Density-matrix Calculations Research Articles

Reducing Numerical Precision Requirements in Quantum Chemistry Calculations.

The abundant demand for deep learning compute resources has created a renaissance in low-precision hardware. Going forward, it will be essential for simulation software to run on this new generation of machines without sacrificing scientific fidelity. In this paper, we examine the precision requirements of a representative kernel from quantum chemistry calculations: the calculation of the single-particle density matrix from a given mean-field Hamiltonian (i.e., Hartree-Fock or density functional theory) represented in an LCAO basis. We find that double precision affords an unnecessarily high level of precision, leading to optimization opportunities. We show how an approximation built from an error-free matrix multiplication transformation can be used to potentially accelerate this kernel on future hardware. Our results provide a roadmap for adapting quantum chemistry software for the next generation of high-performance computing platforms.

Determination of reduced density matrices in the doubly occupied configuration interaction space: A Hellmann-Feynman theorem approach.

In this work, the Hellmann-Feynman theorem is extended within the doubly occupied configuration interaction space to enable practical calculations of reduced density matrices and expected values. This approach is straightforward, employing finite energy differences, yet remains reliable and accurate even with approximate energies from successive approximation methods. The method's validity is rigorously tested against the Richardson-Gaudin-Kitaev and reduced Bardeen-Cooper-Schrieffer models using approximate excitation energies procured from the Hermitian operator method within the same space, effectively proving the approach's reliability with median error rates for reduced density matrix calculations around 0.1%. These results highlight the procedure's potential as a practical tool for computing reduced density matrices and expected values, particularly valuable as an ad hoc method in scenarios where only system energies are easily available.

QSIM: A Quantum-inspired hierarchical semantic interaction model for text classification

Semantic interaction modeling is a fundamental technology in natural language understanding that guides models to extract deep semantic information from text. Currently, the attention mechanism is one of the most effective techniques in semantic interaction modeling, which learns word-level attention representation by measuring the relevance between different words. However, the attention mechanism is limited to word-level semantic interaction, it cannot meet the needs of fine-grained interactive information for some text classification tasks. In recent years, quantum-inspired language modeling methods have successfully constructed quantized representations of language systems in Hilbert spaces, which use density matrices to achieve fine-grained semantic interaction modeling.This paper presents a Quantum-inspired hierarchical Semantic Interaction Model (QSIM), which follows the sememe-word-sentence language construction principle and utilizes quantum entanglement theory to capture hierarchical semantic interaction information in Hilbert space. Our work builds on the idea of the attention mechanism and extends it. Specifically, we explore the original semantic space from a quantum theory perspective and derive the core semantic space using the Schmidt decomposition technique, where: (1) Sememe is represented as the unit vector in the two-dimensional minimum semantic space; (2) Word is represented as reduced density matrices in the core semantic space, where Schmidt coefficients quantify sememe-level semantic interaction. Compared to density matrices, reduced density matrices capture fine-grained semantic interaction information with lower computational cost; (3) Sentence is represented as quantum superposition states of words, and the degree of word-level semantic interaction is measured using entanglement entropy.To evaluate the model’s performance, we conducted experiments on 15 text classification datasets. The experimental results demonstrate that our model is superior to classical neural network models and traditional quantum-inspired language models. Furthermore, the experiment also confirms two distinct advantages of QISM: (1) flexibility, as it can be integrated into various mainstream neural network text classification architectures; and (2) practicability, as it alleviates the problem of parameter growth inherent in density matrix calculation in quantum language model.

Branching-Chain Propagation of Parahydrogen-Derived Nuclear Spin Order on a Catalyst Surface.

This study reveals that, when two hydrogen atoms are produced on the surface of a catalyst (e. g., a metal nanoparticle) upon dissociation of a parahydrogen molecule, their initial nuclear spin correlation can propagate in a branching-chain fashion as they diffuse and combine with random H atoms to produce H2 molecules, which subsequently dissociate. This process leads to a gradual dilution of the non-equilibrium nuclear spin order, but the number of involved H atoms that share the spin order becomes larger. These conclusions, confirmed by the spin density matrix calculations, may be relevant in the context of parahydrogen-induced polarization (PHIP) in heterogeneous hydrogenations catalyzed by supported metal catalysts, the observation of which apparently contradicts the accepted non-pairwise mechanism of the addition of hydrogen to an unsaturated substrate over such catalysts. The potential consequences of the reported findings are discussed in the context of PHIP effects and beyond.

Theoretical investigations on the laser isotope separation of 175Yb for medical applications

The possibility of laser isotope separation of 175Yb from irradiated natural Yb has been investigated. The optimum process parameters such as powers and bandwidths of the lasers, Doppler broadening and the number density of the atoms have been derived through density matrix calculations. It has been shown that it is possible to produce 175Yb (>42% enriched) at a production rate of 62 μg/hour (or 1.5 mg/day). This corresponds to the production rate of 1350 patient doses (of 7.4 GBq each) per day. The radionuclidic purity of the isotopic mixture is expected to be 99.9999%. The method is highly suitable for the countries having only low-flux nuclear reactors.

Nonlinear polarization holography of nanoscale iridium films

Attosecond nonlinear polarization spectroscopy designates the subcycle-precise retrieval of the electric field of a femtosecond laser pulse together with the nonlinear polarization response that the laser pulse triggers in a sample. Here, we introduce a method that is all-optical and applicable to metal films. The method is called nonlinear polarization holography because it is based on the comparison of two time-domain holograms with and without a metal film on a substrate. The working principle can be understood as the time-domain analog of holographic interferometry, in which the comparison of two spatial holograms reveals changes in an object’s size and position with interferometric precision (i.e. to fractions of the wavelength). Analogously, nonlinear polarization holography provides subcycle precision (i.e. to fractions of the optical period). Nonlinear polarization holography is used here to retrieve the time-domain nonlinear response of a nanoscale iridium film. Using density matrix calculations it is shown that the knowledge of the nonlinear response with subcycle precision allows distinguishing excitation and relaxation mechanisms of low-energetic electrons.

Iterative density matrix revisited: Excitonic phenomena on the InAs quantum well as a saturable absorber

By solving the Liouville equation, third-order nonlinear terms of the optical absorptive two quantum-level system are obtained through iterative density matrix calculations. In the improved model, the full frequency range is taken into account instead of just the weak absorptive limit. he process investigated in this study can be likened to saturation fitting for heavy-hole excitons in the InAs quantum well. Additionally, we demonstrate that the iterative method used for analyzing band-to-band excitonic spectra enables easy retrieval of the static dielectric constant.

Knee structure in the laser-intensity dependence of harmonic generation for graphene

We investigate the high-order harmonic generations (HHGs) of graphene irradiated by linearly polarized lasers with intensities in a wide range from $10^{8}$ W/cm$^2$ to $10^{13}$ W/cm$^2$. We find a striking knee structure in the laser intensity dependence of HHGs, which consists of a linear growth regime, followed by a plateau of the saturated HHGs, and then a transition to a nonlinear growth. The knee structure is rather universal for the varied harmonic orders and has been certificated by the calculations of two-band density-matrix equations as well as the \textit{ab initio} calculations of time-dependent density functional theory. Based on the two-band model, we reveal the underlying mechanisms: The behavior of linear growth can be depicted analytically by the perturbative theory of optical conductivity; While, the plateau of saturated HHGs and the transition to a nonlinear growth are caused by the quantum destructive interference and constructive interference of harmonics generated by the electrons corresponding to the lattice momentums around Dirac points and M points in Brillouin zone, respectively. In particular, we find that tuning Fermi energy can effectively alter the knee structure while the profile of the knee structure is not sensitive to the temperature. Our calculations of the third-order harmonic vs. tuning Fermi energy are compared with recent experiment showing a good agreement. Our predicted knee structure and its associated properties are observable with the current experimental techniques.

Atomic memory based on recoil-induced resonances

In this work, we perform a detailed theoretical and experimental investigation of an atomic memory based on recoil-induced resonance in cold cesium atoms. We consider the interaction of nearly degenerate pump and probe beams with an ensemble of two-level atoms. A full theoretical density matrix calculation in the extended Hilbert space of the internal and external atomic degrees of freedom allows us to obtain, from first principles, the transient and stationary responses determining the probe transmission and the forward four-wave-mixing spectra. These two signals are generated together at the same order of perturbation with respect to the intensities of pump and probe beams. Moreover, we have investigated the storage of optical information on the spatial modes of light beams in the atomic external degrees of freedom, which provided a simple interpretation for the previously reported nonvolatile character of this memory. The retrieved signals after storage reveal the equivalent role of probe transmission and four-wave mixing, as the two signals have similar amplitudes. Probe transmission and forward four-wave-mixing spectra were then experimentally measured for both continuous excitation and after storage. The experimental observations are in good agreement with the developed theory, and they open another pathway for the reversible exchange of optical information with atomic systems.

Variational determination of the two-electron reduced density matrix within the doubly occupied configuration interaction framework: Treatments of triplet N-electron systems.

In this work, we perform variational calculations of two-electron reduced density matrices corresponding to open-shell N-electron systems within the framework of the doubly occupied configuration interaction treatment, traditionally limited to studies of closed-shell systems. This has allowed us to provide a satisfactory description of molecular systems in triplet states following two methods. One of them adds hydrogen atoms at an infinite distance of the triplet system studied, constituting a singlet supersystem. The energies and reduced density matrices of the triplet system are obtained by removing the contributions of the added atoms from the singlet supersystem results. The second procedure involves variational determination of the two-electron reduced density matrices corresponding to the triplet systems by means of adequate couplings of basis-set functions. Both models have been studied by imposing N-representability conditions on the reduced density matrix calculations. Results obtained from these methods for molecular systems in triplet ground states are reported and compared with those provided by benchmark methods.

Nonlinear magnetoelectric effect in atomic vapor and its application to precision radio-frequency magnetometry

We demonstrate the nonlinear magnetoelectric (ME) effect in atomic vapor achieved through the parametric interaction of optical electric and radio-frequency (rf) magnetic fields leading to the generation of new optical electric fields. Density matrix calculations are performed to validate the experimental results. Moreover, the predicted dependence of the generated optical electric field amplitudes on the rf magnetic field strength is experimentally verified to confirm the ME effect. The system provides a technique for precision rf magnetometry based on this phenomenon. We could experimentally achieve an rf magnetic field sensitivity of 70 $\mathrm{fT}/\sqrt{\text{Hz}}$ at 1 kHz to 7.5 $\mathrm{pT}/\sqrt{\text{Hz}}$ at 3 MHz for zero bias field in an unshielded environment. The appealing features of the proposed rf magnetometer using our system include a high dynamic range up to ${10}^{12}$, 6 dB bandwidth of 450 kHz, and arbitrary frequency resolution, which are intrinsic to the nonlinear ME effect in the medium.

DFT exploration to tune the silyl group as anchoring unit on the performance of dye-sensitized solar cells: an approach to suppress dye leaching from semiconductor surface.

In this work, we report the lower stability of dyes containing cyanoacrylic acid anchoring group on semiconductor TiO2 surface compared to the corresponding silyl unit in dye-sensitized solar cell. Density functional theory (DFT) calculations have been performed with simple donor (N,N diphenylamine) and π-conjugated spacers, with silyl anchoring groups to examine the efficiency of DSSCs. The calculated results in CAM-B3LYP/6-31G(d)/CPCM(THF) reveal that the cyanoacrylic acid anchoring group would have weaker coordination on semiconductor TiO2 surface compared to the silyl anchoring group on the same surface. The designed dyes 1-7 exhibit comparable or in cases superior optical properties than that of the reference dye molecule with cyanoacrylic acid as an anchoring group. All designed dyes have lower ΔGrejection values implying efficient and faster electron recombination between the dye and electrolyte. The electron transition coefficient for these dyes is higher enough (~72-87%) suggesting successful electron propagation from dye to the semiconductor. The electron-donating methyl and ethyl groups show lower ΔGrejection values than the commonly studied -OEt substitution with the silyl anchoring group. The extended π conjugation for better electronic propagation and higher λmax values have been achieved with simple ethylene and butadiene units in the dye molecules. Dye 7 with butadiene as π-spacer unit shows superior oscillatory strength (f) of 2.19 and light-harvesting efficiency (LHE) of 0.99 than the other studied dyes and reference dye with carboxylic anchoring group (TA-ST-CA). The lowest ΔGrejection value (0.53 eV) of dye 7 suggests better electronic recombination than all the other dyes studied here. Transition Density matrix and PDOS calculations with the representative dye 7 suggest a good electronic propagation from the dye to the semiconductor. The incorporation of a highly π-conjugated spacer 4,8-di(thiophen-2-yl)-1H,5H-benzo[1,2-c:4,5-c']bis([1,2,5]thiadiazole) in dye 7 (7-BBT) showed remarkable enhancement in the absorption maxima ~800 nm corresponds to the UV-vis and NIR regions. The DFT calculated results shed light on designing new DSSCs with silyl anchoring groups for enhanced stability and superior efficiency.

Generation of metastable krypton using a 124-nm laser

We have realized the optical excitation of krypton to a metastable level with an efficiency as high as $23\phantom{\rule{0.16em}{0ex}}%$ using near-resonant 124-nm light produced by four-wave mixing in mercury vapor. Self-absorption in mercury is circumvented by adjusting the detuning and phase matching according to experimental and theoretical characterizations. Density-matrix calculations of the metastable krypton generation agree with the measured dependencies of the excitation efficiency, indicating pathways towards a further improvement. The obtained excitation efficiency, being one order of magnitude higher than that of previously demonstrated techniques, enables an extension of the metastable density regime for atomic physics applications, including magnetometry, atom lithography, and radioisotope dating.

Many-core acceleration of the first-principles all-electron quantum perturbation calculations

The first-principles quantum perturbation theory, also called density-functional perturbation theory (DFPT), is the state-of-the-art formalism to directly link the experimental response properties of the materials with the quantum modeling of the electrons. Here in this work, we present an implementation of all-electron DFPT for massively parallel Sunway many-core architectures to accelerate DFPT calculation. We have paid special attention to the calculation of the response density matrix, the real-space integration of the response density as well as the response Hamiltonian matrix. We also employ the fast and massively parallel linear scaling scheme together with the load balance algorithm for the DFPT calculations to improve the scalability. Using the above approaches, the accurate first-principles quantum perturbation calculations can be extended over millions of cores.

Density matrix calculation of the dark matter abundance in the Higgs induced right-handed neutrino mixing model

We present new results on the calculation of the dark matter relic abundance within the Higgs induced right-handed neutrino mixing model, solving the associated density matrix equation. For a benchmark value of the dark matter mass MDM = 220 TeV, we show the evolution of the abundance and how this depends on reheat temperature, dark matter lifetime and source right-handed neutrino mass MS, with the assumption MS < MDM. We compare the results with those obtained within the Landau-Zener approximation, showing that the latter largely overestimates the final abundance giving some analytical insight. However, we also notice that since in the density matrix formalism the production is non-resonant, this allows source right-handed neutrino masses below the W boson mass, making dark matter more stable at large mass values. This opens an allowed region for initial vanishing source right-handed neutrino abundance. For example, for MS ≳ 1 GeV, we find MDM≳ 20 PeV. Otherwise, for MS > MW∼ 100 GeV, one has to assume a thermalisation of the source right-handed neutrinos prior to the freeze-in of the dark matter abundance. This results into a large allowed range for MDM, depending on MS. For example, imposing MS ≳ 300 GeV, allowing also successful leptogenesis, we find 00.5 ≲ MDM/TeV ≲ 50. We also discuss in detail leptogenesis with two quasi-degenerate right-handed neutrinos, showing a case when observed dark matter abundance and matter-antimatter asymmetry are simultaneously reproduced. Finally, we comment on how an initial thermal source right-handed neutrino abundance can be justified and on how our results suggest that also the interesting case where MDM < MS, embeddable in usual high scale two right-handed neutrino seesaw models, might be viable.

Efficient parallel linear scaling method to get the response density matrix in all-electron real-space density-functional perturbation theory

The real-space density-functional perturbation theory (DFPT) for the computations of the response properties with respect to the atomic displacement and homogeneous electric field perturbation has been recently developed and implemented into the all-electron, numeric atom-centered orbitals electronic structure package FHI-aims. It is found that the bottleneck for large scale applications is the computation of the response density matrix, which scales as O(N3). Here for the response properties with respect to the homogeneous electric field, we present an efficient parallel linear scaling algorithm for the response density matrix calculation. Our scheme is based on the second-order trace-correcting purification and the parallel sparse matrix–matrix multiplication algorithms. The new scheme reduces the formal scaling from O(N3) to O(N), and shows good parallel scalability over tens of thousands of cores. As demonstrated by extensive validation, we achieve a rapid computation of accurate polarizabilities using DFPT. Finally, the computational efficiency of this scheme has been illustrated by making the scaling tests and scalability tests on massively parallel computer systems.

Application of CS in weak signal quantum measurement and protein structure calculation

It has been more than 15 years since the compressed sensing (CS) theory was put forward in 2006. The CS theory has been successfully applied and developed in many classical fields such as the single-pixel camera, CT imaging and radar imaging system, but there is still much space for its applications in quantum and biological system. In this paper, the basic knowledge of CS theory and its application/development history are briefly introduced. Then a review is given on a series of achievements in the CS theory applied in quantum precision measurement and biological system, mainly obtained by the Center for Quantum Technology Research in Beijing Institute of Technology (BIT). The review covers several different topics including the measurement and imaging in extremely weak signals, the density matrix calculation for multi-body quantum state tomography and the protein structure reconstruction from matrix completion theory, which is developed based on the CS theory. With the above reviews, we show that the CS theory has great potential for further application, not only in weak signal detection, but also in quantum calculation and even the research on bio-macromolecules. In the end, the summary and outlook are given on the future developments and applications of the CS theory.

Gapless spin liquid and valence-bond solid in the J1 - J2 Heisenberg model on the square lattice: Insights from singlet and triplet excitations

The spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice represents one of the simplest examples in which the effets of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for $J_2/J_1 \approx 0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48 \lesssim J_2/J_1 \lesssim 0.54$) and a valence-bond solid (for $0.54 \lesssim J_2/J_1 \lesssim 0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A.W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)] reconcile the contraddicting results obtained within different approaches over the years.

Lamb-dips and Lamb-peaks in the saturation spectrum of HD.

The saturation spectrum of the R(1) transition in the (2-0) band in hydrogen deuteride (HD) is found to exhibit a composite line shape, involving a Lamb-dip and a Lamb-peak. We propose an explanation for such behavior based on the effects of crossover resonances in the hyperfine substructure, which is made quantitative in a density matrix calculation. This resolves an outstanding discrepancy on the rovibrational R(1) transition frequency, which is now determined at 217,105,181,901 (50) kHz and in agreement with current theoretical calculations.

Interactions between nonresonant rf fields and atoms with strong spin-exchange collisions

We study the interactions between oscillating nonresonant rf fields and atoms with strong spin-exchange collisions in the presence of a weak dc magnetic field. We find that the atomic Larmor precession frequency shows a new functional form to the rf field parameters when the spin-exchange collision rate is tuned. In the weak rf field amplitude regime, a strong modification of atomic Larmor frequency appears when the spin-exchange rate is comparable to the rf field frequency. This effect has been neglected before due to its narrow observation window. We compare the experimental results with density matrix calculations, and explain the data by an underdamped oscillator model. When the rf field amplitude is large, there is a minimum atomic gyromagnetic ratio point due to the rf photon dressing, and we find that strong spin-exchange interactions modify the position of such a point.