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Understanding the connection between electronic correlation and decoherence

Arnab Kar, Liping Chen, Ignacio Franco

Published Jun 3, 2015• 1 citation
OpenAlex

Abstract

We introduce a theory that exposes the fundamental connection between the correlation among electrons and the degree of quantum coherence of electronic states in molecules and materials. Specifically, we show that the electronic interactions $V^{S}$ that lead to correlation strongly modulate the electronic decoherence and that, conversely, the electron-nuclear interactions $H^{SB}$ that lead to decoherence influence the correlation energy. The effects only decouple when $[V^{S},H^{SB}]=[H^{S},H^{SB}]=0$, where $H^{S}$ is the electronic Hamiltonian. We quantitatively illustrate this connection via numerically exact simulations of a Hubbard-Holstein molecule.

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We introduce a theory that exposes the fundamental connection between the correlation among electrons and the degree of quantum coherence of electronic states in molecules and materials. Specifically, we show that the electronic interactions VSV^{S}VS that lead to correlation strongly modulate the electronic decoherence and that, conversely, the electron-nuclear interactions HSBH^{SB}HSB that lead to decoherence influence the correlation energy. The effects only decouple when [VS,HSB]=[HS,HSB]=0[V^{S},H^{SB}]=[H^{S},H^{SB}]=0[VS,HSB]=[HS,HSB]=0, where HSH^{S}HS is the electronic Hamiltonian. We quantitatively illustrate this connection via numerically exact simulations of a Hubbard-Holstein molecule.
We introduce a theory that exposes the fundamental and previously overlooked connection between the correlation among electrons and the degree of quantum coherence of electronic states in matter. For arbitrary states, the effects only decouple when the electronic dynamics induced by the nuclear bath is pure-dephasing in nature such that [H(S),H(SB)] = 0, where H(S) is the electronic Hamiltonian and H(SB) is the electron-nuclear coupling. We quantitatively illustrate this connection via exact simulations of a Hubbard-Holstein molecule using the Hierarchical Equations of Motion that show that increasing the degree of electronic interactions can enhance or suppress the rate of electronic coherence loss.
The relationship between electronic interactions and electronic decoherence is a fundamental problem in chemistry. Here we show that varying the electron-electron interactions does not affect the electronic decoherence in the pure-dephasing limit. In this limit, the effect of varying the electronic interactions is to rigidly shift in energy the diabatic potential energy surfaces without changing their shape, thus keeping the nuclear dynamics in these surfaces that leads to the electronic decoherence intact. This analysis offers a simple and intuitive understanding of previous theoretical and computational efforts to characterize the influence of electronic interactions on the decoherence and opens opportunities to study exact electronic decoherence with approximate electronic structure theories.
Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the electronic decoherence dynamics of a model many-body molecular system described by the Su-Schrieffer-Heeger Hamiltonian with Hubbard electron-electron interactions using an exact method in which both electronic and nuclear degrees of freedom are taken into account explicitly and fully quantum mechanically. To represent the electron-nuclear Hamiltonian in matrix form and propagate the dynamics, the computations employ the Jordan-Wigner transformation for the fermionic creation/annihilation operators and the discrete variable representation for the nuclear operators. The simulations offer a standard for electronic decoherence that can be used to test approximations. They also provide a useful platform to answer fundamental questions about electronic decoherence that cannot be addressed through approximate or implicit schemes. Specifically, through simulations, we isolate basic mechanisms for electronic coherence loss and demonstrate that electronic decoherence is possible even for one-dimensional nuclear bath. Furthermore, we show that (i) decreasing the mass of the bath generally leads to faster electronic decoherence; (ii) electron-electron interactions strongly affect the electronic decoherence when the electron-nuclear dynamics is not pure-dephasing; (iii) classical bath models with initial conditions sampled from the Wigner distribution accurately capture the short-time electronic decoherence dynamics; (iv) model separable initial superpositions often used to understand decoherence after photoexcitation are only relevant in experiments that employ delta-like laser pulses to initiate the dynamics. These insights can be employed to interpret and properly model coherence phenomena in molecules.
Dynamical mean-field theory computations of the electron self energy of the Hubbard-Holstein model as a function of electron-phonon and electron-electron interactions are analyzed to gain insight into the dependence of electron-phonon couplings on correlation strength in quantum materials. We find that the electron-phonon interaction is strongly suppressed by electronic correlations, while electron-electron correlation effects at Fermi liquid scales are only weakly modified by coupling to phonons, with phonon-induced modifications most evident at high frequencies on the order of the electronic bandwidth. Implications for beyond-density functional theories of the electron-phonon interaction are discussed.
Electronic Correlation in Molecules - Some Fundamental Problems Improving the Panoply of Quantum Chemical Methods for the Study of Correlated Extended Systems Lie-Algebraic Structure and the Coupled Cluster Method Configuration Interaction Studies Using Biorthogonal Approach to VB Basis Optimised Virtual Orbitals for the Calculation of Molecular Properties of Excited Electronic States A Novel MO-VB Scheme for Excitation Gaps in Correlated Mode Hamiltonians Correlated Approach to Molecular Properties Infinite Volume Extrapolations of Finite Clusters Calculations - How Correct are These? Calculation of the Hyperpolarisabilities of Organic Molecules and their Role in the Interpretation of Nonlinear Optical Phenomena in Organic Crystals Energy Thresholds in Polysilanes - Elementary Excitations of Alternating Conjugated Chains Inter- and Intramolecular Spin Coupling in Organics Electron Correlation Effects in Semiconductorquantum Dot Nanostructures Numerical Simulations of Strongly-Correlated Systems-Interlayer Tunnelling Mechanism, Spin-Charge Separation and Odd-Gap Pairing Metal Insulator Transition in 3rd Transition Metal Oxides Superconductivity in Doped Fullerenes.