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arXiv:2506.12487

Defect-Mediated Pairing and Dissociation of Strongly Correlated Electrons in Low Dimensional Lattices: The Quantum Taxi Effect

Vincent Pouthier, Saad Yalouz

Published Jun 14, 2025• 0 citations
arXivHTMLPDF

Abstract

We study the quantum dynamics of a strongly correlated electron pair in a one-dimensional lattice, focusing on the occurrence of local dissociation/pairing mechanisms induced by a site energy defect. To this end, we simulate the time evolution of two interacting electrons on a finite-size chain governed by an extended Hubbard Hamiltonian including on-site Coulomb repulsion $ U $ and nearest-neighbor interaction $V$, along with single-electron hopping $J$. By introducing a local site energy defect with amplitude $ Δ$, we show that a transition between spatially paired/dissociated electrons can occur in the vicinity of this site. Such mechanisms arise in a strongly correlated regime with non-zero nearest neighbor Coulomb interactions and under the conditions $ (U \sim V \sim Δ) \gg J$. To rationalize these phenomena, we reformulate the two-electron dynamics of the original Hubbard chain as an effective single-particle problem on a two-dimensional network. Within this framework, we show that the pairing/dissociation dynamics are driven by resonances between two distinct families of two-electron eigenstates: $(i)$ states with two spatially well-separated electrons with one located at the site defect, and $(ii)$ states with locally bound electron located away from the defect. At resonance, these states hybridize, allowing transitions from locally paired to dissociated electrons (and vice versa) in the vicinity of the defect. These results provide new insights into exotic pairing phenomena in strongly correlated electronic systems and may have implications for the design of tunable many-body states in low-dimensional quantum materials.

DOI
10.48550/arxiv.2506.12487

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We study the quantum dynamics of a strongly correlated electron pair in a one-dimensional lattice, focusing on the occurrence of local dissociation/pairing mechanisms induced by a site energy defect. To this end, we simulate the time evolution of two interacting electrons on a finite-size chain governed by an extended Hubbard Hamiltonian including on-site Coulomb repulsion UUU and nearest-neighbor interaction VVV, along with single-electron hopping JJJ. By introducing a local site energy defect with amplitude Δ ΔΔ, we show that a transition between spatially paired/dissociated electrons can occur in the vicinity of this site. Such mechanisms arise in a strongly correlated regime with non-zero nearest neighbor Coulomb interactions and under the conditions (U∼V∼Δ)≫J (U \sim V \sim Δ) \gg J(U∼V∼Δ)≫J. To rationalize these phenomena, we reformulate the two-electron dynamics of the original Hubbard chain as an effective single-particle problem on a two-dimensional network. Within this framework, we show that the pairing/dissociation dynamics are driven by resonances between two distinct families of two-electron eigenstates: (i)(i)(i) states with two spatially well-separated electrons with one located at the site defect, and (ii)(ii)(ii) states with locally bound electron located away from the defect. At resonance, these states hybridize, allowing transitions from locally paired to dissociated electrons (and vice versa) in the vicinity of the defect. These results provide new insights into exotic pairing phenomena in strongly correlated electronic systems and may have implications for the design of tunable many-body states in low-dimensional quantum materials.
We study the quantum dynamics of a strongly correlated electron pair in a one-dimensional lattice, focusing on the occurrence of local dissociation/pairing mechanisms induced by a site energy defect. To this end, we simulate the time evolution of two interacting electrons on a finite-size chain governed by an extended Hubbard Hamiltonian including on-site Coulomb repulsion UUU and nearest-neighbor interaction VVV, along with single-electron hopping JJJ. By introducing a local site energy defect with amplitude $\mathrm{\ensuremath{\Delta}}$, we show that a transition between spatially paired/dissociated electrons can occur in the vicinity of this site. Such mechanisms arise in a strongly correlated regime with nonzero nearest-neighbor Coulomb interactions and under the conditions $(U\ensuremath{\sim}V\ensuremath{\sim}\mathrm{\ensuremath{\Delta}})\ensuremath{\gg}J$. To rationalize these phenomena, we reformulate the two-electron dynamics of the original Hubbard chain as an effective single-particle problem on a two-dimensional network. Within this framework, we show that the pairing/dissociation dynamics are driven by resonances between two distinct families of two-electron eigenstates: (i) states with two spatially well-separated electrons with one located at the site defect, and (ii) states with a locally bound electron located away from the defect. At resonance, these states hybridize, allowing transitions from locally paired to dissociated electrons---and vice versa---in the vicinity of the defect. These results provide further insights into exotic pairing phenomena in strongly correlated electronic systems and may have implications for the design of tunable many-body states in low-dimensional quantum materials.
The physical property of strongly correlated electrons on a three-dimensional (3D) 3 x 3 x 3 cluster of the simple cubic lattice is here presented.In the work we developed the unit step Hamiltonian as a solution to the single band Hubbard Hamiltonian for the case of two electrons interaction in a finite three dimensional lattice.The approximation to the Hubbard Hamiltonian study is actually necessary because of the strong limitation and difficulty pose by the Hubbard Hamiltonian as we move away from finite -size lattices to larger N -dimensional lattices.Thus this work has provided a means of overcoming the finite -size lattice defects as we pass on to a higher dimension.We have shown in this study, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength.This study reveals that when the Coulomb interaction is zero, that is, for free electron system (non-interacting), thevariational parameters which describe the probability distribution of lattice electron system is the same.The spectra intensity for on-site electrons is zero for all values of the interaction strength.
In order to understand various local phenomena related to electronic phase separation discovered recently in strongly correlated materials, quantum cluster methods are applied to a theoretical model, i.e., Hubbard model, which has successfully predicted basic properties of strongly correlated systems. Our calculations are performed at two levels: exact calculations based on the isolated small clusters via exact diagonalization and approximate calculations applied to large lattices using the variational cluster approximation (VCA).\nWe first study phase separation instabilities with the formation of a pairing gap in the two-dimensional Hubbard model for 8-site Betts clusters. The exact diagonalization method is applied to extract exact ground and excited states of the Hubbard model. The results show that the electronic states with one hole off half filling are unstable and they energetically prefer creating the spatial phase separation. The effect of next nearest hopping is also discussed in this part.\nWe studied the variation of the pairing when the out-of-plane correlation is present by adding an interacting apical site above the two-dimensional cluster plane. The calculations indicate that the out-of-plane correlation can be detrimental to the in-plane pairing effect. When it is not too strong to destroy electron pairs on the plane, the modulation of the apical site can drive the pairing gap to show a sinusoidal variation which is consistent with recent experimental discoveries.\nVariational cluster approximation is introduced to explore local properties of larger lattices. The local nematic state is studied in the square lattice using this method, which indicates that it is possible that the electronic states can locally break the C4 symmetry (90o$ rotational symmetry) to form a pattern where the electronic properties, such as charge and spin correlations, are different in x and y directions.\nThe spatial phase separation in the square and honeycomb lattices is also investigated by the variational cluster approximation. The study shows that Coulomb interaction and lattice geometry are both crucial for electronic phase separation. We propose that electronic phase separation is the result of an instability of the Fermi surface at the boundary of the first Brillouin zone of antiferromagnetic states.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
This thesis addresses the question of a strongly interacting many-body problem: the Hubbard model on one- and two-dimensional lattices. The technique employed is the small-cluster method wherein the full many-body Hamiltonian for finite clusters with periodic boundary conditions (PBC's) is solved exactly. We first apply this technique to an extended one-dimensional chain and a two-dimensional square-lattice Hubbard model. We then construct a two-dimensional overlayer/substrate Hubbard model with first- and second-nearest-neighbor hopping, on-site and nearest-neighbor interactions, and overlayer-site orbital energy. The ground-state properties are investigated and discussed in a many-body picture.