Studying dynamics in two-dimensional quantum lattices using tree tensor network states
arXiv:2003.08944 · doi:10.21468/SciPostPhys.9.5.070
Abstract
We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle in a manifold of binary and quaternary Tree Tensor Network States. The approach is found to be competitive with existing matrix product state approaches. We discuss issues related to the convergence of the method, which could be relevant to a broader set of numerical techniques used for the study of two-dimensional systems.
arXiv comment11 pages, 10 figures
References in corpus (51)
- Many-Body Physics with Ultracold Gases
- The density-matrix renormalization group in the age of matrix product states
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Entanglement renormalization
- An Area Law for One Dimensional Quantum Systems
- Time-dependent variational principle for quantum lattices
- Unifying time evolution and optimization with matrix product states
- Time-evolution methods for matrix-product states
- Criticality, the area law, and the computational power of PEPS
- Stripe order in the underdoped region of the two-dimensional Hubbard model
- Classical simulation of quantum many-body systems with a tree tensor network
- Entanglement and thermodynamics after a quantum quench in integrable systems
- Studying Two Dimensional Systems With the Density Matrix Renormalization Group
- Spread of correlations in long-range interacting quantum systems
- Entanglement Entropy dynamics in Heisenberg chains
- Time-evolving a matrix product state with long-ranged interactions
- Entanglement entropy for the long range Ising chain
- Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
- Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
- Quantum many-body dynamics in two dimensions with artificial neural networks
- Applying matrix product operators to model systems with long-range interactions
- Time integration of tensor trains
- Lecture Notes of Tensor Network Contractions
- Entanglement renormalization and topological order
- Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
- Time Dependent Variational Principle with Ancillary Krylov Subspace
- Isometric Tensor Network States in Two Dimensions
- Unifying Projected Entangled Pair States contractions
- Quantum dynamics of thermalizing systems
- Multiple steady-states in nonequilibrium quantum systems with electron-phonon interactions
- Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
- Fermionic orbital optimisation in tensor network states
- Efficient simulation of infinite tree tensor network states on the Bethe lattice
- Tensor operators: constructions and applications for long-range interaction systems
- Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
- Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
- The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
- Breaking the entanglement barrier: Tensor network simulation of quantum transport
- T3NS: three-legged tree tensor network states
- Time Dependent Variational Principle for Tree Tensor Networks
- Slow many-body delocalization beyond one dimension
- Finding purifications with minimal entanglement
- Conformational Dynamics Guides Coherent Exciton Migration in Conjugated Polymer Materials: A First-Principles Quantum Dynamical Study
- Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
- Time evolution of projected entangled pair states in the single layer picture
- The area law and real-space renormalization
- Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
- Comb tensor networks
- Simulating the out-of-equilibrium dynamics of local observables by trading entanglement for mixture
- Tensor network renormalization group study of spin-1 random Heisenberg chains
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- Tensor Network Algorithms: a Route Map
- Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
- Tree tensor network state approach for solving hierarchical equations of motion
- Automatic structural optimization of tree tensor networks
- Many-body localization in large systems: Matrix-product-state approach
- Gauging tensor networks with belief propagation
- Time-dependent variational principle with controlled bond expansion for matrix product states
- Variational classical networks for dynamics in interacting quantum matter
- Time Evolution of ML-MCTDH Wavefunctions II: Application of the Projector Splitting Integrator
- Time Evolution of ML-MCTDH Wavefunctions I: Gauge Conditions, Basis Functions, and Singularities
- Using tensor network states for multi-particle Brownian ratchets
- Dynamical correlation functions from complex time evolution
- Roughening dynamics of interfaces in the two-dimensional quantum Ising model
- Optimal Symbolic Construction of Matrix Product Operators and Tree Tensor Network Operators
- Fermionic Isometric Tensor Network States in Two Dimensions
- Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
- Quantum Gauge Networks: A New Kind of Tensor Network
- Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm