arXiv subjects

Ville J. Härkönen

Publications and source records attributed to Ville J. Härkönen.

13 recordsLinked to original sources

arXiv2026

From Symmetry and Reduction to Physically Meaningful Relational Observables in Many-Body Quantum Theory

We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified framework based on two additional postulates supplementing the standard quantum-mechanical formalism. For stable systems, the physically relevant states are normalizable stationary states, while physically meaningful observables are required to be invariant under a selected subgroup of the symmetry group and under Galilean boosts. In addition, we postulate the existence of a map from the set of all observables allowed by quantum mechanics to the corresponding invariant physically meaningful observables. The originality of the present work does not lie in specific reductions, but in the unified framework that connects symmetry reduction and relational many-body quantum theory. We interpret entities like superselection rules and quantum reference frames as important parts of the postulated process of obtaining the physically meaningful relational description. In particular, the requirement of Galilean-boost invariance added strengthens the criterion for physical observability by excluding quantities that depend on the choice of inertial frame. An important consequence of the postulates is that in the considered cases every physically meaningful observable necessarily depends on more than one non-invariant observable, the latter being typically associated with degrees of freedom assigned to a single particle. The postulates thus lead to theories that are well aligned with the literature on reduction and the description of molecules, while at the same time being consistent with the relational interpretation of quantum mechanics, according to which the complete physical description of a system is defined only relative to other systems.

quant-ph↗

arXiv2026

Giant Kohn anomaly and chiral phonons in the charge density wave phase of 1H-NbSe$_2$

Despite extensive investigations, many aspects of charge density waves (CDWs) remain elusive, especially the relative roles of electron-phonon coupling and Fermi surface nesting as the underlying driving mechanisms responsible for the emergence of the CDW vector $Q_{CDW}$. It is puzzling that even though electrons interact strongly with optical phonons in many correlated systems, the actual mode softening is of an acoustic mode. Here we consider monolayer 1H-NbSe$_2$ as an exemplar system, and through an accurate computation of the phonon self-energy, including its off-diagonal components, we provide compelling evidence that the relevant mode is a longitudinal optical phonon that softens by anti-crossing several intervening phonon bands, i.e. a Kohn ladder which has been only observed previously in high temperature superconductors. We also show that $Q_{CDW}$ is fixed by the convolution of the susceptibility and electron-phonon coupling, and that the softened phonons are circularly polarized.

cond-mat.str-el↗

arXiv2026

On the breakdown of the Born-Oppenheimer approximation in LiH and LiD

We compute the ab-initio electron density beyond the strict Born-Oppenheimer approximation in crystalline LiH and LiD with density functional methods. By taking into account the quantum mechanical nature of the nuclei, an aspect absent in the strict Born-Oppenheimer approximation, we find significant corrections to electron density in the vicinity of nuclei equilibrium positions. We compare our results with earlier experimental findings that have suggested a breakdown of the Born-Oppenheimer approximation in these solids and obtain improved agreement between experiment and theory when quantum nuclear effects are included. A notable temperature dependence of electron density is found. The results indicate the existence of beyond strict Born-Oppenheimer effects in solids at normal pressures and suggest that such effects can be significant also in materials containing light elements other than hydrogen.

cond-mat.mtrl-sci↗

arXiv2025

Beyond Born-Oppenheimer Green's function theories: absolute and relational

We consider quantum field theoretic many-body Green's function approach to solve the Coulomb many-body problem. The earlier beyond Born-Oppenheimer Green's function theories are absolute in nature and are based on the non-reduced Hamiltonian. Motivated by the issues following this approach we have developed a reduced Green's function theory which is relational in nature. The central differences between these approaches trace back to the relational-absolute debate, which has continued for over two thousand years since the time of Aristotle and still persists today. We highlight that these aspects of the theories are connected to several areas of modern physics, including relational quantum mechanics, quantum reference frames, superselection rules, the separation of different types of motion and spontaneous symmetry breaking. The starting point of any such exact theory must be absolute, given that the global conservation laws hold. However, for the observables to be meaningful, they must be defined with respect to the relative space. Approximations, such as the one introduced by Born and Oppenheimer, can break global symmetries and make certain parts of the absolute description well-defined. We highlight that spontaneous symmetry breaking is not necessary to explain the existence of solids, but entities such as phonons can be naturally explained within the relational theory.

cond-mat.other↗

arXiv2024

Quantum Field Theory of Electrons and Nuclei

We develop a non-relativistic quantum field theory of electrons and nuclei based on the Coulomb Hamiltonian. We derive the exact equations of motion and write these equations in the form of Hedin's equations for all species of identical particles involved. Theory derived allows the computation of exact observables and provides a rigorous starting point to derive approximations in a systematic way.

quant-ph↗

arXiv2023

Breakdown of the Born-Oppenheimer approximation in solid hydrogen and hydrogen-rich solids

Hydrogen has been the subject of intense research following the discovery of high-temperature superconductivity in hydrides, and as a result of continuous efforts to produce solid hydrogen. The Born-Oppenheimer approximation is the central piece of the quantum mechanical description of molecules and solids and it is expected to have its weakest validity in hydrogen containing matter as it is the lightest element of all. The Born-Oppenheimer approximation is almost always assumed in the description of solids. Some beyond Born-Oppenheimer effects are likely included in the state-of-art method used to describe hydrogen-rich materials, but the effects on the electronic structure in solids have not been considered before. Here we compute the beyond Born-Oppenheimer corrections to electron density and report a breakdown of the Born-Oppenheimer approximation in experimentally known hydride superconductor YH6 and in Cs-IV structure of solid hydrogen. In both of these materials, we find a significant transfer of electron density from the volumes surrounding the expected positions of the hydrogen nuclei to volumes in between the nuclei. We expect these results to be the starting point of the beyond Born-Oppenheimer studies of electronic structure in solids, which is likely necessary to understand these forms of hydrogen-containing materials, also having significant technological importance.

cond-mat.mtrl-sci↗

arXiv2022

Exact factorization of the many-body Green's function theory of electrons and nuclei

We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach beyond the Born-Oppenheimer approximation. The lowest order approximation to the exact electronic Green's function is found to be an expected value of the Born-Oppenheimer electronic Green's function with respect to the nuclear density.

cond-mat.other↗

arXiv2021

On the diagonalization of quadratic Hamiltonians

A new procedure to diagonalize quadratic Hamiltonians is introduced. We show that one can find a unitary transformation such that the transformed quadratic Hamiltonian is diagonal but still written in terms of the original position and momentum observables. We give a general method to diagonalize an arbitrary quadratic Hamiltonian and derive a few of the simplest special cases in detail.

quant-ph↗

arXiv2020

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.

cond-mat.other↗

arXiv2016

Elastic constants and thermodynamical quantities for crystal lattices from many-body perturbation theory

The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and isothermal) and the coefficient of thermal expansion. The perturbation expansion is developed up to third-order and diagrams corresponding to the equations are represented. The present results extend the existing ones by giving expressions for the elastic constants of arbitrary order and terms which are higher-order in the interatomic force constants that have been obtained earlier. The perturbation expansion in terms of arbitrary macroscopical parameters is considered and the similarity of expansions with respect to different parameters is emphasized. A physical interpretation of the harmonic phonon eigenvectors is considered. To the author's knowledge, no such similar interpretation of the harmonic phonon eigenvectors has been given in the literature before.

cond-mat.other↗

arXiv2016

Ab initio computational study on the lattice thermal conductivity of Zintl clathrates [Si$_{19}$P$_{4}$]Cl$_{4}$ and Na$_{4}$[Al$_{4}$Si$_{19}$]

The lattice thermal conductivity of silicon clathrate framework Si$_{23}$ and two Zintl clathrates, [Si$_{19}$P$_{4}$]Cl$_{4}$ and Na$_{4}$[Al$_{4}$Si$_{19}$], is investigated by using an iterative solution of the linearized Boltzmann transport equation (BTE) in conjuntion with ab initio lattice dynamical techniques. At 300 K, the lattice thermal conductivities for Si$_{23}$, [Si$_{19}$P$_{4}$]Cl$_{4}$, and Na$_{4}$[Al$_{4}$Si$_{19}$] were found to be 43 W/(m K), 25 W/(m K), and 2 W/(m K), respectively. In the case of Na$_{4}$[Al$_{4}$Si$_{19}$], the order-of-magnitude reduction in the lattice thermal conductivity was found to be mostly due to relaxation times and group velocities differing from Si$_{23}$ and [Si$_{19}$P$_{4}$]Cl$_{4}$. The difference in the relaxation times and group velocities arises primarily due to the phonon spectrum at low frequencies, resulting eventually from the differences in the second-order interatomic force constants (IFCs). The obtained third-order IFCs were rather similar for all materials considered here.

cond-mat.mtrl-sci↗

arXiv2016

Ab initio studies on the lattice thermal conductivity of silicon clathrate frameworks II and VIII

The lattice thermal conductivities of silicon clathrate frameworks II and VIII are investigated by using ab initio lattice dynamics and iterative solution of the linearized Boltzmann transport equation(BTE) for phonons. Within the temperature range 100-350 K, the clathrate structures II and VIII were found to have lower lattice thermal conductivity values than silicon diamond structure (d-Si) by factors of 1/2 and 1/5, respectively. The main reason for the lower lattice thermal conductivity of the clathrate structure II in comparison to d-Si was found to be the harmonic phonon spectra, while in the case of the clathrate structure VIII, the difference is mainly due to the harmonic phonon spectra and partly due to shorter relaxation times of phonons. In the studied clathrate frameworks, the anharmonic effects have larger impact on the lattice thermal conductivity than the size of the unit cell. For the structure II, the predicted lattice thermal conductivity differs approximately by factor of 20 from the previous experimental results obtained for a polycrystalline sample at room temperature.

cond-mat.mtrl-sci↗

arXiv2014

Ab initio lattice dynamical studies of silicon clathrate frameworks and their negative thermal expansion

The thermal and lattice dynamical properties of seven silicon clathrate framework structures are investigated with ab initio density functional methods (frameworks I, II, IV, V, VII, VIII, and H). The negative thermal expansion (NTE) phenomenon is investigated by means of quasiharmonic approximation and applying it to equal time displacement correlation functions. The thermal properties of the studied clathrate frameworks, excluding the VII framework, resemble those of the crystalline silicon diamond structure. The clathrate framework VII was found to have anomalous NTE temperature range up to 300 K and it is suitable for further studies of the mechanisms of NTE. Investigation of the displacement correlation functions revealed that in NTE, the volume derivatives of the mean square displacements and mean square relative displacements of atoms behave similarly to the vibrational entropy volume derivatives and consequently to the coefficients of thermal expansion as a function of temperature. All studied clathrate frameworks, excluding the VII framework, possess a phonon band gap or even two in the case of the framework V.

cond-mat.mtrl-sci↗