Many-body physics in small systems: Observing the onset and saturation of correlation in linear atomic chains

Townsend, Emily; Neuman, Tomáš; Debrecht, Alex; Aizpurua, Javier; Bryant, Garnett W.

doi:10.1103/physrevb.103.195429

Cited by 6 publications

(3 citation statements)

References 39 publications

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“…Due to the computationally challenging problems that arise in the context of quantum chemistry, this may prove beneficial for the benchmarking of existing numerical techniques and development of new theoretical methods. In addition, these well-controlled quantum systems with long-range interactions are also promising for future investigations of other debated phenomena, such as Wigner crystallization [41,42], exciton formation [3], high-temperature superconductivity [4,7], and the nature of manybody excited states [43].…”

Section: Discussionmentioning

confidence: 99%

Long-range electron-electron interactions in quantum dot systems and applications in quantum chemistry

Knörzer,

van Diepen,

Hsiao

et al. 2022

Preprint

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Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present the first detailed experimental characterization of long-range electron-electron interactions in an array of gatedefined semiconductor quantum dots. We demonstrate significant interaction strength among electrons that are separated by up to four sites, and show that our theoretical prediction of the screening effects matches well the experimental results. Based on these findings, we investigate how long-range interactions in quantum-dot arrays may be utilized for analog simulations of artificial quantum matter. We numerically show that about ten quantum dots are sufficient to observe binding for a one-dimensional H2-like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry.

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Section: Discussionmentioning

confidence: 99%

Long-range electron-electron interactions in quantum dot systems and applications in quantum chemistry

Knörzer,

van Diepen,

Hsiao

et al. 2022

Preprint

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“…In insulating electronic systems whose optical properties are predominantly characterized by single-particle transitions, Coulomb interaction may often be safely neglected [19]. However, previous contributions have revealed that, especially in the metallic linear chain, Coulomb interaction leading to collective plasmonic charge carrier oscillations plays a significant role for determining resonant modes [19,[64][65][66][67][68][69].…”

Section: Interacting Hybrid Systemmentioning

confidence: 99%

Modification of the optical properties of molecular chains upon coupling to adatoms

et al. 2021

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Adsorbed atoms (adatoms) coupled to the matrix of solid state host materials as impurities can significantly modify their properties. Especially in low-dimensional materials, such as one-dimensional organic polymer chains or quasi-one-dimensional graphene nanoribbons, intriguing manipulation of the optical properties, such as the absorption cross section, is possible. The most widely used approach to couple quantum emitters to optical antennas is based on the Purcell effect. This formalism, however, does not comprise charge transfer from the emitter to the antenna, but only spontaneous emission of the quantum emitter into the tailored photonic environment, that is evoked by the antenna. To capture such effects, we present a tight-binding formalism to couple an adatom to a finite Su-Schrieffer-Heeger chain, where the former is treated as a two-level system and the latter acts as an optical antenna. We systematically analyze how the coupling strength and the position of the adatom influence the optical properties of the molecular chains in the model. We take into account charge transfer from the adatom to the chain and vice versa via an intersystem hopping parameter, and also include Coulomb interaction within the chain as well as between the adatom and the chain. We show that coupling the adatom to one of the bulk atoms of the linear chain results in a substantial change in optical properties already for comparatively small coupling strengths. We also find that the position of the adatom crucially determines if and how the optical properties of the chains are altered. Therefore, we identify this adatom-chain hybrid system as a tunable platform for light-matter interaction at the nanoscale.

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“…These together allow for a two-way correspondence between donor chains or arrays and lattice models of the Fermi-Hubbard type [33]. With this, an interesting path of observing and describing the onset of collective effects in small many-body systems opens [34].…”

Section: Introductionmentioning

confidence: 99%

Bardeen's tunneling theory applied to intraorbital and interorbital hopping integrals between dopants in silicon

Gawełczyk

Zieliński²

2022

Phys. Rev. B

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We utilize Bardeen's tunneling theory to calculate intra-and interorbital hopping integrals between phosphorus donors in silicon using known orbital wave functions. While the two-donor problem can be solved directly, the knowledge of hoppings for various pairs of orbitals is essential for constructing multi-orbital Hubbard models for chains and arrays of donors. To assure applicability to long-range potentials, we rederive Bardeen's formula for the matrix element without assuming non-overlapping potentials. Moreover, we find a correction to the original expression allowing us to use it at short distances. We also show that accurate calculation of the lowest donor-pair eigenstates is possible based on these tunnel couplings, and we characterize the obtained states. The results are in satisfactory quantitative agreement with those obtained with the standard Hückel tight-binding method. The calculation relies solely on the wave functions in the barrier region and does not explicitly involve donor or lattice potentials, which has practical advantages. We find that neglecting the central correction potential in the standard method may lead to qualitatively incorrect results, while its explicit inclusion raises severe numerical problems, as it is contained in a tiny volume. In contrast, using wave functions obtained with this correction in the proposed method does not raise such issues. Nominally, the computational cost of the method is to calculate a double integral along the plane that separates donors. For donor separation in directions where valley interference leads to oscillatory behavior, additional averaging over the position of the integration plane is needed. Despite this, the presented approach offers a competitive computational cost as compared to the standard one. This work may be regarded as a benchmark of a promising method for calculating hopping integrals in lattice models with known or postulated orbital wave functions.

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Many-body physics in small systems: Observing the onset and saturation of correlation in linear atomic chains

Cited by 6 publications

References 39 publications

Long-range electron-electron interactions in quantum dot systems and applications in quantum chemistry

Long-range electron-electron interactions in quantum dot systems and applications in quantum chemistry

Modification of the optical properties of molecular chains upon coupling to adatoms

Bardeen's tunneling theory applied to intraorbital and interorbital hopping integrals between dopants in silicon

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