Time-evolution of local information: thermalization dynamics of local observables

Abstract

Quantum many-body dynamics generically results in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such decoupling of local degrees of freedom for the mixed field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we can motivate algorithms based on the intuition that information for statistical reasons flow from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.

38 pages, 9 figures

References in corpus (5)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Spectral functions in one-dimensional quantum systems at T>0
• Quantum dynamics of thermalizing systems
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• On the informational completeness of local observables

Cited by in corpus (23)

• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Scrambling Transition in a Radiative Random Unitary Circuit
• Classical simulation of short-time quantum dynamics
• Operator backflow and the classical simulation of quantum transport
• Transport and entanglement growth in long-range random Clifford circuits
• Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution
• The operator growth hypothesis in open quantum systems
• Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model
• Converting long-range entanglement into mixture: tensor-network approach to local equilibration
• Corrections to diffusion in interacting quantum systems
• Effective dissipation rate in a Liouvillian graph picture of high-temperature quantum hydrodynamics
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Open-system spin transport and operator weight dissipation in spin chains
• Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain
• Probing Hilbert space fragmentation and the block inverse participation ratio
• Universal Characterization of Quantum Many-Body States through Local Information
• Approximation theory for Green's functions via the Lanczos algorithm
• Nanoscale engineering and dynamical stabilization of mesoscopic spin textures
• Local Information Flow in Quantum Quench Dynamics
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Emergent random matrix universality in quantum operator dynamics
• Multipartite entanglement structures in quantum stabilizer states
• Learning the non-Markovian features of subsystem dynamics