Linear Response Formalism Research Articles

Noisy qudit vs multiple qubits: conditions on gate efficiency for enhancing fidelity

As qubit-based platforms face near-term technical challenges in terms of scalability, qudits, d-level bases of quantum information, are being implemented in multiple platforms as an alternative for Quantum Information Processing (QIP). We compare the infidelity scalings of single qudit and multiqubit systems within identical Hilbert space dimensions and noisy environments in the Lindblad formalism. We find them to be gate-independent to first-order and present an analytically-derived critical curve (d2−1)/3log2(d)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({d}^{2}-1)/3{\\log }_{2}(d)$$\\end{document} that benchmarks the operational time efficiency of qudits and qubits relative to their decoherence times. This comparison reveals conditions under which qudits offer competitive gate efficiencies compared to leading qubit platforms. Our findings, supported by numerical simulations testing the applicability and limits of the linear response formalism, highlight the relevance of qudits in near-term QIP. This provides a benchmark for evaluating qudit platforms, specifically those with lower dimensionality, in terms of their operational efficiency relative to the qubit state-of-the-art.

Influence of a transverse magnetic field on wakefield oscillations around a charged dust grain in complex plasma

In the presence of ion streaming, the potential around dust particles immersed in plasma becomes anisotropic. In this scenario, the repulsive Debye–Hückel potential is superimposed with an attractive wake potential. This work presents an analytical study of the complex behavior of such a wake potential in the presence of a magnetic field (oriented transversely to the ion flow) and ion-neutral collisions using linear response formalism, both in subsonic and supersonic regimes. The amplitude and periodicity of this potential are found to be controlled by the interplay among ion streaming velocity, ion cyclotron frequency, and ion-neutral collision frequency. Due to the tunable nature of this potential, it is possible to control the crystal formation, phase transitions, and transport properties of dusty plasma by adjusting the external magnetic field. The study also reveals that the wake potential almost disappears in a collision-dominant regime.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory: Multireference Advantages with the Practicality of Linear Response Theory.

The density functional theory (DFT) and linear response (LR) time-dependent (TD)-DFT are of the utmost importance for routine computations. However, the single reference formulation of DFT suffers in the description of open-shell singlet systems such as diradicals and bond-breaking. LR-TDDFT, on the other hand, finds difficulties in the modeling of conical intersections, doubly excited states, and core-level excitations. In this Perspective, we demonstrate that many of these limitations can be overcome by recently developed mixed-reference (MR) spin-flip (SF)-TDDFT, providing an alternative yet accurate route for such challenging situations. Empowered by the practicality of the LR formalism, it is anticipated that MRSF-TDDFT can become one of the major workhorses for general routine tasks.

Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies.

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional incorporates the short-range electron correlation effects missing in the basis set. This results in accelerated basis convergences of ground-state energies to the complete-basis-set limit. In this work, we extend the basis-set correction method to a linear-response formalism for calculating excited-state energies. We give the general linear-response equations as well as the more specific equations for configuration-interaction wave functions. As a proof of concept, we apply this approach to the calculations of excited-state energies in a one-dimensional two-electron model system with harmonic potential and a Dirac-delta electron-electron interaction. The results obtained with full-configuration-interaction wave functions expanded in a basis of Hermite functions and a local-density-approximation basis-set correction functional show that the present approach does not help in accelerating the basis convergence of excitation energies. However, we show that it significantly accelerates basis convergences of excited-state total energies.

Resistance saturation in semi-conducting polyacetylene molecular wires

Realizing the promises of molecular electronic devices requires an understanding of transport on the nanoscale. Here, we consider a Su-Schrieffer-Heeger model for semi-conducting trans-polyacetylene molecular wires in which we endow charge carriers with a finite lifetime. The aim of this exercise is two-fold: (i) the simplicity of the model allows an insightful numerical and analytical comparison of the Landauer and Kubo linear-response formalism; (ii) we distill the prototypical characteristics of charge transport through gapped mesoscopic systems and compare these to bulk semiconductors. We find that both techniques yield a residual differential conductance at low temperatures for contacted polyacetylene chains of arbitrary length—in line with the resistivity saturation in some correlated narrow-gap semiconductors. Quantitative agreement, however, is limited to not too long molecules. Indeed, while the Landauer transmission is suppressed exponentially with the system size, the Kubo response only decays hyperbolically. Our findings inform the choice of transport methodologies for the ab initio modelling of molecular devices.

Electron-phonon interaction and phonon frequencies in two-dimensional doped semiconductors

Electron-phonon interaction and phonon frequencies of doped polar semiconductors are sensitive to long-range Coulomb forces and can be strongly affected by the screening effects of free carriers, the latter changing significantly when approaching the two-dimensional limit. We tackle this problem within a linear-response dielectric-matrix formalism, where the screening effects can be properly taken into account by generalized effective charge functions and the inverse scalar dielectric function, allowing for controlled approximations in relevant limits. We propose complementary computational methods to evaluate from first principles both effective charges---encompassing all multipolar components beyond dynamical dipoles and quadrupoles---and the static dielectric function of doped two-dimensional semiconductors and provide analytical expressions for the long-range part of the dynamical matrix and the electron-phonon interaction in the long-wavelength limit. As a representative example, we apply our approach to study the impact of doping in disproportionated graphene, showing that optical Fr\"ohlich and acoustic piezoelectric couplings, as well as the slope of optical longitudinal modes, are strongly reduced, with a potential impact on the electronic/intrinsic scattering rates and related transport properties.

Microrheology near jamming.

The jamming transition is a nonequilibrium critical phenomenon, which governs characteristic mechanical properties of jammed soft materials, such as pastes, emulsions, and granular matters. Both experiments and theory of jammed soft materials have revealed that the complex modulus measured by conventional macrorheology exhibits a characteristic frequency dependence. Microrheology is a new type of method to obtain the complex modulus, which transforms the microscopic motion of probes to the complex modulus through the generalized Stokes relation (GSR). Although microrheology has been applied to jammed soft materials, its theoretical understanding is limited. In particular, the validity of the GSR near the jamming transition is far from obvious since there is a diverging length scale lc, which characterizes the heterogeneous response of jammed particles. Here, we study the microrheology of jammed particles by theory and numerical simulation. First, we develop a linear response formalism to calculate the response function of the probe particle, which is transformed to the complex modulus via the GSR. Then, we apply our formalism to a numerical model of jammed particles and find that the storage and loss modulus follow characteristic scaling laws near the jamming transition. Importantly, the observed scaling law coincides with that in macrorheology, which indicates that the GSR holds even near the jamming transition. We rationalize this equivalence by asymptotic analysis of the obtained formalism and numerical analysis on the displacement field of jammed particles under a local perturbation.

TRACK: A python code for calculating the transport properties of correlated electron systems using Kubo formalism

Exploring the transport properties of different materials brings new avenue for basic understanding of emergent phenomena and practical applications in many different fields. Here, we report a program named as TRACK (TRAnsport properties for Correlated materials using Kubo formalism) which is written in Python 3 for calculating temperature dependent electrical conductivity, electronic part of thermal conductivity, Seebeck coefficient and Lorenz number. In this code, Kubo linear-response formalism is utilized for computing these parameters using both interacting and non-interacting electronic structure methods. The formula for transport coefficients is accordingly modified to obtain the transport parameters under relaxation time approximation using band-theory. The basic inputs of this program are the structural information, dense k-points sampling in the irreducible part of the Brillouin zone and the information of velocity matrix elements, which can be calculated using third-party ab-initio package. TRACK is expected to calculate the transport properties of different class of materials. The code has been benchmarked by performing calculation on three different types of materials namely Vanadium (V), FeSi and LaCoO3, which are metal, semiconductor and Mott insulator, respectively. The temperature dependent behaviour of the transport coefficients for these materials show fairly good agreement with the corresponding experimental data. Program summaryProgram Title: TRACKCPC Library link to program files:https://doi.org/10.17632/jdt9tfkt4v.1Developer's repository link:https://sourceforge.net/projects/track-code/files/TRACK.zip/downloadLicensing provisions: GPLv3Programming language: Python3External routines/libraries: NumPy, SciPy, TimeNature of problem: Calculating the transport parameters using the Kubo linear-response formalism.Solution method: We present a Python3 open source code for calculating transport coefficients using Kubo formalism. Both interacting and non-interacting electronic structure methodology are possible to be used for computing transport parameters.

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States.

The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

Statistical Equilibrium Principles in 2D Fluid Flow: From Geophysical Fluids to the Solar Tachocline

An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety of physical phenomena that can be explored, are highlighted. These span, roughly in order of increasing complexity, Euler flow, nonlinear Rossby waves, 3D axisymmetric flow, shallow water dynamics, and 2D magnetohydrodynamics. The classical field theories describing these systems bear some resemblance to perhaps more familiar fluctuating membrane and continuous spin models, but the fluid physics drives these models into unconventional regimes exhibiting large scale jet and eddy structures. From a dynamical point of view these structures are the end result of various conserved variable forward and inverse cascades. The resulting balance between large scale structure and small scale fluctuations is controlled by the competition between energy and entropy in the system free energy, in turn highly tunable through setting the values of the conserved integrals. Although the statistical mechanical description of such systems is fully self-consistent, with remarkable mathematical structure and diversity of solutions, great care must be taken because the underlying assumptions, especially ergodicity, can be violated or at minimum lead to exceedingly long equilibration times. Generalization of the theory to include weak driving and dissipation (e.g., non-equilibrium statistical mechanics and associated linear response formalism) could provide additional insights, but has yet to be properly explored.

First-principles theory of intrinsic spin and orbital Hall and Nernst effects in metallic monoatomic crystals

The generation of spin and orbital currents is of crucial importance in the field of spin-orbitronics. In this work, using relativistic density functional theory and the Kubo linear-response formalism, we systematically investigate the spin Hall and orbital Hall effects for 40 monoatomic metals. The spin Hall conductivity and orbital Hall conductivity (OHC) are computed as a function of the electrochemical potential and the influence of the spin-orbit interaction strength is also investigated. Our calculations predict a rather small OHC in $sp$ metals, but a much larger OHC in $d$-band metals, with maximum values $[\ensuremath{\sim}8000(\ensuremath{\hbar}/e)\phantom{\rule{0.28em}{0ex}}{(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}]$ near the middle of the $d$ series. Using the Mott formula, we evaluate the thermal counterparts of the spin and orbital Hall effects, the spin Nernst effect (SNE), and the orbital Nernst effect (ONE). We find that the as-yet unobserved ONE is significantly larger $(\ensuremath{\sim}10\ifmmode\times\else\texttimes\fi{})$ than the SNE and has maximum values for group 10 elements (Ni, Pd, and Pt). Our work provides a broad overview of electrically and thermally induced spin and orbital transport in monoatomic metals.

Dynamical magnetic response in superconductors with finite-momentum pairs

We derive the dynamical magnetic response functions in the Fulde-Ferrell (FF) state of a superconductor with inversion symmetry. The pair momentum 2q is obtained by minimization of the condensation energy and the resulting quasiparticle states and spectral functions exhibit the segmentation into paired and unpaired regions due to the finite q. The dynamical magnetic susceptibility is then calculated in linear response formalism in the FF state with finite-q condensate resulting from s-wave or d-wave pairing. We show that quasiparticle excitations inside as well as between paired and unpaired segments contribute to the dynamical response. We discuss its dependence on frequency and momentum transfer which develops a characteristic symmetry-breaking parallel to q. Furthermore, we investigate the possible influence on Knight shift and in the case of d-wave pairing on the spin resonance formation in the FF state.

Frequency-Dependent Sternheimer Linear-Response Formalism for Strongly Coupled Light-Matter Systems.

The rapid progress in quantum-optical experiments, especially in the field of cavity quantum electrodynamics and nanoplasmonics, allows one to substantially modify and control chemical and physical properties of atoms, molecules, and solids by strongly coupling to the quantized field. Alongside such experimental advances has been the recent development of ab initio approaches such as quantum electrodynamical density-functional theory (QEDFT), which is capable of describing these strongly coupled systems from first principles. To investigate response properties of relatively large systems coupled to a wide range of photon modes, ab initio methods that scale well with system size become relevant. In light of this, we extend the linear-response Sternheimer approach within the framework of QEDFT to efficiently compute excited-state properties of strongly coupled light–matter systems. Using this method, we capture features of strong light–matter coupling both in the dispersion and absorption properties of a molecular system strongly coupled to the modes of a cavity. We exemplify the efficiency of the Sternheimer approach by coupling the matter system to the continuum of an electromagnetic field. We observe changes in the spectral features of the coupled system as Lorentzian line shapes turn into Fano resonances when the molecule interacts strongly with the continuum of modes. This work provides an alternative approach for computing efficiently excited-state properties of large molecular systems interacting with the quantized electromagnetic field.

Gilbert damping, electronic and magnetic properties for quaternary Heusler alloys CrYCoZ: First-principles and Monte Carlo studies

We systematically study the stability, Gilbert damping parameters, electronic structure, exchange interaction and Curie temperature of CrYCoZ (Z = Al, Ga, In, Tl) alloys. Stability is estimated from the perspective of thermodynamics, dynamics and mechanics. Gilbert damping parameters are calculated by using the linear response formalism, and the values 0.6∼4.1× 10−3 are observed at room temperature. Electronic calculations show that the CrYCoZ alloys are half-metallic ferrimagnets, and their integer magnetic moments follow the Mt=Zt−18. Origin of gap is discussed by the hybridization, distribution and occupation of electronic states as well as the charge transfer. In addition, the effect of GGA+U on electronic structure is also discussed. Based on the Heisenberg model, we calculate the exchange interactions between atomic components, and analyze the competition and collaboration between d–d exchange, super-exchange and RKKY exchange, finally offer the dominant mechanism of appearance of ferrimagnetic order phase. Furthermore, we calculate the Curie temperatures of CrYCoZ alloys, which are much higher than room temperature. Overall, the CrYCoZ alloys can be considered as a prospective candidates in spintronics application.

Internal Conversion between Bright (11Bu+) and Dark (21Ag-) States in s-trans-Butadiene and s-trans-Hexatriene.

Internal conversion (IC) between the two lowest singlet excited states, 11Bu+ and 21Ag-, of s-trans-butadiene and s-trans-hexatriene is investigated using a series of single- and multi- reference wave function and density functional theory (DFT) methodologies. Three independent types of the equation-of-motion coupled-cluster (EOMCC) theory capable of providing an accurate and balanced description of one- as well as two-electron transitions, abbreviated as δ-CR-EOMCC(2,3), DIP-EOMCC(4h2p){No}, and DEA-EOMCC(4p2h){Nu} or DEA-EOMCC(3p1h,4p2h){Nu}, consistently predict that the 11Bu+/21Ag- crossing in both molecules occurs along the bond length alternation coordinate. However, the analogous 11Bu+ and 21Ag- potentials obtained with some multireference approaches, such as CASSCF and MRCIS(D), as well as with the linear-response formulation of time-dependent DFT (TDDFT), do not cross. Hence, caution needs to be exercised when studying the low-lying singlet excited states of polyenes with conventional multiconfigurational methods and TDDFT. The multistate many-body perturbation theory methods, such as XMCQDPT2, do correctly reproduce the curve crossing. Among the simplest and least expensive computational methodologies, the DFT approaches that incorporate the contributions of doubly excited configurations, abbreviated as MRSF (mixed reference spin-flip) TDDFT and SSR(4,4), accurately reproduce our best EOMCC results. This is highly promising for nonadiabatic molecular dynamics simulations in larger systems.

Thermal conductivity of molten alkali halides: The phenomenology and molecular dynamic simulations

Semi-phenomenological consideration of the thermal conductivity based on experimental and molecular dynamics (MD) data for molten alkali halides (AHs) near their melting points was carried out on the basis of scaling concepts associated with the vibrational mechanism of heat transfer. As a result, a general formula for the thermal conductivity is proposed for all molten alkali halides which takes into account the difference in vibrational motion of cation and anion. Characteristic frequencies of the cation and anion vibrations were evaluated through vibrational densities of states. These frequencies allow the values of the thermal conductivity among all AHs melts near their melting points to be estimated to a degree of accuracy close to 10%. Additionally, independent of the assumed heat transfer mechanism, direct simulation of the heat flux was performed within the non-equilibrium molecular dynamics approach. The estimated thermal conductivity of alkali halides’ (AHs) melts (M = Li, Na, K; X = F, Cl, Br, I) are in good agreement with most experimental and MD studies via the Kubo-Green linear response formalism.

Absolute NMR shielding scales in methyl halides obtained from experimental and calculated nuclear spin-rotation constants

The nonrelativistic ``Ramsey-Flygare relationship'' is the most used procedure to obtain semiexperimental nuclear magnetic resonance (NMR) absolute shieldings by a correspondence between NMR shieldings ($\mathbit{\ensuremath{\sigma}}$) and nuclear spin-rotation constants ($\mathbit{M}$). One of its generalizations to the relativistic framework is known as the M-V model, which was proposed few year ago by some of the authors of the present work and right now is only applied to linear molecules. This model includes terms that do not have nonrelativistic counterparts and also include the paramagnetic contribution to the NMR shielding of nuclei in free atoms. All this ensures that its results fit quite well with those of four-component (4c) calculations. The first application of the M-V model to nonlinear molecules, like methyl halides or ${\mathrm{CH}}_{3}X$ molecules ($X=\mathrm{F}$, Cl, Br, and I), is given here. The analysis of each electronic mechanism of $\mathbit{\ensuremath{\sigma}}$ shows that most of their electron correlation effects are strongly related with the same effects in $\mathbit{M}$. By including experimental data of $M$ in the M-V model most of the correlation effects are accurately taken into account for the absolute values of $\mathbit{\ensuremath{\sigma}}$. Calculations of ${\mathbit{M}}_{Y}$ and ${\mathbit{\ensuremath{\sigma}}}_{Y}$ ($Y=\mathrm{H}$, C, and $X$) were carried out within the linear response formalism at the random-phase level of approach and density functional theory in both 4c and nonrelativistic frameworks. The best fits between calculations of $\mathbit{M}$ and experimental data are obtained from calculations at 4c-PBE0 level of theory in all cases, but not for ${M}_{\ensuremath{\parallel},\mathrm{Cl}}$, which suggests that a revision of the available experimental data may be necessary. There is an additional advantage of using the M-V model: one can indirectly calculate shieldings of open-shell free atoms, which cannot be obtained at the moment by applying 4c methods.

Origins of anisotropic transport in the electrically switchable antiferromagnet Fe1/3NbS2

Recent experiments on the antiferromagnetic intercalated transition metal dichalcogenide $\mathrm{Fe_{1/3}NbS_2}$ have demonstrated reversible resistivity switching by application of orthogonal current pulses below its magnetic ordering temperature, making $\mathrm{Fe_{1/3}NbS_2}$ promising for spintronics applications. Here, we perform density functional theory calculations with Hubbard U corrections of the magnetic order, electronic structure, and transport properties of crystalline $\mathrm{Fe_{1/3}NbS_2}$, clarifying the origin of the different resistance states. The two experimentally proposed antiferromagnetic ground states, corresponding to in-plane stripe and zigzag ordering, are computed to be nearly degenerate. In-plane cross sections of the calculated Fermi surfaces are anisotropic for both magnetic orderings, with the degree of anisotropy sensitive to the Hubbard U value. The in-plane resistance, computed within the Kubo linear response formalism using a constant relaxation time approximation, is also anisotropic, supporting a hypothesis that the current-induced resistance changes are due to a repopulating of AFM domains. Our calculations indicate that the transport anisotropy of $\mathrm{Fe_{1/3}NbS_2}$ in the zigzag phase is reduced relative to stripe, consistent with the relative magnitudes of resistivity changes in experiment. Finally, our calculations reveal the likely directionality of the current-domain response, specifically, which domains are energetically stabilized for a given current direction.

Magneto-Optical Conductivity of Graphene: Signatures of a Uniform Y-Shaped Kekule Lattice Distortion

Recent experiments have revealed Y-shaped Kekulé lattice distortions in the honeycomb lattice on a graphene-copper superlattice[Nat. Phys. 12 (2016) 950]. In this paper the effects of such lattice distortions on the magneto-optical properties of graphene are investigated within Kubo linear-response formalism. It is found that the Y-shaped Kekulé lattice distortion lifts the valley degeneracy of all Landau levels except zero-energy mode, leading to six categories of absorption peaks in the optical absorption spectra with a distinct optical selection rule. Particular attention is paid to the absorption frequency, peak intensity of each category and its redistribution as the chemical potential is varied. Their main features are found to be different from those in undistorted graphene having their origin in the Kekulé lattice distortion. The optical response of the Y-shaped Kekulé-patterned graphene to left- and right-handed circular light is also discussed in details. The present results also suggest that magneto-optical measurements will allow to determine the Kekulé bond-texture amplitude.