Hörmann M, Schmidt KP (2023)
Publication Type: Journal article
Publication year: 2023
Book Volume: 15
Article Number: 097
Journal Issue: 3
DOI: 10.21468/SciPostPhys.15.3.097
We construct a projection-based cluster-additive transformation that block-diagonalizes wide classes of lattice Hamiltonians H = H0 + V. Its cluster additivity is an essential ingredient to set up perturbative or non-perturbative linked-cluster expansions for degenerate excitation subspaces of H0. Our transformation generalizes the minimal transformation known amongst others under the names Takahashi’s transformation, Schrieffer-Wolff transformation, des Cloiseaux effective Hamiltonian, canonical van Vleck effective Hamiltonian or two-block orthogonalization method. The effective cluster-additive Hamiltonian and the transformation for a given subspace of H, that is adiabatically connected to the eigenspace of H0 with eigenvalue e0n, solely depends on the eigenspaces of H connected to e0m with e0m ≤ e0n. In contrast, other cluster-additive transformations like the multi-block orthogonalization method or perturbative continuous unitary transformations need a larger basis. This can be exploited to implement the transformation efficiently both perturbatively and non-perturbatively. As a benchmark, we perform perturbative and non-perturbative linked-cluster expansions in the low-field ordered phase of the transverse-field Ising model on the square lattice for single spin-flips and two spin-flip bound-states.
APA:
Hörmann, M., & Schmidt, K.P. (2023). Projective cluster-additive transformation for quantum lattice models. SciPost Physics, 15(3). https://doi.org/10.21468/SciPostPhys.15.3.097
MLA:
Hörmann, Max, and Kai Phillip Schmidt. "Projective cluster-additive transformation for quantum lattice models." SciPost Physics 15.3 (2023).
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