Density Matrix Renormalization Group in the Heisenberg Picture

Abstract

In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some non-trivial cases, this approach can even be exact for finite bond dimensions.

version to appear in PRL, acronyms in title and abstract expanded, new improved numerical examples

References in corpus (28)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group
• Efficient classical simulation of slightly entangled quantum computations
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Efficient simulation of one-dimensional quantum many-body systems
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• An Area Law for One Dimensional Quantum Systems
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Effective quantum spin systems with ion traps
• Quantum phase transitions of light
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays
• Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Entanglement Properties of the Harmonic Chain
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• An entanglement-area law for general bosonic harmonic lattice systems
• Operator space entanglement entropy in transverse Ising chain
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• On the entanglement entropy for a XY spin chain
• On entropy growth and the hardness of simulating time evolution
• Double wells, scalar fields and quantum phase transitions in ions traps

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• Self-Consistent Projection Operator Theory for Quantum Many-Body Systems
• Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain
• Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
• Efficient simulation of open quantum systems coupled to a fermionic bath
• Quantum dynamics in photonic crystals
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• Multimode entanglement in coupled cavity arrays
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
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• Probing thermalization through spectral analysis with matrix product operators
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• Real time evolution at finite temperatures with operator space matrix product states
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• Dissipation-induced correlations in 1D bosonic systems
• Boundary Chaos: Exact Entanglement Dynamics
• Bridging Entanglement and Magic Resources within Operator Space
• On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension
• Particle number conservation in quantum many-body simulations with matrix product operators
• Dynamics of noisy quantum systems in the Heisenberg picture: application to the stability of fractional charge
• Simulating local measurements on a quantum many body system with stochastic matrix product states
• Robust construction of entangled coherent GHZ and W states in a cavity QED system
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• Numerical operator method for the real time dynamics of strongly-correlated quantum impurity systems far from equilibrium
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