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DAOE

The DAOE utilities build diagonal projector MPOs that damp operator components according to a notion of operator size rather than bond dimension. They are intended for operator-space workflows where the goal is to preserve hydrodynamic transport while suppressing entanglement growth.

MPSToolkit.jl currently provides two related projectors:

  • pauli_daoe_projector for the original DAOE construction, where size is measured by Pauli weight
  • fdaoe_projector for the fermionic generalization, where size is measured by fermionic weight

DAOE Vs FDAOE

The difference is the notion of locality that is being damped:

  • DAOE is the natural choice for spin chains written in a local Pauli basis, where operator complexity is tracked by how many non-identity Pauli factors appear in a string.
  • FDAOE is the natural choice for fermionic systems, where Jordan-Wigner strings make plain Pauli weight a poor proxy for physical operator size.

So the practical rule of thumb is:

  • use pauli_daoe_projector for spin models and Pauli-basis transport calculations
  • use fdaoe_projector when fermionic structure matters and Pauli-weight damping would distort the relevant operator hierarchy

DAOE Example

using MPSToolkit

sites = pauli_siteinds(8)
projector = pauli_daoe_projector(sites; lstar=3, gamma=0.15)

FDAOE Example

using MPSToolkit

sites = pauli_siteinds(8)
projector = fdaoe_projector(sites; wstar=3, gamma=0.15)

Because the projectors are returned as MPOs, you can combine them with your own operator-space pipelines instead of being forced into a single packaged workflow.

API

MPSToolkit.pauli_daoe_projector — Function
pauli_daoe_projector(sites; lstar, gamma)

Construct the DAOE projector MPO that damps Pauli strings by their Pauli weight beyond cutoff lstar. The local operator basis is assumed to be ordered as (I, X, Y, Z).

Arguments

  • sites: Pauli-space site indices.

Keyword Arguments

  • lstar: Pauli-weight cutoff. Strings heavier than lstar acquire exponential damping.
  • gamma: Damping strength.

Returns

  • A diagonal MPO implementing the DAOE projector.
source
MPSToolkit.fdaoe_projector — Function
fdaoe_projector(sites; wstar, gamma)

Construct the FDAOE projector MPO that damps Pauli-basis operator strings by fermionic Majorana weight beyond cutoff wstar. The local operator basis is assumed to be ordered as (I, X, Y, Z).

Arguments

  • sites: Pauli-space site indices.

Keyword Arguments

  • wstar: Fermionic Majorana-weight cutoff.
  • gamma: Damping strength applied beyond the cutoff.

Returns

  • A diagonal MPO implementing the fermionic DAOE projector.
source

Examples

For a simple script-level entry point, see examples/daoe/projectors.jl.

References