Implement cluster expansion MPOs

docs/overrides.jl

@@ -6,7 +6,7 @@ function DocumenterVitepress.vitepress_config_transform(::VitepressOverrides, co
     occursin(marker, config) || error("DocumenterVitepress config has no default export to extend")
     return replace(config, marker => "const upstreamConfig = "; count = 1) * """
 
-    import { withOverrides } from './overrides.mts'
-    export default withOverrides(upstreamConfig)
-    """
+                import { withOverrides } from './overrides.mts'
+                export default withOverrides(upstreamConfig)
+                """
 end

docs/src/assets/mpskit.bib

@@ -773,6 +773,20 @@ @article{vanderstraeten2019
   abstract = {In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of observables, and discuss the concept of a tangent space. We explain how to variationally optimize ground-state approximations, implement real-time evolution and describe elementary excitations for a given model Hamiltonian. Also, we explain how matrix product states approximate fixed points of one-dimensional transfer matrices. We show how all these methods can be translated to the language of continuous matrix product states for one-dimensional field theories. We conclude with some extensions of the tangent-space formalism and with an outlook to new applications.}
 }
 
+@article{vanhecke2021cluster,
+  title = {Symmetric Cluster Expansions with Tensor Networks},
+  author = {Vanhecke, Bram and Vanderstraeten, Laurens and Verstraete, Frank},
+  year = {2021},
+  month = feb,
+  journal = {Physical Review A},
+  volume = {103},
+  number = {2},
+  pages = {L020402},
+  publisher = {American Physical Society},
+  doi = {10.1103/PhysRevA.103.L020402},
+  url = {https://link.aps.org/doi/10.1103/PhysRevA.103.L020402}
+}
+
 @article{vanhecke2021,
   title = {Tangent-Space Methods for Truncating Uniform {{MPS}}},
   author = {Vanhecke, Bram and Van Damme, Maarten and Haegeman, Jutho and Vanderstraeten, Laurens and Verstraete, Frank},

docs/src/changelog.md

@@ -21,6 +21,10 @@ When releasing a new version, move the "Unreleased" changes to a new version sec
 
 ### Added
 
+- `ClusterExpansion` time-evolution algorithm for `make_time_mpo`, constructing evolution MPOs
+  for finite and infinite nearest-neighbor Hamiltonians through a nonperturbative cluster expansion
+  that matches exact exponentials on clusters of up to `N` sites. ([#252](https://github.com/QuantumKitHub/MPSKit.jl/pull/252))
+
 ### Changed
 
 ### Deprecated
@@ -29,6 +33,8 @@ When releasing a new version, move the "Unreleased" changes to a new version sec
 
 ### Fixed
 
+- `convert(TensorMap, H)` for single-site `FiniteMPOHamiltonian`s no longer contracts the site tensor with itself. ([#252](https://github.com/QuantumKitHub/MPSKit.jl/pull/252))
+
 ### Performance
 
 ## [0.14.0](https://github.com/QuantumKitHub/MPSKit.jl/compare/v0.13.13...v0.14.0) - 2026-10-05

docs/src/man/algorithms.md

@@ -123,10 +123,31 @@ Here, there are several algorithms available
 WI
 WII
 TaylorCluster
+ClusterExpansion
 ```
 
 See also [Time evolution accuracy](@ref).
 
+#### Nonperturbative cluster expansion
+
+[`ClusterExpansion`](@ref) constructs evolution MPOs for finite and infinite
+nearest-neighbor Hamiltonians by matching exact exponentials on clusters of up to
+`N` sites [vanhecke2021cluster](@cite). Unlike [`TaylorCluster`](@ref), `N` specifies
+the cluster size rather than a Taylor order. For nearest-neighbor interactions,
+the one-step error is `O(dt^N)`; a finite chain is matched up to roundoff when
+`N` reaches its length.
+
+```julia
+U = make_time_mpo(H, dt, ClusterExpansion(; N = 3))
+ψ, envs, info = approximate(ψ, (U, ψ); trunc = truncrank(32))
+```
+
+Matching small clusters to all orders can permit larger time steps and help grow
+the bond dimension from weakly entangled states. The construction costs more than
+the compact [`WII`](@ref) approximation, and increasing `N` requires exponentially
+larger cluster exponentials and MPO bonds. Check convergence by varying `dt` and
+`N`, as well as the MPS compression settings.
+
 ## Excitations
 
 It might also be desirable to obtain information beyond the lowest energy state of a given system, and study the dispersion relation.

src/MPSKit.jl

@@ -36,7 +36,7 @@ export excitations
 export FiniteExcited, QuasiparticleAnsatz, ChepigaAnsatz, ChepigaAnsatz2
 export time_evolve, timestep, timestep!, make_time_mpo
 export AlgorithmInfo, convergence_measure
-export TDVP, TDVP2, BUG, WI, WII, TaylorCluster
+export TDVP, TDVP2, BUG, WI, WII, TaylorCluster, ClusterExpansion
 export changebonds, changebonds!
 export VUMPSSvdCut, OptimalExpand, SvdCut, RandExpand, SketchedExpand
 export NoiseSchedule, FunctionalSchedule, ExponentialDecay, Warmup, DMRG3S
@@ -174,6 +174,7 @@ include("algorithms/timestep/tdvp.jl")
 include("algorithms/timestep/bug.jl")
 include("algorithms/timestep/taylorcluster.jl")
 include("algorithms/timestep/wii.jl")
+include("algorithms/timestep/clusterexpansion.jl")
 include("algorithms/timestep/integrators.jl")
 include("algorithms/timestep/time_evolve.jl")