entanglement spectra in the Numerical Renormalization Group
• Dynamical properties of the sine-Gordon quantum spin magnet Cu-PM at zero and finite temperature
• Entanglement based observables for quantum impurities
• Quench dynamics of spin in quantum dots coupled to spin-polarized leads
• Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning
• Uncovering nonperturbative dynamics of the biased sub-Ohmic spin-boson model with variational Matrix Product States
• Rich phase diagram of quantum phases in the anisotropic subohmic spin-boson model
• Quantum phase transitions in the spin-boson model without the counterrotating terms
• Root-N Krylov-space correction-vectors for spectral functions with the density matrix renormalization group
• Ancilla-assisted sequential approximation of nonlocal unitary operations
• Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
• Optical conductivity of the Hubbard chain away from half filling
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Ultrafast molecular dynamics in terahertz-STM experiments: Theoretical analysis using Anderson-Holstein model
• Width of the charge-transfer peak in the SU(N) impurity Anderson model and its relevance to non-equilibrium transport
• Open Wilson chains for quantum impurity models: Keeping track of all bath modes
• Scaling of conductance through quantum dots with magnetic field
• Blind deconvolution of density-matrix renormalization-group spectra
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Dynamical correlation functions from complex time evolution
• Thermalization and dynamics in the single impurity Anderson model
• Quantum impurity models using superpositions of fermionic Gaussian states: Practical methods and applications
• Simulations of the dynamics of quantum impurity problems with matrix product states
• Quantum tricritical point emerging in the spin-boson model with two dissipative spins in staggered biases
• Efficient construction of the Feynman-Vernon influence functional as matrix product states
• Engineering the Kondo impurity problem with alkaline-earth atom arrays
• Sequential quantum cloning under real-life conditions
• Efficient construction of tensor-network representations of many-body Gaussian states
• Gutzwiller Renormalization Group
• Magnetotransport in the Kondo model with ferromagnetic exchange interaction
• Coherent exchange-coupled nonlocal Kondo impurities
• Wavefunction Vortex Attachment via Matrix Products: Application to Atomic Fermi Gases in Flat Spin-Orbit Bands
• Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems
• Tensor network non-zero testing
• Dynamical Spectral Function From Numerical Renormalization Group: A Full Excitation Approach
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Efficient tensor network simulation of multi-emitter non-Markovian systems
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Zero-site DMRG and the optimal low-rank correction
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• Scalable tensor network algorithm for quantum impurity problems
• Entropic Quantum Machine
• Unraveling screening mechanisms in Kondo impurities using an NRG-MPS-based method
• Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations
• Charge density wave breakdown in a heterostructure with electron-phonon coupling