Series expansions in closed and open quantum many-body systems with multiple quasiparticle types

Lenke, Lea; Schellenberger, Andreas; Schmidt, Kai Phillip

doi:10.1103/physreva.108.013323

Cited by 3 publications

(1 citation statement)

References 48 publications

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“…There is also a model-dependent method to use η QP perturbatively (epCUT) and non-perturbatively (deepCUT) [43] for H 0 with a non-equidistant spectrum directly in the thermodynamic limit. Also, recently an extension of the pCUT approach to multiple quasiparticle types as well as non-Hermitian Hamiltonians and open systems was introduced under the name pcst ++ [44]. It should also be possible to write down model-independent perturbative expressions for MBOT and H 0 with non-equidistant spectrum similarly as in the Schrieffer-Wolff expansion of the minimal transformation but now using projectors on all eigenspaces of H 0 .…”

Section: Cluster-additive Block Diagonalisation Methodsmentioning

confidence: 99%

Projective cluster-additive transformation for quantum lattice models

Hörmann,

Schmidt

2023

SciPost Phys.

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We construct a projection-based cluster-additive transformation that block-diagonalizes wide classes of lattice Hamiltonians \mathcal{H}=\mathcal{H}_0 +Vℋ=ℋ0+V. Its cluster additivity is an essential ingredient to set up perturbative or non-perturbative linked-cluster expansions for degenerate excitation subspaces of \mathcal{H}_0ℋ0. 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 \mathcal{H}ℋ, that is adiabatically connected to the eigenspace of \mathcal{H}_0ℋ0 with eigenvalue e_0^ne0n, solely depends on the eigenspaces of \mathcal{H}ℋ connected to e_0^me0m with e_0^m\leq e_0^ne0m≤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.

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Section: Cluster-additive Block Diagonalisation Methodsmentioning

confidence: 99%

Projective cluster-additive transformation for quantum lattice models

Hörmann,

Schmidt

2023

SciPost Phys.

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Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain

Zhang,

Song

2024

Phys. Rev. B

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(Almost) everything is a Dicke model - Mapping non-superradiant correlated light-matter systems to the exactly solvable Dicke model

Schellenberger,

Schmidt

2024

SciPost Phys. Core

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We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large number of matter entities, we map the relevant low-energy sector of a broad class of models in the non-superradiant phases onto the exactly solvable Dicke model. We apply the outcomes to the Dicke-Ising model as a paradigmatic example [Phys. Rev. Res. 2, 023131 (2020), Sci. Rep. 4, 4083 (2014)], in agreement with results obtained by mean-field theory [Sci. Rep. 4, 4083 (2014)]. We further accompany and verify our findings with finite-size calculations, using exact diagonalization and the series expansion method pcst^{++}++ [Phys. Rev. A 108, 013323 (2023)]

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Series expansions in closed and open quantum many-body systems with multiple quasiparticle types

Cited by 3 publications

References 48 publications

Projective cluster-additive transformation for quantum lattice models

Projective cluster-additive transformation for quantum lattice models

Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain

(Almost) everything is a Dicke model - Mapping non-superradiant correlated light-matter systems to the exactly solvable Dicke model

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