arXiv subjects

Ryan Requist

Publications and source records attributed to Ryan Requist.

At least 19 recordsLinked to original sources

arXiv2026

Adiabatic perturbation theory of energy transfer and charge transport in condensed matter

Energy and charge transfer in condensed matter systems are often described in terms of quasiparticles. The order of accuracy of the results in terms of the electron-to-nucleus mass ratio $\epsilon$, an adiabatic small parameter, is usually not known. To quantify energy transfer with controlled accuracy in $\epsilon$, we use adiabatic perturbation theory to derive a formula for the rate of change of the nuclear kinetic energy. Applying a sequence of near-identity unitary transformations decouples the electronic and nuclear degrees of freedom to higher and higher order and produces an effective Hamiltonian. In the special case that the nuclei are treated classically, the energy transfer formula reduces to the usual formula for the rate of work done on a classical particle but the mass of the particle is enhanced by the factor $M_0^{-1}(M_0+\epsilon M_1)$, where $M_1$ is a nonadiabatic correction to the bare nuclear mass tensor $M_0$. Additional quantum geometric corrections appear at higher orders. Adiabatic perturbation theory is further used to incorporate, order-by-order in $\epsilon$, nonadiabatic transitions into linear response calculations. The nonadiabatic frequency-dependent conductivity and Drude weight of an electron-ion system are calculated.

cond-mat.other↗

arXiv2026

Adiabatically-induced Kawaguchi geometry and jerk in quantum-classical systems

Adiabatically eliminating the quantum degrees of freedom in a mixed quantum-classical system produces an effective force in the classical equation of motion. The elimination can be made to any order in the adiabatic parameter, generating a series of higher order forces. By applying a sequence of near-identity unitary transformations to the quantum state, we derive a hierarchy of increasingly accurate effective actions for the classical variables. The third order Euler-Lagrange equation is non-Newtonian as the force depends on the jerk, the third order time derivative of position. We find that the third order terms induce a special kind of Kawaguchi geometry on the space of classical variables. This geometry is characterized by an almost symplectic structure and a differential line element that depends on the acceleration in addition to the velocity. Our results can be used to efficiently capture higher order nonadiabatic effects in molecular dynamics simulations.

quant-ph↗

arXiv2026

Application of the exact-factorization density-functional perturbation approach to pentacene crystal and monolayer MoS2

Non-adiabatic effects arising from electron-phonon interactions are often neglected within the Born-Oppenheimer (BO) approximation, which assumes that electronic states adjust instantaneously to nuclear motion. The exact factorization (EF) formalism provides a rigorous framework for treating such effects beyond the adiabatic regime and has recently been adapted to density functional theory (DFT) in the harmonic limit. Building on these foundations, we previously introduced an EF-based perturbative scheme, the EF density-functional perturbation theory (EF-DFPT), that enables the computation of phonon-driven non-adiabatic (NA) corrections to Kohn-Sham (KS) electronic states, up to second order in nuclear displacements. Here, we present the first implementation and application of EF-DFPT to extended periodic materials, focusing on its impact on experimentally relevant observables. Using the pentacene molecular crystal and monolayer MoS2 as representative soft- and stiff-mode systems, respectively, we demonstrate how NA electron-phonon interactions modify the static dielectric response. We show that these modifications originate from the combined effect of NA phonon-dressed electronic wavefunctions and second-order NA energy renormalizations. The resulting behavior is strongly material dependent: NA effects are negligible in monolayer MoS2, whereas in pentacene they lead to pronounced long-range screening effects associated with soft vibrational modes and enhanced electron-phonon coupling.

cond-mat.mtrl-sci↗

arXiv2025

Beyond Born-Oppenheimer Time-Dependent Density Functional Theory

We formulate a time-dependent density functional theory for the coupled dynamics of electrons and nuclei that goes beyond the Born-Oppenheimer (BO) approximation. We prove that the time-dependent marginal nuclear probability density $|\chi({\bdu R},t)|^2$, the conditional electronic density $n_{\bdu R}(\br,t)$, and the current density $\bm J_{\bdu R}(\br,t)$ are sufficient to uniquely determine the full time-evolving electron-nuclear wave function, and thus the dynamics of all observables. Moreover, we propose a time-dependent Kohn-Sham scheme which reproduces the exact conditional electronic density and current density and the exact N-body nuclear density. The remaining task is to look for functional approximations for the Kohn-Sham exchange-correlation scalar and vector potentials. Using a model driven proton transfer system, we numerically demonstrate that the adiabatic extension of a beyond-BO ground state functional captures the dominant nonadiabatic effects in the regime of slow driving.

physics.chem-ph↗

arXiv2025

Non-adiabaticity from first principles: the exact-factorization approach for solids

The thorough treatment of electron-lattice interactions from first principles is one of the main goals in condensed matter physics. While the commonly applied adiabatic Born-Oppenheimer approximation is sufficient for describing many physical phenomena, it is limited in its ability to capture meaningful features originating from non-adiabatic coupling effects. The exact factorization method, starting from the full Hamiltonian of electrons and nuclei, provides a way to systematically account for non-adiabatic effects. This formalism was recently developed into an ab initio density functional theory framework. Within this framework we here develop a perturbative approach to the electronic states in solid state materials. We derive exact-factorization-based perturbations of the Kohn-Sham states up to second order in the nuclear displacements. These non-adiabatic features in the calculated energy and wavefunction corrections are expressed in terms of readily available density functional perturbation theory components.

cond-mat.mtrl-sci↗

arXiv2023

Adiabatic perturbation theory for two-component systems with one heavy component

Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new form of kinetic energy operator with a Hermitian mass tensor and a complex-valued vector potential. All of the potentials in the effective Hamiltonian can be expressed in terms of covariant derivatives and a resolvent operator. The most salient application of the theory is to systems of electrons and nuclei. The accuracy of the theory is verified numerically in a model diatomic molecule and analytically in a vibronic coupling model.

quant-ph↗

arXiv2022

Gauge- and coordinate-invariant equations for two-component systems

The Schr\"odinger-like equations for the marginal and conditional probability amplitudes resulting from the exact factorization of the wavefunction of a two-component system are derived in a form that is invariant to gauge and coordinate transformations. Coupled equations equivalent to the nonrelativistic Schr\"odinger equation of a molecule are derived as an example.

quant-ph↗

arXiv2022

Quantum covariant derivative

The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate transformations and compatible with the quantum geometric tensor. The quantum covariant derivative is used to derive a gauge- and coordinate-invariant adiabatic perturbation theory, providing an efficient tool for calculations of nonlinear adiabatic response properties.

quant-ph↗

arXiv2021

Geometric energy transfer in two-component systems

Factoring a wave function into marginal and conditional factors partitions the subsystem kinetic energy into two terms. The first depends solely on the marginal wave function, through its gauge-covariant derivative, while the second depends on the quantum metric of the conditional wave function over the manifold of marginal variables. We derive an identity for the rate of change of the second term.

quant-ph↗

arXiv2019

Fock space embedding theory for strongly correlated topological phases

A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schr\"odinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce the topological phase diagram of a multiband Hubbard model as a function of crystal field and Hubbard parameters. The roles of band filling and interband fluctuations are elucidated.

cond-mat.str-el↗

arXiv2019

Energy, Momentum and Angular Momentum Transfer Between Electrons and Nuclei

The recently developed exact factorization approach condenses all electronic effects on the nuclear subsystem into scalar and vector potentials that appear in an effective time dependent Schr\"{o}dinger equation. Starting from this equation, we derive subsystem Ehrenfest identities characterizing the energy, momentum and angular momentum transfer between electrons and nuclei. An effective electromagnetic force operator induced by the electromagnetic field corresponding to the effective scalar and vector potentials appears in all three identities. The effective magnetic field has two components that can be identified with the Berry curvature calculated with (a) different cartesian coordinates of the same nucleus and (b) arbitrary cartesian coordinates of two different nuclei. (a) has a classical interpretation as the induced magnetic field felt by the nucleus, while (b) has no classical analog. Subsystem Ehrenfest identities are ideally suited for quantifying energy transfer in electron-phonon systems. With two explicit examples we demonstrate the usefulness of the new identities.

physics.chem-ph↗

arXiv2019

Exact factorization-based density functional theory of electron-phonon systems

Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(\mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode amplitudes $U=\{U_{\mathbf{q}\lambda}\}$, is coupled to the nuclear Schr\"odinger equation of the exact factorization method. The phonon modes are defined from the harmonic expansion of the nuclear Schr\"odinger equation. A nonzero Berry curvature on nuclear configuration space affects the phonon modes, showing that the potential energy surface alone is generally not sufficient to define the phonons. An orbital-dependent functional approximation for the non\-adiabatic exchange-correlation energy reproduces the leading-order nonadiabatic electron-phonon-induced band structure renormalization in the Fr\"ohlich model.

cond-mat.mtrl-sci↗

arXiv2018

Model Hamiltonian for strongly-correlated systems: Systematic, self-consistent, and unique construction

An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The strongly-correlated subspace is identified from the occupation number band structure as opposed to a mean-field energy band structure. The self-consistent solution of the many-body model Hamiltonian and a generalized Kohn-Sham equation exactly incorporates momentum-dependent and crystal-symmetric correlations into electronic structure calculations in a way that does not rely on a separation of energy scales. Calculations for a multiorbital Hubbard model demonstrate that the theory accurately reproduces the many-body polarization.

cond-mat.str-el↗

arXiv2017

Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF

We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length $R=R_c$, where a barely avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the $R$-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical $R_c$ by 0.5 Bohr. This effect is very accurately captured by a simple and rigorously-derived correction, with an $M^{-1}$ prefactor, to the exchange-correlation potential in density functional theory; $M=$ reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wavefunction and conditional electronic density, $\nabla_R \chi(R)$ and $\nabla_R n(\mathbf{r},R)$, it couples the Kohn-Sham equations at neighboring $R$ points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation -- an approximation that reduces the search for nonadiabatic density functionals to the search for a single function $y(n)$.

physics.chem-ph↗

arXiv2017

Asymptotic analysis of the Berry curvature in the $E\otimes e$ Jahn-Teller model

The effective Hamiltonian for the linear $E\otimes e$ Jahn-Teller model describes the coupling between two electronic states and two vibrational modes in molecules or bulk crystal impurities. While in the Born-Oppenheimer approximation the Berry curvature has a delta function singularity at the conical intersection of the potential energy surfaces, the exact Berry curvature is a smooth peaked function. Numerical calculations revealed that the characteristic width of the peak is $\hbar K^{1/2}/gM^{1/2}$, where $M$ is the mass associated with the relevant nuclear coordinates, $K$ is the effective internuclear spring constant and $g$ is the electronic-vibrational coupling. This result is confirmed here by an asymptotic analysis of the $M\rightarrow\infty$ limit, an interesting outcome of which is the emergence of a separation of length scales. Being based on the exact electron-nuclear factorization, our analysis does not make any reference to adiabatic potential energy surfaces or nonadiabatic couplings. It is also shown that the Ham reduction factors for the model can be derived from the exact geometric phase.

physics.chem-ph↗

arXiv2017

Approximate formula for the macroscopic polarization including quantum fluctuations

The many-body Berry phase formula for the macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This reduced formula accurately reproduces the exact polarization in the Rice-Mele-Hubbard model across the band insulator-Mott insulator transition. A similar formula based on a one-body reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping.

cond-mat.str-el↗

arXiv2016

Exact factorization-based density functional theory of electrons and nuclei

The ground state energy of a system of electrons and nuclei is proven to be a variational functional of the conditional electronic density $n_R(\mathbf{r})$, the nuclear wavefunction $\chi(R)$ and an induced vector potential $A_{\mu}(R)$ and quantum geometric tensor $\mathcal{T}_{\mu\nu}(R)$ derived from the conditional electronic wavefunction $\Phi_R(r)$ over nuclear configuration space, where $r=\mathbf{r}_1,\mathbf{r}_2,\ldots$ are electronic coordinates and $R=\mathbf{R}_1,\mathbf{R}_2,\ldots$ are nuclear coordinates. The ground state $(n_R,\chi,A_{\mu},\mathcal{T}_{\mu\nu})$ can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing an effective potential $v_{\rm s}(\mathbf{r})$ that depends parametrically on $R$, (ii) the Schr\"odinger equation for $\chi(R)$ and (iii) Euler-Lagrange equations that determine $\mathcal{T}_{\mu\nu}$. The theory is applied to the $E\otimes e$ Jahn-Teller model.

physics.chem-ph↗

arXiv2016

Metallic, Magnetic and Molecular Nanocontacts

Scanning tunnelling microscopy and break-junction experiments realize metallic and molecular nanocontacts that act as ideal one-dimensional channels between macroscopic electrodes. Emergent nanoscale phenomena typical of these systems encompass structural, mechanical, electronic, transport, and magnetic properties. This Review focuses on the theoretical explanation of some of these properties obtained with the help of first-principles methods. By tracing parallel theoretical and experimental developments from the discovery of nanowire formation and conductance quantization in gold nanowires to recent observations of emergent magnetism and Kondo correlations, we exemplify the main concepts and ingredients needed to bring together ab initio calculations and physical observations. It can be anticipated that diode, sensor, spin-valve and spin-filter functionalities relevant for spintronics and molecular electronics applications will benefit from the physical understanding thus obtained.

cond-mat.mes-hall↗