Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit

Abstract

We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically growable) finite region with fixed boundary conditions. The suppression of unphysical quasiparticle reflections from the boundary of the nonuniform region is also discussed. Using this algorithm we study the dynamics of localized excitations in infinite systems, which we illustrate in the case of the spin-1 anti-ferromagnetic Heisenberg model and the ${\varphi }^4$ model.

8 pages, 5 figures, tensor network diagrams. Code available at http://amilsted.github.io/evoMPS/

References in corpus (8)

• 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
• Post-Matrix Product State Methods: To tangent space and beyond
• Matrix Product States for dynamical simulation of infinite chains
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Infinite boundary conditions for matrix product state calculations
• Improved numerical methods for infinite spin chains with long-range interactions
• Dynamical windows for real-time evolution with matrix product states

Cited by in corpus (37)

• Spread of correlations in long-range interacting quantum systems
• Tangent-space methods for uniform matrix product states
• Many-body localization and delocalization in large quantum chains
• Lecture Notes of Tensor Network Contractions
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Many-body delocalization dynamics in long Aubry-André quasiperiodic chains
• Conformal Data from Finite Entanglement Scaling
• Collisions of false-vacuum bubble walls in a quantum spin chain
• Statistical translation invariance protects a topological insulator from interactions
• Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
• High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Commensurate and Incommensurate States of Topological Quantum Matter
• Light cone tensor network and time evolution
• Variational methods for contracting projected entangled-pair states
• Neutral Excitations of Quantum Hall States: a Density Matrix Renormalization Group Study
• Real-time scattering of interacting quasiparticles in quantum spin chains
• Nonlinear spectroscopy of bound states in perturbed Ising spin chains
• Finite-temperature dynamic structure factor of the spin-1 XXZ chain with single-ion anisotropy
• Quantum dimensions from local operator excitations in the Ising model
• Criticality at the Haldane-insulator charge-density-wave quantum phase transition
• Numerical Simulation of Critical Quantum Dynamics without Finite Size Effects
• Dynamical Spectral Response of Fractonic Quantum Matter
• Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid
• Real-Time Scattering in Ising Field Theory using Matrix Product States
• Infinite boundary conditions for response functions and limit cycles in iDMRG, demonstrated for bilinear-biquadratic spin-1 chains
• Time-dependent variational principle of mixed matrix product states in the thermodynamic limit
• Momentum-resolved time evolution with matrix product states
• Detection of anyon braiding through pump-probe spectroscopy
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• The Software Landscape for the Density Matrix Renormalization Group
• Metal-insulator transition of spinless fermions coupled to dispersive optical bosons
• Characterization of localized effective spins in gapped quantum spin chains
• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold
• Numerical Probe of Dynamical Properties of a Two-Dimensional Triangular Ising Lattice with Long-Range Interaction
• Dissipative dynamics in isolated quantum spin chains after a local quench
• Dynamical correlations and nonequilibrium sum rules in photodoped Hubbard ladders