Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution
PRX Quantum(2023)
Abstract
During time evolution of many-body systems entanglement grows rapidly,
limiting exact simulations to small-scale systems or small timescales. Quantum
information tends however to flow towards larger scales without returning to
local scales, such that its detailed large-scale structure does not directly
affect local observables. This allows for the removal of large-scale quantum
information in a way that preserves all local observables and gives access to
large-scale and large-time quantum dynamics. To this end, we use the recently
introduced information lattice to organize quantum information into different
scales, allowing us to define local information and information currents which
we employ to systematically discard long-range quantum correlations in a
controlled way. Our approach relies on decomposing the system into subsystems
up to a maximum scale and time evolving the subsystem density matrices by
solving the subsystem von Neumann equations in parallel. Importantly, the
information flow needs to be preserved during the discarding of large-scale
information. To achieve this without the need to make assumptions about the
microscopic details of the information current, we introduce a second scale at
which information is discarded while using the state at the maximum scale to
accurately obtain the information flow. The resulting algorithm, which we call
local information time evolution (LITE), is highly versatile and suitable for
investigating many-body quantum dynamics in both closed and open quantum
systems with diverse hydrodynamic behaviors. We present results for energy
transport in the mixed-field Ising model and magnetization transport in an open
XX spin chain where we accurately determine the diffusion coefficients. The
information lattice framework employed here promises to offer insightful
results about the spatial and temporal behavior of entanglement in many-body
systems.
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