Numerical block diagonalization and linked-cluster expansion for deriving effective Hamiltonians: Applications to spin excitations
Year: 2026
Type: article
Abstract: We present a numerical, non-perturbative framework for constructing effective Hamiltonians that describe the dynamics of low-energy degrees of freedom within a restricted Hilbert space in quantum many-body systems. The approach is based on block diagonalization guided by a minimal-deformation principle imposed within a selected target sector. The formulation is designed to remain compatible with the numerical linked-cluster expansion. For gapped systems, the relation between minimal deformation and cluster additivity requires careful treatment when excited eigenstates contain finite admixtures of the ground state. After establishing a cluster-additive basis that reproduces the Hörmann-Schmidt construction, the minimal-deformation criterion uniquely determines the effective Hamiltonian within each excitation sector. The same criterion also provides a practical numerical procedure for selecting relevant low-energy eigenstates, including regimes characterized by strong level mixing and avoided crossings. The framework is illustrated using two spin models: the one-dimensional transverse-field Ising model as a benchmark and the two-dimensional Shastry-Sutherland model with Dzyaloshinskii-Moriya interactions, relevant to SrCu _2 2 (BO _3 3 ) _2 2 . In both cases, the resulting effective Hamiltonians accurately capture the excitation dynamics and the associated band structures.
Source: SciPost Physics
Authors: Tsutomu Momoi, Owen Benton
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4417093926
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