Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

Abstract

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.

19 pages, 12 figures

References in corpus (26)

• The density-matrix renormalization group
• Entanglement in quantum critical phenomena
• Efficient classical simulation of slightly entangled quantum computations
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Efficient simulation of one-dimensional quantum many-body systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• An Area Law for One Dimensional Quantum Systems
• Area laws in quantum systems: mutual information and correlations
• Lieb-Schultz-Mattis in Higher Dimensions
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• DMRG and periodic boundary conditions: a quantum information perspective
• Spectral Gap and Exponential Decay of Correlations
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Entanglement Entropy dynamics in Heisenberg chains
• Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
• Solving Gapped Hamiltonians Locally
• General entanglement scaling laws from time evolution
• Evolution of entanglement after a local quench
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Bounds on Information Propagation in Disordered Quantum Spin Chains
• Quantum Belief Propagation
• Random Antiferromagnetic Spin-1/2 Chains with Competing Interactions
• The antiferromagnetic order in an F-AF random alternating quantum spin chain : (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3

Cited by in corpus (24)

• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• Entanglement entropy and conformal field theory
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• The Future of Quantum Computing with Superconducting Qubits
• Information Scrambling in Computationally Complex Quantum Circuits
• Matrix Product States for dynamical simulation of infinite chains
• Hamiltonian complexity
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Probing local relaxation of cold atoms in optical superlattices
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• Information propagation for interacting particle systems
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
• Supersonic quantum communication
• Making Almost Commuting Matrices Commute
• Information propagation through quantum chains with fluctuating disorder
• Light Cone Matrix Product
• Transport and Control in One-Dimensional Systems
• Analytical Framework for Quantum Alternating Operator Ansätze
• Transport Control in Low-Dimensional Spin-1/2 Heisenberg Systems
• Approximating open quantum system dynamics in a controlled and efficient way: A microscopic approach to decoherence
• Locally accurate tensor networks for thermal states and time evolution