Transient translation symmetry breaking via quartic-order negative light-phononcoupling at Brillouin zone boundary in KTaO3{}_{3}

KTaO${}_{3}$ presents a rich hyper-Raman spectrum originating from two-phonon processes at the Brillouin zone boundary, indicating the possibility of driving these phonon modes using intense midinfrared laser sources. We obtained the coupling of light to the highest-frequency longitudinal optic phonon mode $Q_{\rm{HY}}$ at the $X$ $(0,0, \frac{1}{2})$ point by first principles calculations of the total energy as a function of the phonon coordinate $Q_{\rm{HY}}$ and electric field $E$. We find that the energy curve as a function of $Q_{\rm{HY}}$ softens for finite values of electric field, indicating the presence of $Q_{\rm{HY}}^2 E^2$ nonlinearity with negative coupling coefficient. We studied the feasibility of utilizing this nonlinearity to transiently break the translation symmetry of the material by making the $Q_{\rm{HY}}$ mode unstable with an intense midinfrared pump pulse. We also considered the possibility that nonlinear phonon-phonon couplings can excite the lowest-frequency phonon coordinates $Q_{\rm{LZ}}$ and $Q_{\rm{LX}}$ at $X$ when the $Q_{\rm{HY}}$ mode is externally driven. The nonlinear phonon-phonon couplings were also obtained from first principles via total-energy calculations as a function of the phonon coordinates, and these were used to construct the coupled classical equations of motion for the phonon coordinates in the presence of an external pump term on $Q_{\rm{HY}}$. We numerically solved them for a range of pump frequencies and amplitudes and found three regimes where the translation symmetry is broken: i) rectification of the lowest-frequency coordinates due to large amplitude oscillation of the $Q_{\rm{HY}}$ coordinate about its equilibrium position, ii) rectification of only the $Q_{\rm{HY}}$ coordinate without displaced oscillations of the lowest-frequency coordinates, and iii) rectification of all three coordinates.Comment: Replaced some figures and caption

Computational and Theoretical Developements for (Time Dependent) Density Functional Theory

En esta tesis se presentan avances computacionales y teoricos en la teoria de funcionales de la densidad (DFT) y en la teoria de funcionales de la densidad dependientes del tiempo (TDDFT). Hemos explorado una posible nueva ruta para la mejora de los funcionales de intercambio y correlacion (XCF) en DFT, comprobado y desarrollado propagadores numericos para TDDFT, y aplicado una combinacion de la teoria de control optimo con TDDFT.En los ultimos anos, DFT se ha convertido en el metodo mas utilizado en el area de estructura electronica gracias a su inigualable relacion entre coste y precision. Podemos usar DFT para calcular multitud de propiedades fisicas y quimicas de atomos, moleculas, nanoestructuras, y materia macroscopica. El factor principal que determina la precision que podemos alcanzar usando DFT es el XCF, un objeto desconocido para el cual se han propuesto cientos de aproximaciones distintas. Algunas de estas aproximaciones funcionan correctamente en ciertas situaciones, pero a dia de hoy no existe un XCF que pueda aplicarse con certeza sobre su validez a un sistema arbitrario. Mas aun, no hay una forma sistematica de refinar estos funcionales. Proponemos y exploramos, para sistemas unidimensionales, una nueva manera de estudiarlos y optimizarlos basada en establecer una relacion con la interaccion entre electrones.TDDFT es la extension de DFT a problemas dependientes del tiempo y problemas conestados excitados, y es tambien uno de los metodos mas populares (a veces el unico metodo que se puede poner en practica) en la comunidad de estructura electronica para tratar conellos. De nuevo, la razon detras de su popularidad reside en su relacion precision/coste computacional, que nos permite tratar sistemas mayores y mas complejos. Puede usarse en combinacion con la dinamica de Ehrenfest, un tipo de dinamica molecular no adiabatica.Hemos ido mas alla y hemos combinado TDDFT y la dinamica de Ehrenfest con la teoria de control optimo, creando un instrumento que nos permite, por ejemplo, predecir la forma de los pulsos laser que inducen una explosion de Coulomb en clusters de sodio. A pesar del buen rendimiento computacional de TDDFT en comparacion con otros metodos, hallamos que el coste de estos calculos era bastante elevado.Motivados por este hecho, tambien dedicamos una parte del trabajo de la tesis a la investigacion computacional. En particular, hemos estudiado e implementado familias de propagadores numericos que no se habian examinado en el contexto de TDDFT. Mas concretamente, metodos con varios pasos previos, formulas Runge-Kutta exponenciales, y las expansiones de Magnus sin conmutadores. Finalmente, hemos implementado modificaciones de estas expansiones de Magnus sin conmutadores para la propagacion de las ecuaciones clasico-cuanticas que resultan de la combinacion de la dinamica de Ehrenfest con TDDFT.In this thesis we present computational and theoretical developments for density functional theory (DFT) and time dependent density functional theory (TDDFT). We have explored a new possible route to improve exchange and correlation functionals (XCF) in DFT, tested and developed numerical propagators for TDDFT, and applied a combination of optimal control theory with TDDFT. In recent years, DFT has become the most used method in the electronic structure field thanks to its unparalleled precision/computational cost relationship. We can use DFT to accurately calculate many physical and chemical properties of atoms, molecules, nanostructures, and bulk materials. The main factor that determines the precision that we can obtain using DFT is the XCF, an unknown object for which hundreds of different approximations have been proposed. Some of these approximations work well enough for certain situations, but to this day there is no XCF that can be reliably applied to any arbitrary system. Moreover, there is no clear way for a systematic refinement of these functionals. We propose and explore, for one-dimensional systems, a new way to optimize them, based on establishing a relationship with the electron-electron interaction. TDDFT is the extension of DFT to time-dependent and excited-states problems, and it is also one of the most popular methods (sometimes the only practical one) in the electronic structure community to deal with them. Once again, the reason behind its popularity is its accuracy/computational cost ratio, which allows us to tackle bigger, more complex systems. It can be used in combination with Ehrenfest dynamics, a non-adiabatic type of molecular dynamics. We have furthermore combined both TDDFT and Ehrenfest dynamics with optimal control theory, a scheme that has allowed us, for example, to predict the shapes of the laser pulses that induce a Coulomb explosion in different sodium clusters. Despite the good numerical performance of TDDFT compared to other methods, we found that these computations were still quite expensive. Motivated by this fact, we have also dedicated a part of the thesis work to computational research. In particular, we have studied and implemented families of numerical propagators that had not been tested in the context of TDDFT. More concretely, linear multistep schemes, exponential Runge-Kutta formulas, and commutator-free Magnus expansions. Moreover, we have implemented modifications of these commutator-free Magnus methods for the propagation of the classical-quantum equations that result of combining Ehrenfest dynamics with TDDFT.<br /

Propagators for Quantum-Classical Models: Commutator-Free Magnus Methods

[EN] We consider the numerical propagation of models that combine both quantum and classical degrees of freedom, usually, electrons and nuclei, respectively. We focus, in our computational examples, on the case in which the quantum electrons are modeled with time-dependent density-functional theory, although the methods discussed below can be used with any other level of theory. Often, for these so-called quantum classical molecular dynamics models, one uses some propagation technique to deal with the quantum part and a different one for the classical equations. While the resulting procedure may, in principle, be consistent, it can however spoil some of the properties of the methods, such as the accuracy order with respect to the time step or the preservation of the geometrical structure of the equations. Few methods have been developed specifically for hybrid quantum-classical models. We propose using the same method for both the quantum and classical particles, in particular, one family of techniques that proves to be very efficient for the propagation of Schrodinger-like equations: the (quasi)-commutator free Magnus expansions. These have been developed, however, for linear systems, yet our problem is nonlinear: formally, the full quantum-classical system can be rewritten as a nonlinear Schrodinger equation, i.e., one in which the Hamiltonian depends on the system itself. The Magnus expansion algorithms for linear systems require the application of the Hamiltonian at intermediate points in a given propagating interval. For nonlinear systems, this poses a problem as this Hamiltonian is unknown due to its dependence on the state. We approximate it by employing a higher order extrapolation using previous steps as input. The resulting technique can then be regarded as a multistep technique or, alternatively, as a predictor corrector formula.A.C. acknowledges support from the MINECO FIS2017-82426-P grant. S.B. acknowledges the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the program "Geometry, compatibility and structure preservation in computational differential equations (2019)", EPSRC grant number EP/R014604/1. S.B. also acknowledges funding by the Ministerio de Economia y Competitividad (Spain) through project MTM2016-77660-P (AEI/FEDER, UE) and the Ministerio de Ciencia Innovacion y Universidades, through Programa de Estancias de profesores e investigadores senior en centros extranjeros, incluido el Programa "Salvador de Madariaga" 2019 (PRX19/00295).Gómez Pueyo, A.; Blanes Zamora, S.; Castro, A. (2020). Propagators for Quantum-Classical Models: Commutator-Free Magnus Methods. Journal of Chemical Theory and Computation. 16(3):1420-1430. https://doi.org/10.1021/acs.jctc.9b01031S14201430163Molner, S. P. (1999). The Art of Molecular Dynamics Simulation (Rapaport, D. C.). Journal of Chemical Education, 76(2), 171. doi:10.1021/ed076p171Fermi, E.; Pasta, J.; Ulam, S. Studies of Nonlinear Problems I, Los Alamos Report LA 1940; Los Alamos Scientific Laboratory, 1955; reproduced in Nonlinear Wave Motion. Providence, RI, 1974.Alder, B. J., & Wainwright, T. E. (1959). Studies in Molecular Dynamics. I. General Method. The Journal of Chemical Physics, 31(2), 459-466. doi:10.1063/1.1730376Bornemann, F. A., Nettesheim, P., & Schütte, C. (1996). Quantum‐classical molecular dynamics as an approximation to full quantum dynamics. The Journal of Chemical Physics, 105(3), 1074-1083. doi:10.1063/1.471952DOLTSINIS, N. L., & MARX, D. (2002). FIRST PRINCIPLES MOLECULAR DYNAMICS INVOLVING EXCITED STATES AND NONADIABATIC TRANSITIONS. Journal of Theoretical and Computational Chemistry, 01(02), 319-349. doi:10.1142/s0219633602000257Runge, E., & Gross, E. K. U. (1984). Density-Functional Theory for Time-Dependent Systems. Physical Review Letters, 52(12), 997-1000. doi:10.1103/physrevlett.52.997Marques, M. A. L., Maitra, N. T., Nogueira, F. M. S., Gross, E. K. U., & Rubio, A. (Eds.). (2012). Fundamentals of Time-Dependent Density Functional Theory. Lecture Notes in Physics. doi:10.1007/978-3-642-23518-4Verlet, L. (1967). Computer «Experiments» on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physical Review, 159(1), 98-103. doi:10.1103/physrev.159.98Hairer, E., & Wanner, G. (1996). Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics. doi:10.1007/978-3-642-05221-7Castro, A., Marques, M. A. L., & Rubio, A. (2004). Propagators for the time-dependent Kohn–Sham equations. The Journal of Chemical Physics, 121(8), 3425-3433. doi:10.1063/1.1774980Schleife, A., Draeger, E. W., Kanai, Y., & Correa, A. A. (2012). Plane-wave pseudopotential implementation of explicit integrators for time-dependent Kohn-Sham equations in large-scale simulations. The Journal of Chemical Physics, 137(22), 22A546. doi:10.1063/1.4758792Russakoff, A., Li, Y., He, S., & Varga, K. (2016). Accuracy and computational efficiency of real-time subspace propagation schemes for the time-dependent density functional theory. The Journal of Chemical Physics, 144(20), 204125. doi:10.1063/1.4952646Kidd, D., Covington, C., & Varga, K. (2017). Exponential integrators in time-dependent density-functional calculations. Physical Review E, 96(6). doi:10.1103/physreve.96.063307Dewhurst, J. K., Krieger, K., Sharma, S., & Gross, E. K. U. (2016). An efficient algorithm for time propagation as applied to linearized augmented plane wave method. Computer Physics Communications, 209, 92-95. doi:10.1016/j.cpc.2016.09.001Akama, T., Kobayashi, O., & Nanbu, S. (2015). Development of efficient time-evolution method based on three-term recurrence relation. The Journal of Chemical Physics, 142(20), 204104. doi:10.1063/1.4921465Kolesov, G., Grånäs, O., Hoyt, R., Vinichenko, D., & Kaxiras, E. (2015). Real-Time TD-DFT with Classical Ion Dynamics: Methodology and Applications. Journal of Chemical Theory and Computation, 12(2), 466-476. doi:10.1021/acs.jctc.5b00969Schaffhauser, P., & Kümmel, S. (2016). Using time-dependent density functional theory in real time for calculating electronic transport. Physical Review B, 93(3). doi:10.1103/physrevb.93.035115O’Rourke, C., & Bowler, D. R. (2015). Linear scaling density matrix real time TDDFT: Propagator unitarity and matrix truncation. The Journal of Chemical Physics, 143(10), 102801. doi:10.1063/1.4919128Oliveira, M. J. T., Mignolet, B., Kus, T., Papadopoulos, T. A., Remacle, F., & Verstraete, M. J. (2015). Computational Benchmarking for Ultrafast Electron Dynamics: Wave Function Methods vs Density Functional Theory. Journal of Chemical Theory and Computation, 11(5), 2221-2233. doi:10.1021/acs.jctc.5b00167Zhu, Y., & Herbert, J. M. (2018). Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation. The Journal of Chemical Physics, 148(4), 044117. doi:10.1063/1.5004675Rehn, D. A., Shen, Y., Buchholz, M. E., Dubey, M., Namburu, R., & Reed, E. J. (2019). ODE integration schemes for plane-wave real-time time-dependent density functional theory. The Journal of Chemical Physics, 150(1), 014101. doi:10.1063/1.5056258Gómez Pueyo, A., Marques, M. A. L., Rubio, A., & Castro, A. (2018). Propagators for the Time-Dependent Kohn–Sham Equations: Multistep, Runge–Kutta, Exponential Runge–Kutta, and Commutator Free Magnus Methods. Journal of Chemical Theory and Computation, 14(6), 3040-3052. doi:10.1021/acs.jctc.8b00197Stoer, J., & Bulirsch, R. (2002). Introduction to Numerical Analysis. doi:10.1007/978-0-387-21738-3Blanes, S., & Casas, F. (2017). A Concise Introduction to Geometric Numerical Integration. doi:10.1201/b21563Flocard, H., Koonin, S. E., & Weiss, M. S. (1978). Three-dimensional time-dependent Hartree-Fock calculations: Application toO16+O16collisions. Physical Review C, 17(5), 1682-1699. doi:10.1103/physrevc.17.1682Chen, R., & Guo, H. (1999). The Chebyshev propagator for quantum systems. Computer Physics Communications, 119(1), 19-31. doi:10.1016/s0010-4655(98)00179-9Hochbruck, M., & Lubich, C. (1997). On Krylov Subspace Approximations to the Matrix Exponential Operator. SIAM Journal on Numerical Analysis, 34(5), 1911-1925. doi:10.1137/s0036142995280572Frapiccini, A. L., Hamido, A., Schröter, S., Pyke, D., Mota-Furtado, F., O’Mahony, P. F., … Piraux, B. (2014). Explicit schemes for time propagating many-body wave functions. Physical Review A, 89(2). doi:10.1103/physreva.89.023418Caliari, M., Kandolf, P., Ostermann, A., & Rainer, S. (2016). The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential. SIAM Journal on Scientific Computing, 38(3), A1639-A1661. doi:10.1137/15m1027620Schaefer, I., Tal-Ezer, H., & Kosloff, R. (2017). Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems. Journal of Computational Physics, 343, 368-413. doi:10.1016/j.jcp.2017.04.017Trotter, H. F. (1959). On the product of semi-groups of operators. Proceedings of the American Mathematical Society, 10(4), 545-545. doi:10.1090/s0002-9939-1959-0108732-6Strang, G. (1968). On the Construction and Comparison of Difference Schemes. SIAM Journal on Numerical Analysis, 5(3), 506-517. doi:10.1137/0705041Feit, M. ., Fleck, J. ., & Steiger, A. (1982). Solution of the Schrödinger equation by a spectral method. Journal of Computational Physics, 47(3), 412-433. doi:10.1016/0021-9991(82)90091-2Suzuki, M. (1990). Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations. Physics Letters A, 146(6), 319-323. doi:10.1016/0375-9601(90)90962-nSuzuki, M. (1992). General theory of higher-order decomposition of exponential operators and symplectic integrators. Physics Letters A, 165(5-6), 387-395. doi:10.1016/0375-9601(92)90335-jYoshida, H. (1990). Construction of higher order symplectic integrators. Physics Letters A, 150(5-7), 262-268. doi:10.1016/0375-9601(90)90092-3Sugino, O., & Miyamoto, Y. (1999). Density-functional approach to electron dynamics: Stable simulation under a self-consistent field. Physical Review B, 59(4), 2579-2586. doi:10.1103/physrevb.59.2579McLachlan, R. I., & Quispel, G. R. W. (2002). Splitting methods. Acta Numerica, 11, 341-434. doi:10.1017/s0962492902000053Ascher, U. M., Ruuth, S. J., & Wetton, B. T. R. (1995). Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. SIAM Journal on Numerical Analysis, 32(3), 797-823. doi:10.1137/0732037Cooper, G. J., & Sayfy, A. (1983). Additive Runge-Kutta methods for stiff ordinary differential equations. Mathematics of Computation, 40(161), 207-218. doi:10.1090/s0025-5718-1983-0679441-1Hochbruck, M., Lubich, C., & Selhofer, H. (1998). Exponential Integrators for Large Systems of Differential Equations. SIAM Journal on Scientific Computing, 19(5), 1552-1574. doi:10.1137/s1064827595295337Hochbruck, M., & Ostermann, A. (2005). Exponential Runge–Kutta methods for parabolic problems. Applied Numerical Mathematics, 53(2-4), 323-339. doi:10.1016/j.apnum.2004.08.005Hochbruck, M., & Ostermann, A. (2005). Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems. SIAM Journal on Numerical Analysis, 43(3), 1069-1090. doi:10.1137/040611434Hochbruck, M., & Ostermann, A. (2010). Exponential integrators. Acta Numerica, 19, 209-286. doi:10.1017/s0962492910000048Houston, W. V. (1940). Acceleration of Electrons in a Crystal Lattice. Physical Review, 57(3), 184-186. doi:10.1103/physrev.57.184Chen, Z., & Polizzi, E. (2010). Spectral-based propagation schemes for time-dependent quantum systems with application to carbon nanotubes. Physical Review B, 82(20). doi:10.1103/physrevb.82.205410Sato, S. A., & Yabana, K. (2014). Efficient basis expansion for describing linear and nonlinear electron dynamics in crystalline solids. Physical Review B, 89(22). doi:10.1103/physrevb.89.224305Wang, Z., Li, S.-S., & Wang, L.-W. (2015). Efficient Real-Time Time-Dependent Density Functional Theory Method and its Application to a Collision of an Ion with a 2D Material. Physical Review Letters, 114(6). doi:10.1103/physrevlett.114.063004Magnus, W. (1954). On the exponential solution of differential equations for a linear operator. Communications on Pure and Applied Mathematics, 7(4), 649-673. doi:10.1002/cpa.3160070404Blanes, S., Casas, F., Oteo, J. A., & Ros, J. (2009). The Magnus expansion and some of its applications. Physics Reports, 470(5-6), 151-238. doi:10.1016/j.physrep.2008.11.001Nettesheim, P., Bornemann, F. A., Schmidt, B., & Schütte, C. (1996). An explicit and symplectic integrator for quantum-classical molecular dynamics. Chemical Physics Letters, 256(6), 581-588. doi:10.1016/0009-2614(96)00471-xHochbruck, M., & Lubich, C. (1999). A Bunch of Time Integrators for Quantum/Classical Molecular Dynamics. Lecture Notes in Computational Science and Engineering, 421-432. doi:10.1007/978-3-642-58360-5_24Hochbruck, M., & Lubich, C. (1999). Bit Numerical Mathematics, 39(4), 620-645. doi:10.1023/a:1022335122807Nettesheim, P., & Reich, S. (1999). Symplectic Multiple-Time-Stepping Integrators for Quantum-Classical Molecular Dynamics. Lecture Notes in Computational Science and Engineering, 412-420. doi:10.1007/978-3-642-58360-5_23Nettesheim, P., & Schütte, C. (1999). Numerical Integrators for Quantum-Classical Molecular Dynamics. Lecture Notes in Computational Science and Engineering, 396-411. doi:10.1007/978-3-642-58360-5_22Reich, S. (1999). Multiple Time Scales in Classical and Quantum–Classical Molecular Dynamics. Journal of Computational Physics, 151(1), 49-73. doi:10.1006/jcph.1998.6142Jiang, H., & Zhao, X. S. (2000). New propagators for quantum-classical molecular dynamics simulations. The Journal of Chemical Physics, 113(3), 930-935. doi:10.1063/1.481873Grochowski, P., & Lesyng, B. (2003). Extended Hellmann–Feynman forces, canonical representations, and exponential propagators in the mixed quantum-classical molecular dynamics. The Journal of Chemical Physics, 119(22), 11541-11555. doi:10.1063/1.1624062Blanes, S., & Moan, P. C. (2006). Fourth- and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems. Applied Numerical Mathematics, 56(12), 1519-1537. doi:10.1016/j.apnum.2005.11.004Bader, P., Blanes, S., & Kopylov, N. (2018). Exponential propagators for the Schrödinger equation with a time-dependent potential. The Journal of Chemical Physics, 148(24), 244109. doi:10.1063/1.5036838Marques, M. (2003). octopus: a first-principles tool for excited electron–ion dynamics. Computer Physics Communications, 151(1), 60-78. doi:10.1016/s0010-4655(02)00686-0Castro, A., Appel, H., Oliveira, M., Rozzi, C. A., Andrade, X., Lorenzen, F., … Rubio, A. (2006). octopus: a tool for the application of time-dependent density functional theory. physica status solidi (b), 243(11), 2465-2488. doi:10.1002/pssb.200642067Schwerdtfeger, P. (2011). The Pseudopotential Approximation in Electronic Structure Theory. ChemPhysChem, 12(17), 3143-3155. doi:10.1002/cphc.201100387Alonso, J. L., Castro, A., Clemente-Gallardo, J., Cuchí, J. C., Echenique, P., & Falceto, F. (2011). Statistics and Nosé formalism for Ehrenfest dynamics. Journal of Physics A: Mathematical and Theoretical, 44(39), 395004. doi:10.1088/1751-8113/44/39/395004Iserles, A., & Nørsett, S. P. (1999). On the solution of linear differential equations in Lie groups. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 357(1754), 983-1019. doi:10.1098/rsta.1999.0362Munthe–Kaas, H., & Owren, B. (1999). Computations in a free Lie algebra. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 357(1754), 957-981. doi:10.1098/rsta.1999.0361Alvermann, A., & Fehske, H. (2011). High-order commutator-free exponential time-propagation of driven quantum systems. Journal of Computational Physics, 230(15), 5930-5956. doi:10.1016/j.jcp.2011.04.006Blanes, S., & Moan, P. C. (2000). Splitting methods for the time-dependent Schrödinger equation. Physics Letters A, 265(1-2), 35-42. doi:10.1016/s0375-9601(99)00866-xAuer, N., Einkemmer, L., Kandolf, P., & Ostermann, A. (2018). Magnus integrators on multicore CPUs and GPUs. Computer Physics Communications, 228, 115-122. doi:10.1016/j.cpc.2018.02.019Thalhammer, M. (2006). A fourth-order commutator-free exponential integrator for nonautonomous differential equations. SIAM Journal on Numerical Analysis, 44(2), 851-864. doi:10.1137/05063042Bader, P., Blanes, S., Ponsoda, E., & Seydaoğlu, M. (2017). Symplectic integrators for the matrix Hill equation. Journal of Computational and Applied Mathematics, 316, 47-59. doi:10.1016/j.cam.2016.09.04

Light-induced translation symmetry breaking via nonlinear phononics

Light has a wavelength that is usually longer than the size of the unit cell of crystals. Hence, even intense light pulses are not expected to break the translation symmetry of materials. However, certain materials, including KTaO$_3$, exhibit peaks in their Raman spectra corresponding to their Brillouin zone boundary phonons due to second-order Raman processes, which provide a mechanism to drive these phonons using intense midinfrared lasers. We investigated the possibility of breaking the translation symmetry of KTaO$_3$ by driving its highest-frequency transverse optic mode $Q_{\textrm{HX}}$ at the $X$ $(0,\frac{1}{2},0)$ point. Our first principles calculations show that the energy curve of the transverse acoustic mode $Q_{\textrm{LZ}}$ at $X$ softens and develops a double-well shape as the value of the $Q_{\textrm{HX}}$ coordinate is increased, while that of the other transverse acoustic component $Q_{\textrm{LX}}$ hardens when the value of the $Q_{\textrm{HX}}$ coordinate is similarly varied. We performed similar total energy calculations as a function of the $Q_{\textrm{HX}}$ coordinate and electric field to extract the nonlinear coupling between them. These were then used to construct the coupled equations of motion for the three phonon coordinates in the presence of an external pump term on the $Q_{\textrm{HX}}$ mode, which we numerically solved for a range of pump frequencies and amplitudes. We find that 465 MV/cm is the smallest pump amplitude that leads to an oscillation of the $Q_{\textrm{LZ}}$ mode at a displaced position, hence, breaking the translation symmetry of the material. Such highly intense light pulses cannot be generate by currently available laser sources, and they have the possibility to damage the material. Nevertheless, our work shows that light can in principle be used to break the translation symmetry of a material via nonlinear phononics

About the relation of electron–electron interaction potentials with exchange and correlation functionals

We investigate, numerically, the possibility of associating to each approximation to the exchange-and-correlation functional in density-functional theory (DFT), an optimal electron–electron interaction potential for which it performs best. The fundamental theorems of density-functional theory (DFT) make no assumption about the precise form of the electron–electron interaction: to each possible electron–electron interaction corresponds an exchange-and-correlation functional. This fact suggests the opposite question: given some functional of the density, is there any electron–electron interaction for which it is the exact exchange-and-correlation functional? And, if not, what is the interaction for which the functional produces the best results? Within the context of lattice DFT, we study these questions by working on the one-dimensional Hubbard chain. The idea of associating an optimal interaction potential to each approximation to the exchange and correlation functionals suggests, finally, a procedure to optimise parameterised families of functionals: find that one whose associated interaction most closely resembles the real one

Un Método para el Cálculo de la Mejor Función de Interacción Electrón-Electrón para un Funcional de Intercambio y Correlación Dado

La teoría del funcional de la densidad (DFT) es un método para abordar el problema de varios electrones. Es aproximada, ya que uno de los ingredientes, el llamado ``funcional de intercambio y correlación'', no puede calcularse de manera exacta, y deben usarse diversas formulaciones aproximadas. En este trabajo de fin de máster abordamos el problema de la mejora de estas formulaciones de una manera alternativa: estudiando la relación entre la forma potencial de interacción electrónica y el funcional de intercambio y correlación. En principio, a cada forma de la interacción electrónica (que en la realidad es la forma Coulombiana) corresponde un potencial de intercambio y correlación. De forma que es imaginable que, dado un funcional de intercambio y correlación no exacto para la interacción Coulombiana, exista una interacción electrónica ficticia que le corresponda de forma exacta, o bien que le corresponda de forma aproximada pero óptima. Hemos construido un código que permite investigar numéricamente este problema, y en la presente memoria describimos los resultados obtenidos más relevantes

Performance of fourth and sixth-order commutator-free Magnus expansion integrators for Ehrenfest dynamics

This is the peer reviewed version of the following article: Gómez Pueyo, A, Blanes, S, Castro, A. Performance of fourth and sixth-order commutator-free Magnus expansion integrators for Ehrenfest dynamics. Comp and Math Methods. 2021; 3:e1100, which has been published in final form at https://doi.org/10.1002/cmm4.1100. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] Hybrid quantum-classical systems combine both classical and quantum degrees of freedom. Typically, in Chemistry, Molecular Physics, or Materials Science, the classical degrees of freedom describe atomic nuclei (or cations with frozen core electrons), whereas the quantum particles are the electrons. Although many possible hybrid dynamical models exist, the basic one is the so-called Ehrenfest dynamics that results from the straightforward partial classical limit applied to the full quantum Schrödinger equation. Few numerical methods have been developed specifically for the integration of this type of systems. Here we present a preliminary study of the performance of a family of recently developed propagators: the (quasi) commutator-free Magnus expansions. These methods, however, were initially designed for nonautonomous linear equations. We employ them for the nonlinear Ehrenfest system, by approximating the state value at each time step in the propagation, using an extrapolation from previous time steps.A.C. acknowledges support from the MINECO FIS2017-82426-P grant. S.B. acknowledges MTM2016-77660-P grant (AEI/FEDER, UE).Gómez Pueyo, A.; Blanes Zamora, S.; Castro, A. (2021). Performance of fourth and sixth-order commutator-free Magnus expansion integrators for Ehrenfest dynamics. Computational and Mathematical Methods. 3:1-12. https://doi.org/10.1002/cmm4.1100S112