The density-matrix renormalization group in the age of matrix product states

From MaRDI portal

Publication:624838

Jump to:navigation, search

DOI10.1016/j.aop.2010.09.012zbMath1213.81178arXiv1008.3477OpenAlexW3103713775WikidataQ59486657 ScholiaQ59486657MaRDI QIDQ624838

Ulrich Schollwöck

Publication date: 10 February 2011

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.3477

zbMATH Keywords

entanglement matrix product states quantum lattices matrix product operators density-matrix renormalization group numerical renormalization group

Mathematics Subject Classification ID

Renormalization group methods applied to problems in quantum field theory (81T17) Renormalization group methods in equilibrium statistical mechanics (82B28) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items

Two-electron wavefunctions are matrix product states with bond dimension three, Entanglement at the interplay between single- and many-bodyness, Rank-Adaptive Time Integration of Tree Tensor Networks, Entanglement dynamics of thermofield double states in integrable models, Integrability breaking in the Rule 54 cellular automaton, Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format, Emergent O(4) symmetry at an one-dimensional deconfined quantum tricritical point, Learning quantum structures in compact localized eigenstates, Tensor Completion in Hierarchical Tensor Representations, Non‐equilibrium dynamics in dissipative Bose‐Hubbard chains, Superdiffusive transport of energy in one-dimensional metals, Alternating Linear Scheme in a Bayesian Framework for Low-Rank Tensor Approximation, Lower bounds for Ramsey numbers as a statistical physics problem, Dynamical quantum phase transitions in the one-dimensional extended Fermi–Hubbard model, Quench dynamics of the Anderson impurity model at finite temperature using matrix product states: entanglement and bath dynamics, Computing Low-Rank Approximations of Large-Scale Matrices with the Tensor Network Randomized SVD, Entanglement entropy in excited states of the quantum Lifshitz model, Quantized Tensor FEM for Multiscale Problems: Diffusion Problems in Two and Three Dimensions, Low-rank tensor structure preservation in fractional operators by means of exponential sums, Quantum dynamics of Gaudin magnets, Representations of hypergraph states with neural networks*, Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model, Low-rank tensor methods for partial differential equations, The dissipative generalized hydrodynamic equations and their numerical solution, Two-step relaxation in local many-body Floquet systems, Quantum Phase Transition of a Quantum Mixed Spin Chain by Employing Density Matrix Renormalization Group Method, Group-Invariant Tensor Train Networks for Supervised Learning, Streaming Tensor Train Approximation, Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics, A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model, Irreducible forms of matrix product states: Theory and applications, Tensor Network Skeletonization, Non-Markovianity and memory of the initial state, Symmetry protected phases in inhomogeneous spin chains, Explicit properties of the simplest inhomogeneous matrix-product-state including the Riemann metric of the MPS manifold, Phenomenology of anomalous transport in disordered one-dimensional systems, Lower bounds for ground states of condensed matter systems, Open source matrix product states: exact diagonalization and other entanglement-accurate methods revisited in quantum systems, A scalable maximum likelihood method for quantum state tomography, Low temperature dynamics of nonlinear Luttinger liquids, Tensor Ring Decomposition: Optimization Landscape and One-loop Convergence of Alternating Least Squares, Topological minimally entangled states via geometric measure, Entanglement negativity after a global quantum quench, Corner contribution to the entanglement entropy of anO(3) quantum critical point in 2 + 1 dimensions, Hybridization expansion Monte Carlo simulation of multi-orbital quantum impurity problems: matrix product formalism and improved sampling, Physical consequences of P≠NP and the density matrix renormalization group annealing conjecture, Rényi entropies of interacting fermions from determinantal quantum Monte Carlo simulations, Entanglement entropies of the quarter filled Hubbard model, Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble, Inversion Symmetry of Singular Values and a New Orbital Ordering Method in Tensor Train Approximations for Quantum Chemistry, Low-Rank Representation of Tensor Network Operators with Long-Range Pairwise Interactions, Corner transfer matrices for 2D strongly coupled many-body Floquet systems, Quantum quenches in 1 + 1 dimensional conformal field theories, Matrix product states forsu(2) invariant quantum spin chains, Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains, Rényi entropies after releasing the Néel state in theXXZspin-chain, The tensor network theory library, Rényi entropies of generic thermodynamic macrostates in integrable systems, Integrable quenches in nested spin chains I: the exact steady states, Jacobi--Davidson Method on Low-Rank Matrix Manifolds, Petz recovery versus matrix reconstruction, A Quantum Kinetic Monte Carlo Method for Quantum Many-Body Spin Dynamics, Classical restrictions of generic matrix product states are quasi-locally Gibbsian, Unifying neural-network quantum states and correlator product states via tensor networks, Obtaining highly excited eigenstates of the localized XX chain via DMRG-X, Exploiting matrix symmetries and physical symmetries in matrix product states and tensor trains, Unnamed Item, Geometry of matrix product states: Metric, parallel transport, and curvature, Fast tensor method for summation of long‐range potentials on 3D lattices with defects, Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure, Algorithm 941, Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications, A Low-Rank Tensor Method for PDE-Constrained Optimization with Isogeometric Analysis, Non-Markovian Master Equation for Distant Resonators Embedded in a One-Dimensional Waveguide, Efficient simulation of non-Markovian system-environment interaction, Unusual area-law violation in random inhomogeneous systems, Area laws and efficient descriptions of quantum many-body states, Time Integration of Tensor Trains, Non-equilibrium quantum spin dynamics from classical stochastic processes, The matrix product approximation for the dynamic cavity method, Fast Multidimensional Convolution in Low-Rank Tensor Formats via Cross Approximation, Construction of many-body-localized models where all the eigenstates are matrix-product-states, Entanglement revivals as a probe of scrambling in finite quantum systems, Disentanglement approach to quantum spin ground states: field theory and stochastic simulation, Computing Eigenspaces With Low Rank Constraints, Tensor Spaces and Hierarchical Tensor Representations, Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects, Corrected One-Site Density Matrix Renormalization Group and Alternating Minimal Energy Algorithm, Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format, Time evolution of entanglement negativity across a defect, Matrix product operator representation of polynomial interactions, Matrix product state of multi-time correlations, Inaccessible entanglement in symmetry protected topological phases, Fluctuations and non-Hermiticity in the stochastic approach to quantum spins, Low-complexity eigenstates of a ν = 1/3 fractional quantum Hall system, Hand-waving and interpretive dance: an introductory course on tensor networks, Compact neural-network quantum state representations of Jastrow and stabilizer states, Entanglement spreading after local and extended excitations in a free-fermion chain, Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1 + 1d, Large-\(N\) Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect, Tensor rank bounds for point singularities in \(\mathbb{R}^3\), Extending the range of real time density matrix renormalization group simulations, Time evolution of entanglement entropy from black hole interiors, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Cluster expansion for ground states of local Hamiltonians, Tensor-based dynamic mode decomposition, Computation of extreme eigenvalues in higher dimensions using block tensor train format, Non-abelian string breaking phenomena with matrix product states, Particle number conservation and block structures in matrix product states, Fundamental limitations in the purifications of tensor networks, CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry, Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma, On the closedness and geometry of tensor network state sets, Topological many-body states in quantum antiferromagnets via fuzzy supergeometry, Low rank tensor recovery via iterative hard thresholding, Complex best \(r\)-term approximations almost always exist in finite dimensions, MERACLE: constructive layer-wise conversion of a tensor train into a MERA, Born machine model based on matrix product state quantum circuit, Rigorous RG algorithms and area laws for low energy eigenstates in 1D, Tensor Approximation of Stationary Distributions of Chemical Reaction Networks, Simultaneous state-time approximation of the chemical master equation using tensor product formats, CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension, Computations in quantum tensor networks, Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation, A parallel low-rank solver for the six-dimensional Vlasov-Maxwell equations, Non-abelian symmetries in tensor networks: a quantum symmetry space approach, Quantum phase transitions and scaling behaviors of extended 1D compass spin-chain model, Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions, Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach, Recognizable series on graphs and hypergraphs, Analysis of weighted quantum secret sharing based on matrix product states, Quantum Enhanced Estimation of a Multidimensional Field, Time evolution of the Haldane state after a quantum quench, Probabilistic nonunitary gate in imaginary time evolution, Quantum dimensions from local operator excitations in the Ising model, On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems, Using the Tensor-Train Approach to Solve the Ground-State Eigenproblem for Hydrogen Molecules, Modeling complex quantum dynamics: evolution of numerical algorithms in the HPC context, Nonlinear system identification with regularized tensor network B-splines, Optimized implementation for calculation and fast-update of Pfaffians installed to the open-source fermionic variational solver mVMC, Establishing simple relationship between eigenvector and matrix elements, Approximation rates for the hierarchical tensor format in periodic Sobolev spaces, Computing the density of states for optical spectra of molecules by low-rank and QTT tensor approximation, Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs, Low-rank Riemannian eigensolver for high-dimensional Hamiltonians, Tensor network states and geometry, Tensor Product Approach to Quantum Control, A class of two-dimensional AKLT models with a gap, Geometric Methods on Low-Rank Matrix and Tensor Manifolds, Biorthonormal matrix-product-state analysis for the non-Hermitian transfer-matrix renormalization group in the thermodynamic limit, Exact bosonic matrix product states (and holography), Entanglement entropy scaling of the XXZ chain, Full counting statistics and the Edgeworth series for matrix product states, Entanglement negativity and conformal field theory: a Monte Carlo study, Quench dynamics of a Tonks–Girardeau gas released from a harmonic trap, Stationary entanglement entropies following an interaction quench in 1D Bose gas, Bound states and entanglement in the excited states of quantum spin chains, Fast tensor product solvers for optimization problems with fractional differential equations as constraints, Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations, Entanglement of purification: from spin chains to holography, Quantum chaos and thermalization in isolated systems of interacting particles, Matrix product state applications for the ALPS project, Multigrid renormalization, Algorithms for entanglement renormalization: boundaries, impurities and interfaces, Critical dynamics of transverse-field quantum Ising model using finite-size scaling and matrix product states, Time-evolution methods for matrix-product states, Statistical mechanical models for quantum codes with correlated noise, Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values, Prospects of tensor-based numerical modeling of the collective electrostatics in many-particle systems, Quantum impurity models from conformal field theory, Regularized Computation of Approximate Pseudoinverse of Large Matrices Using Low-Rank Tensor Train Decompositions, Novel families of SU \((N)\) AKLT states with arbitrary self-conjugate edge states, Effect of fluctuation in the coupling strength on critical dynamics of 1D transverse field quantum Ising model, Classes of topological qubits from low-dimensional quantum spin systems, Low-rank tensor approximation of singularly perturbed boundary value problems in one dimension, Many-body localization in large systems: matrix-product-state approach, Nonergodic dynamics in disorder-free potentials, Topological order in Mott insulators, Properties of the simplest inhomogeneous and homogeneous tree-tensor-states for long-ranged quantum spin chains with or without disorder, New applications of the renormalization group method in physics: a brief introduction, The density-matrix renormalization group: a short introduction, A tensor decomposition algorithm for large ODEs with conservation laws, Projection methods for dynamical low-rank approximation of high-dimensional problems, Tucker tensor analysis of Matérn functions in spatial statistics, Time evolution of coupled spin systems in a generalized Wigner representation, Two types of dynamic quantum state secret sharing based on tensor networks states, Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms, Uniform matrix product states from an algebraic geometer's point of view, Fundamental tensor operations for large-scale data analysis using tensor network formats, Mathematical open problems in projected entangled pair states, Cost-efficient cutoff method for tensor renormalization group with randomized singular value decomposition, Boundary theories of critical matchgate tensor networks, Long-distance entanglement in antiferromagnetic XXZ spin chain with alternating interactions, The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition, Entanglement entropy and negativity in the Ising model with defects, A literature survey of low-rank tensor approximation techniques, Dynamic and compressed quantum many-body state secret sharing based on site-independent matrix product states, MATRIX PRODUCT STATE REPRESENTATION FOR SLATER DETERMINANTS AND CONFIGURATION INTERACTION STATES, Surveying structural complexity in quantum many-body systems, MPS-VQE: a variational quantum computational chemistry simulator with matrix product states, Entanglement Hamiltonians: From Field Theory to Lattice Models and Experiments, Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature, Tensor product approach to modelling epidemics on networks, Resource-saving quantum key distribution based on three-photon matrix product states, Analysis of a density matrix renormalization group approach for transport in open quantum systems, Scrambling and thermalization in a diffusive quantum many-body system, Optimized auxiliary representation of non-Markovian impurity problems by a Lindblad equation, Interaction effects in a microscopic quantum wire model with strong spin–orbit interaction, Effective spin physics in two-dimensional cavity QED arrays, Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures, TNQMetro: tensor-network based package for efficient quantum metrology computations, Tensor network renormalization group study of spin-1 random Heisenberg chains, Non-adiabatic quantum state preparation and quantum state transport in chains of Rydberg atoms, Strong-coupling limit of depleted Kondo- and Anderson-lattice models, Open source matrix product states: opening ways to simulate entangled many-body quantum systems in one dimension, Representations of graph states with neural networks, A prototype of quantum von Neumann architecture, Critical phenomena and Kibble–Zurek scaling in the long-range quantum Ising chain, FDTD: solving \(1+1\)D delay PDE in parallel, Comparative study of state-of-the-art matrix-product-state methods for lattice models with large local Hilbert spaces without \(U(1)\) symmetry, Multipartite quantum nonlocality in two-dimensional transverse-field Ising models on \((N \times N\) square lattices, Frustration-free Hamiltonians supporting Majorana zero edge modes, Flow equations for cold Bose gases, Calculating composite-particle Spectra in Hamiltonian formalism and demonstration in 2-flavor \(\mathrm{QED}_{1+1\mathrm{d}}\), Entanglement asymmetry in the ordered phase of many-body systems: the Ising field theory, Strongly correlated one-dimensional Bose–Fermi quantum mixtures: symmetry and correlations, Spatial correlations in driven-dissipative photonic lattices

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:624838&oldid=12519620"