DMRG and periodic boundary conditions: a quantum information perspective
arXiv:cond-mat/0404706 · doi:10.1103/PhysRevLett.93.227205
Abstract
We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which the results are dramatically improved. The picture also explains some features of the method in terms of entanglement and teleportation.
4 pages
References in corpus (2)
Cited by in corpus (163)
- The density-matrix renormalization group in the age of matrix product states
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Classical simulation of infinite-size quantum lattice systems in one spatial dimension
- A class of quantum many-body states that can be efficiently simulated
- Matrix product states represent ground states faithfully
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Criticality, the area law, and the computational power of PEPS
- From density-matrix renormalization group to matrix product states
- Strong and weak thermalization of infinite non-integrable quantum systems
- Quantum Noise as an Entanglement Meter
- Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
- New Trends in Density Matrix Renormalization
- Time-evolving a matrix product state with long-ranged interactions
- The density matrix renormalization group for ab initio quantum chemistry
- Continuous Matrix Product States for Quantum Fields
- String order and symmetries in quantum spin lattices
- Localizable Entanglement
- Multipartite entanglement in spin chains
- Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
- Matrix Product States for dynamical simulation of infinite chains
- Applying matrix product operators to model systems with long-range interactions
- Ground state fidelity from tensor network representations
- Variational quantum Monte Carlo simulations with tensor-network states
- Quantum circuits for strongly correlated quantum systems
- The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
- Infinite density matrix renormalization group for multicomponent quantum Hall systems
- Time evolution algorithms for Matrix Product States and DMRG
- Quantum Graphical Models and Belief Propagation
- Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
- Finite automata for caching in matrix product algorithms
- Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
- Tensor Network Algorithms: a Route Map
- Chebyshev matrix product state approach for spectral functions
- Sequential Generation of Matrix-Product States in Cavity QED
- Using Quantum Computers for Quantum Simulation
- Quantum simulation of the Schwinger model: A study of feasibility
- Variational Quantum Reinforcement Learning via Evolutionary Optimization
- Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
- Lattice Gauge Tensor Networks
- Quantum MERA Channels
- Monte Carlo simulation with Tensor Network States
- Coherent superposition of current flows in an Atomtronic Quantum Interference Device
- Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
- Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
- Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
- Inductive classification of multipartite entanglement under SLOCC
- Lanczos algorithm with Matrix Product States for dynamical correlation functions
- Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
- Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models
- The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
- Ground state approximation for strongly interacting systems in arbitrary dimension
- Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
- Flux insertion, entanglement, and quantized responses
- Unifying variational methods for simulating quantum many-body systems
- Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
- Simulation of time evolution with the MERA
- The computational difficulty of finding MPS ground states
- Computations in Quantum Tensor Networks
- Matrix product state comparison of the numerical renormalization group and the variational formulation of the density matrix renormalization group
- Fermionic Implementation of Projected Entangled Pair States Algorithm
- Sequentially generated states for the study of two dimensional systems
- Area law and vacuum reordering in harmonic networks
- Pfaffian-like ground state for 3-body-hard-core bosons in 1D lattices
- Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions
- On the simulation of quantum circuits
- Exact ground state of the sine-square deformed XY spin chain
- Entropy and Exact Matrix Product Representation of the Laughlin Wave Function
- Suppression of finite-size effects in one-dimensional correlated systems
- Entanglement properties and moment distributions of a system of hard-core anyons on a ring
- Time evolution of projected entangled pair states in the single layer picture
- Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
- Anyonic entanglement renormalization
- Light cone tensor network and time evolution
- Ultrafast ab-initio Quantum Chemistry Using Matrix Product States
- Gauging tensor networks with belief propagation
- Sequential Implementation of Global Quantum Operations
- Entanglement entropy in dynamic quantum-coherent conductors
- The matrix product representations for all valence bond states
- Controlled bond expansion for DMRG ground state search at single-site costs
- Pair condensation of bosonic atoms induced by optical lattices
- Entanglement and Density Matrix of a Block of Spins in AKLT Model
- Towards overcoming the Monte Carlo sign problem with tensor networks
- Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States
- Quantum Phase Transitions and Matrix Product States in Spin Ladders
- Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement
- Compressive gate set tomography
- Ultracold atomic Bose and Fermi spinor gases in optical lattices
- Renormalization algorithm with graph enhancement
- The Computational Power of Symmetric Hamiltonians
- Continuous matrix product states with periodic boundary conditions and an application to atomtronics
- A variational method based on weighted graph states
- Automated construction of -invariant matrix-product operators from graph representations
- Topological pumping in the one-dimensional Bose-Hubbard model
- Qubit phase-space: SU(n) coherent state P-representations
- Density matrix renormalization group algorithms for Y-junctions
- Density-matrix renormalization group: a pedagogical introduction
- From classical to quantum criticality
- Entanglement bipartitioning and tree tensor networks
- Local Hamiltonians in Quantum Computation
- Boundary effects to the entanglement entropy and two-site entanglement of the spin-1 valence-bond solid
- Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities
- Loop-Free Tensor Networks for High-Energy Physics
- Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model
- Monogamy and ground-state entanglement in highly connected systems
- Approximating the ground state of gapped quantum spin systems
- Variational determination of multi-qubit geometrical entanglement in NISQ computers
- The minimal canonical form of a tensor network
- Spin-supersolid phase in Heisenberg chains: a characterization via Matrix Product States with periodic boundary conditions
- The nested Algebraic Bethe Ansatz for the supersymmetric t-J and Tensor Networks
- Entropy of entanglement and multifractal exponents for random states
- Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval
- Multipartite purification protocols: upper and optimal bounds
- Asymmetric spin-1/2 two-leg ladders
- Two holes in a two-dimensional quantum antiferromagnet: A variational study based on entangled-plaquette states
- Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
- Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
- Elastic and inelastic transmission in guided atom lasers: a truncated Wigner approach
- Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
- Entanglement area law violation from field-curvature coupling
- Ground states of long-range interacting fermions in one spatial dimension
- Quantum criticality of a symmetric spin chain with long-range interactions
- Matrix product state approach to a frustrated spin chain with long-range interactions
- Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems
- Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems
- Matrix Product State representation for Slater Determinants and Configuration Interaction States
- Exact symmetry breaking ground states for quantum spin chains
- The Nonequilibrium Many-Body Problem as a paradigm for extreme data science
- The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated - Heisenberg model
- Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
- Sequential quantum cloning under real-life conditions
- Efficient simulation of inhomogeneously correlated systems using block interaction product states
- Simulation of Charge Stability Diagrams for Automated Tuning Solutions (SimCATS)
- Open system approach to Neutrino oscillations in a quantum walk framework
- Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case
- Block Spin Density Matrix of the Inhomogeneous AKLT Model
- Many-body correlations in one-dimensional optical lattices with alkaline-earth(-like) atoms
- Relation between phase space coverage and entanglement for spin-1/2 systems
- Quantum Coherence of Topologically Frustrated Spin Chains
- Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
- Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
- Extended Delta-map: a map-based foreground removal method for CMB polarization observations
- Entanglement entropy evolution during gravitational collapse
- Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
- Particle Correlations in Bose-Einstein Condensates
- Quantum generative modeling for financial time series with temporal correlations
- Developments in entanglement theory and applications to relevant physical systems
- An Improved Initialization Procedure for the Density-Matrix Renormalization Group
- Les Houches Lecture Notes on Tensor Networks
- First-principle construction of U(1) symmetric matrix product states
- Decoherence and relaxation in the interacting quantum dot system
- A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
- The Software Landscape for the Density Matrix Renormalization Group
- Characterizing maximal families of mutually unbiased bases
- Fractal Path Strategies for Efficient 2D DMRG Simulations
- Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
- Machine Learning Green's Functions of Strongly Correlated Hubbard Models
- Long-range bipartite entanglement in XXZ spin chains with the exponential and power-law long-range interactions
- Ground-state phase diagram of quantum link electrodynamics in -d
- Phase structure of the one-dimensional lattice gauge theory with second nearest-neighbor interactions
- Probing Genuine Multipartite Entanglement in Large Systems
- Quantum Singular Value Decomposition of Spin Correlation Matrix in One-Dimensional Heisenberg Model
- Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas