Ab-Initio Approach to Many-Body Quantum Spin Dynamics
arXiv:2411.13190 · doi:10.1103/PhysRevResearch.7.023039
Abstract
A fundamental longstanding problem in studying spin models is the efficient and accurate numerical simulation of the long-time behavior of larger systems. The exponential growth of the Hilbert space and the entanglement accumulation at long times pose major challenges for current methods. To address these issues, we employ the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) framework to simulate the many-body spin dynamics of the Heisenberg model in various settings, including the Ising and XYZ limits with different interaction ranges and random couplings. Benchmarks with analytical and exact numerical approaches show that ML-MCTDH accurately captures the time evolution of one- and two-body observables in both one- and two-dimensional lattices. A comparison with the discrete truncated Wigner approximation (DTWA) highlights that ML-MCTDH is particularly well-suited for handling anisotropic models and provides more reliable results for two-point observables across all tested cases. The behavior of the corresponding entanglement dynamics is analyzed to reveal the complexity of the quantum states. Our findings indicate that the rate of entanglement growth strongly depends on the interaction range and the presence of disorder. This particular relationship is then used to examine the convergence behavior of ML-MCTDH. Our results indicate that the multilayer structure of ML-MCTDH is a promising numerical framework for handling the dynamics of generic many-body spin systems.
16 pages, 10 figures
References in corpus (89)
- The density-matrix renormalization group in the age of matrix product states
- Quantum sensing
- Quantum Simulation
- Area laws for the entanglement entropy - a review
- Nonequilibrium dynamics of closed interacting quantum systems
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Quantum Spin Liquids
- Efficient simulation of one-dimensional quantum many-body systems
- Real time evolution using the density matrix renormalization group
- Quantum Communication Through an Unmodulated Spin Chain
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
- Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
- Realizing a lattice spin model with polar molecules
- Effective quantum spin systems with ion traps
- Observation of entanglement propagation in a quantum many-body system
- Time-dependent variational principle for quantum lattices
- A Rydberg Quantum Simulator
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Unifying time evolution and optimization with matrix product states
- Non-local propagation of correlations in long-range interacting quantum systems
- Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
- Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
- Dynamical quantum phase transitions: a review
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Many-body localization in a disordered quantum Ising chain
- Classical simulation of quantum many-body systems with a tree tensor network
- Tensor networks for complex quantum systems
- Entanglement versus Correlations in Spin Systems
- Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
- Entropy scaling and simulability by Matrix Product States
- The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
- Entanglement entropy of random quantum critical points in one dimension
- Entanglement and Tunable Spin-Spin Couplings Between Trapped Ions Using Multiple Transverse Modes
- Dynamical crystallization in a low-dimensional Rydberg gas
- Dynamics of Entanglement in One-Dimensional Spin Systems
- Exotic topological order in fractal spin liquids
- Entanglement entropy for the long range Ising chain
- The Propagation of Quantum Information Through a Spin System
- Coherent many-body spin dynamics in a long-range interacting Ising chain
- Role of excited states in the splitting dynamics of interacting Bose-Einstein condensates when ramping-up a barrier
- Prediction of Toric Code Topological Order from Rydberg Blockade
- Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
- What limits the simulation of quantum computers?
- Many-body dynamics of dipolar molecules in an optical lattice
- Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunnelling models
- The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
- Many-body spin interactions and the ground state of a dense Rydberg lattice gas
- Information-capacity description of spin-chain correlations
- Eigenstate thermalization in the two-dimensional transverse field Ising model
- The Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons: Theory, Implementation and Applications
- A unified ab-initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures
- Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
- On entropy growth and the hardness of simulating time evolution
- Non-Equilibrium Quantum Dynamics of Ultra-Cold Atomic Mixtures: the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons
- Entanglement equipartition in critical random spin chains
- Entanglement dynamics in quantum many-body systems
- Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model
- Relaxation of an isolated dipolar-interacting Rydberg quantum spin system
- Relaxation timescales and decay of correlations in a long-range interacting quantum simulator
- Glassy dynamics in a disordered Heisenberg quantum spin system
- Computing vibrational eigenstates with tree tensor network states (TTNS)
- Quantum correlation in disordered spin systems: entanglement and applications to magnetic sensing
- Tunable itinerant spin dynamics with polar molecules
- Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: A phase-space Monte-Carlo study
- Realizing distance-selective interactions in a Rydberg-dressed atom array
- Enhancement of entanglement transfer in a spin chain by phase shift-control
- Simulation of Quantum Spin Dynamics by Phase Space Sampling of BBGKY Trajectories
- Entanglement flow in multipartite systems
- Effect of long-range hopping and interactions on entanglement dynamics and many-body localization
- Floquet quantum simulation with superconducting qubits
- Quantum simulation of interacting high-dimensional systems: the influence of noise
- Test of quantum thermalization in the two-dimensional transverse-field Ising model
- Discrete truncated Wigner approach to dynamical phase transitions in Ising models after a quantum quench
- A tensor network view of multilayer multiconfiguration time-dependent Hartree methods
- Two-axis twisting using Floquet-engineered XYZ spin models with polar molecules
- Entanglement contour perspective for strong area law violation in a disordered long-range hopping model
- Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
- Analysis of continuous and discrete Wigner approximations for spin dynamics
- Non-adiabatic quantum dynamics without potential energy surfaces based on second-quantized electrons: application within the framework of the MCTDH method
- Optimal Tree Tensor Network Operators for Tensor Network Simulations: Applications to Open Quantum Systems
- The multi-configurational time-dependent Hartree approach in optimized second quantization: imaginary time propagation and particle number conservation
- Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions
- Dynamics of correlation spreading in low-dimensional transverse-field Ising models
- Exploring Disordered Quantum Spin Models with a Multi-Layer Multi-Configurational Approach
- Quantum simulation of long range quantum spin glass with strong area-law violation using trapped ions