Deconfinement transition and bound states in frustrated Heisenberg chains: Regimes of forced and spontaneous dimerization

Zheng, Weitao; Hamer, C. J.; Singh, Rajiv R. P.; Monien, H.

doi:10.1103/physrevb.63.144411

Cited by 20 publications

(1 citation statement)

References 19 publications

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“…Triplet-pair interactions within a dimerized antiferromagnetic chain have been investigated in Refs. [12,29,30], while stabilization of the 2A g state via configuration interactions was also discussed in Ref. [31].…”

Section: Introductionmentioning

confidence: 99%

Theory of the dark state of polyenes and carotenoids

Barford

2022

Phys. Rev. B

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A theory is developed to describe the singlet dark state (usually labeled S 1 or 2A g ) of polyenes and carotenoids. The properties of this state explain the nonemissive properties of linear polyenes, it is responsible for the photoprotection properties of carotenoids in light harvesting complexes, and because of its triplet-pair character, it is thought to be the cause of singlet fission in polyene-type systems. The theory described here assumes that in principle this state is a linear combination of singlet triplet-pairs and a singlet charge-transfer exciton. Crucially, these components only couple when the triplet pair occupies neighboring C-C dimers, such that an electron transfer between the triplets creates a nearest-neighbor singlet charge-transfer excitation. This local coupling stabilizes the 2A g state and induces a nearest-neighbor attraction between the triplets. In addition, because of the electron-hole Coulomb attraction in the exciton, the increased probability that the electron-hole pair occupies neighboring dimers enhances the triplet-triplet attraction: the triplet pair is "slaved" to the singlet exciton. The theory also predicts that as the Coulomb interaction is increased, the 2A g state evolves from a predominately charge-transfer exciton with a small component of triplet-pair character to a state predominately composed of a triplet pair with some exciton character. Above a critical Coulomb interaction there is a decoupling of the triplet-pair and exciton subspaces, such that the 2A g state becomes entirely composed of unbound spin-correlated triplet pairs. The predictions of this theory of a triplet-pair binding energy in carotenoids of ca. 0.4 eV are consistent with density matrix renormalization group calculations of the Pariser-Parr-Pople (or extended Hubbard) model. It also predicts that the single-triplet component of the 2A g state in carotenoids is ca. 50%.

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Section: Introductionmentioning

confidence: 99%

Theory of the dark state of polyenes and carotenoids

Barford

2022

Phys. Rev. B

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The structure of operators in effective particle-conserving models

Knetter

Schmidt

Uhrig

2003

J. Phys. A: Math. Gen.

128

216

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For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians conserving the number of excitations. The same transformation must be used to obtain effective observables.The analysis of the structure shows that effective operators give rise to a simple and intuitive perspective on the initial problem. The systematic calculation of n-particle irreducible quantities becomes possible constituting a significant progress. Details how to implement the approach perturbatively for a large class of systems are presented.

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Linked cluster series expansions for two-particle bound states

et al. 2001

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We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an orthogonality transformation to generate this block diagonalization, and find that maintaining orthogonality is crucial for systems where the ground state and the two-particle subspace are characterized by identical quantum numbers. We discuss the solution of the two-particle Schrödinger equation by using a finite lattice approach in coordinate space or by an integral equation in momentum space. These methods allow us to precisely determine the low-lying excitation spectra of the models at hand, including all two-particle bound/antibound states. Further, we discuss how to generate series expansions for the dispersions of the bound/antibound states. These allow us to employ series extrapolation techniques, whereby binding energies can be determined even when the expansion parameters are not small. We apply the method to the ͑1ϩ1͒-dimensional transverse Ising model and the two-leg spin-1 2 Heisenberg ladder. For the latter model, we also calculate the coherence lengths and determine the critical properties where bound states merge with the two-particle continuum.

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Deconfinement transition and bound states in frustrated Heisenberg chains: Regimes of forced and spontaneous dimerization

Cited by 20 publications

References 19 publications

Theory of the dark state of polyenes and carotenoids

Theory of the dark state of polyenes and carotenoids

The structure of operators in effective particle-conserving models

Linked cluster series expansions for two-particle bound states

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