Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors

Abstract

Matrix product states (MPSs) and matrix product operators (MPOs) are fundamental tools in the study of quantum many-body systems, particularly in the context of tensor network methods such as Time-Evolving Block Decimation (TEBD). However, constructing compact MPO representations for Hamiltonians with interactions beyond nearest-neighbors, such as those arising in atomic, molecular, and optical (AMO) systems or in systems with ring geometry, remains a challenge. In this paper, we propose a novel approach for the direct construction of compact MPOs tailored specifically for the exponential of spin Hamiltonians. This approach allows for a more efficient time evolution, using TEBD, of spin systems with interactions beyond nearest-neighbors, such as long-range spin-chains, periodic systems and more complex cluster model, with interactions involving more than two spins.

References in corpus (50)

• The density-matrix renormalization group in the age of matrix product states
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Time-dependent variational principle for quantum lattices
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Time-evolution methods for matrix-product states
• Dynamical quantum phase transitions: a review
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Matrix product operator representations
• Spread of correlations in long-range interacting quantum systems
• Time-evolving a matrix product state with long-ranged interactions
• Long-range interacting quantum systems
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Time-step targetting methods for real-time dynamics using DMRG
• Statistical mechanics of the Cluster-Ising model
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Unveiling phase transitions with machine learning
• Finite-range interacting Ising quantum magnets with Rydberg atoms in optical lattices - From Rydberg superatoms to crystallization
• Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians
• Tunable itinerant spin dynamics with polar molecules
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Dynamical phase transitions in the two-dimensional transverse-field Ising model
• One-dimensional many-body entangled open quantum systems with tensor network methods
• Evidence for a floating phase of the transverse ANNNI model at high frustration
• Quantum phase detection generalisation from marginal quantum neural network models
• Density Matrix Renormalization Group Study of the Disorder Line in the Quantum ANNNI Model
• Parallel time-dependent variational principle algorithm for matrix product states
• Genuine Multipartite Entanglement in the Cluster-Ising Model
• Quantum Phase Transition induced by Topological Frustration
• The Frustration of being Odd: How Boundary Conditions can destroy Local Order
• Exact results for persistent currents of two bosons in a ring lattice
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
• Simulating quantum circuits using tree tensor networks
• Density-matrix renormalization group: a pedagogical introduction
• Controlled flow of excitations in a ring-shaped network of Rydberg atoms
• n-cluster models in a transverse magnetic field
• Odd thermodynamic limit for the Loschmidt echo
• Long-range entanglement and topological excitations
• Simulating continuous symmetry models with discrete ones
• Anomalous diffusion in the Long-Range Haken-Strobl-Reineker model
• Towards a phase diagram of the topologically frustrated XY chain
• Coherent excitation transport through ring-shaped networks
• Exponentiation of Parametric Hamiltonians via Unitary interpolation