Nonperturbative Method Research Articles

Floquet bands and photon-induced topological edge states of graphene nanoribbons* *Project supported by the starting foundation of Chongqing University (Grant No. 0233001104429), the National Natural Science Foundation of China (Grant No. 11847301), and the Fundamental Research Funds for the Central Universities, China (Grant No. 2020CQJQY-Z003).

Floquet theorem is widely used in the light-driven systems. But many 2D-materials models under the radiation are investigated with the high-frequency approximation, which may not be suitable for the practical experiment. In this work, we employ the non-perturbative Floquet method to strictly investigate the photo-induced topological phase transitions and edge states properties of graphene nanoribbons under the light irradiation of different frequencies (including both low and high frequencies). By analyzing the Floquet energy bands of ribbon and bulk graphene, we find the cause of the phase transitions and its relation with edge states. Besides, we also find the size effect of the graphene nanoribbon on the band gap and edge states in the presence of the light.

Towards fully nonperturbative computations of inelastic ℓN scattering cross sections from lattice QCD

We propose a fully nonperturbative method to compute inelastic lepton-nucleon ($\ensuremath{\ell}N$) scattering cross sections using lattice quantum chromodynamics (QCD). The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino-nucleon scattering experiments, for which perturbative analysis is invalidated. The basic building block is the forward Compton-scattering amplitude, or the hadronic tensor, computed on a Euclidean lattice. A total cross section is constructed from the hadronic tensor by multiplying a phase space factor and integrating over the energy and momentum of final hadronic states. The energy integral that induces a sum over all possible final states is performed implicitly by promoting the phase space factor to an operator written in terms of the transfer matrix on the lattice. The formalism is imported from that of the inclusive semileptonic $B$ meson decay [P. Gambino and S. Hashimoto, Phys. Rev. Lett. 125, 032001 (2020)] and generalized to compute the $\ensuremath{\ell}N$ scattering cross sections and their moments, as well as the virtual correction to the nuclear $\ensuremath{\beta}$ decay.

Intense-terahertz-laser modulated photoionization cross section of shallow-donor impurity in semiconductors in a magnetic field

The effects of intense terahertz laser and magnetic fields on the photoionization cross section (PICS) of shallow-donor impurity in semiconductors are investigated within the Faraday configuration. The donor ground-state energy level and its wave function are calculated using a combination of nonperturbative and variational methods where radiation field is exactly included through a laser-dressed Coulomb potential (LdCP). We find that a competition between donor ground-state binding energy and optical integrals in tailoring the magnitudes and peak positions of PICS is achieved by external fields via the LdCP. In this way, the magnitudes and peak positions of PICS can be decreased or increased and effectively tuned with an appropriate choice of external fields. The overall shape of PICS is optically anisotropic, which is more pronounced in the z-polarization direction for large laser field intensity or low magnetic field. In the vicinity of ωc, the overall shape of PICS in the z-polarization direction changes into that of PICS in the x-polarization direction. Our theoretical findings hold promising applications in designing and developing new efficient impurity-based devices manipulated by external fields.

The effects of hydrostatic pressure and temperature on photoionization cross section of impurities in semiconductors under magnetic and intense terahertz laser fields

Abstract We have presented a theoretical study on shallow-donor-related photoionization cross section (PICS) in semiconductors subjected to hydrostatic pressure, magnetic field, and intense laser field within the Vogit configuration. Calculations are performed for the donor ground state using a combination of nonperturbative and variational methods in which intense laser field is exactly taken into account via a laser-dressed Coulomb potential (LdCP). We find that the overall shape of shallow-donor-related PICS depends upon the incident optical field polarization, which is more significant when the incident optical field polarization is parallel to the magnetic field. The donor ground-state binding energy and the optical integrals act in an opposite manner to tailor the magnitudes and peak positions of shallow-donor-related PICS by changing radiation field through the LdCP or by changing magnetic field, hydrostatic pressure, and temperature, leading to a blueshift or redshift of shallow-donor-related PICS spectrum and to a decrease or increase of shallow-donor-related PICS magnitude manipulated by these factors. Thus, we can control the properties of shallow-donor-related PICS with an appropriate choice of two external applied fields, hydrostatic pressure, and temperature to meet some special needs in designing and developing new efficient optoelectronic devices.

Facile All-Optical Method for In Situ Detection of Low Amounts of Ammonia.

SummaryAs a key precursor for nitrogenous compounds and fertilizer, ammonia affects our lives in numerous ways. Rapid and sensitive detection of ammonia is essential, both in environmental monitoring and in process control for industrial production. Here we report a novel and nonperturbative method that allows rapid detection of ammonia at low concentrations, based on the all-optical detection of surface-enhanced Raman signals. We show that this simple and affordable approach enables ammonia probing at selected regions of interest with high spatial resolution, making in situ and operando observations possible.

Impact of exciton delocalization on exciton-vibration interactions in organic semiconductors

Organic semiconductors exhibit properties of individual molecules and extended crystals simultaneously. The strongly bound excitons they host are typically described in the molecular limit, but excitons can delocalize over many molecules, raising the question of how important the extended crystalline nature is. Using accurate Green's function based methods for the electronic structure and non-perturbative finite difference methods for exciton-vibration coupling, we describe exciton interactions with molecular and crystal degrees of freedom concurrently. We find that the degree of exciton delocalization controls these interactions, with thermally activated crystal phonons predominantly coupling to delocalized states, and molecular quantum fluctuations predominantly coupling to localized states. Based on this picture, we quantitatively predict and interpret the temperature and pressure dependence of excitonic peaks in the acene series of organic semiconductors, which we confirm experimentally, and we develop a simple experimental protocol for probing exciton delocalization. Overall, we provide a unified picture of exciton delocalization and vibrational effects in organic semiconductors, reconciling the complementary views of finite molecular clusters and periodic molecular solids.

Functional renormalization group study of the critical region of the quark-meson model with vector interactions

The critical region of the two flavour quark-meson model with vector interactions is explored using the Functional Renormalization Group, a non-perturbative method that takes into account quantum and thermal fluctuations. Special attention is given to the low temperature and high density region of the phase diagram, which is very important to construct the equation of state of compact stars. As in previous studies, without repulsive vector interaction, an unphysical region of negative entropy density is found near the first order chiral phase transition. We explore the connection between this unphysical region and the chiral critical region, especially the first order line and spinodal lines, using also different values for vector interactions. We find that the unphysical negative entropy density region appears because the s=0 isentropic line, near the critical region, is displaced from its T=0 location. For certain values of vector interactions this region is pushed to lower temperatures and high chemical potentials in such way that the negative entropy density region on the phase diagram can even disappear. In the case of finite vector interactions, the location of the critical end point has a non-trivial behaviour in the T-mu _B plane, which differs from that in mean field calculations.

Bootstrapping massive quantum field theories

We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of the matrix of inner products between asymptotic states (in and out) and states created by the action of local operators on the vacuum. The corresponding matrix elements involve scattering amplitudes, form factors and spectral densities of local operators. We test this method in two-dimensional QFTs by setting up a linear optimization problem that gives a lower bound on the central charge of the UV CFT associated to a QFT with a given mass spectrum of stable particles (and couplings between them). Some of our numerical bounds are saturated by known form factors in integrable theories like the sine-Gordon, E8 and O(N) models.

Anharmonicity of the acoustic modes of graphene

The anharmonicity of the acoustic phonon dispersion of graphene has been studied by the harmonic linear response (HLR) approach at finite temperature. This is a non-perturbative method based on the linear response of the system to applied forces, as derived from equilibrium computer simulations. Anharmonic shifts are analyzed in the long-wavelength limit at room temperature, with emphasis in the effect of applied tensile or compressive in-plane stress. The simulation results are compared with available analytical models, based either on first-order perturbation theory or on a description by anomalous exponents. The simulations show better agreement to the expectations of the perturbational approach. The effect of temperature and zero-point vibrations on the acoustic out-of-plane anharmonic shifts of graphene are briefly reviewed.

The effects of hydrostatic pressure and temperature on the nonlinear optical properties of shallow-donor impurities in semiconductors in a magnetic field

We present a theoretical study of the nonlinear optical properties of shallow-donor impurities in semiconductors subjected to magnetic fields, hydrostatic pressures, and intense laser illumination within the Voigt configuration. The donor energy levels and their wave functions are obtained using a combination of nonperturbative and variational methods where intense laser field effects are exactly taken into account through a laser-dressed Coulomb potential (LdCP). The combined effects of radiation and magnetic fields, hydrostatic pressures, and temperatures on the linear, third-order nonlinear, and total optical absorption coefficients (OACs) for the 1s→2p± and 2pz transitions are investigated using a compact density-matrix approach. We find that the transition energies and geometric factors can be increased or decreased by changing external fields via the LdCP or by changing hydrostatic pressures and temperatures. In this way, saturable absorption depends not only on the incident optical intensity but also on the laser field, which is more easily realized in the z-polarization direction. The peak positions and magnitudes of the linear, third-order nonlinear, and total OACs can be effectively adjusted with an appropriate choice of these external perturbations. Moreover, hydrostatic pressures and temperatures affect these OACs in an opposite way. This opens a promising route to design new and efficient impurity-based devices manipulated by external perturbations.

Non-Destructive, Non-Invasive Noise Measurements for Metallic Lithium Anodes for Lithium Ion Batteries

Electrochemical Noise measurements have been in the spotlight of electrochemical analysis for measurements on stochastic modes of corrosion since the days of Dawson (Hladky and Dawson Corrosion Science 21(4), (1981),317-322). More recently, electrochemical noise measurements for fuel cells and batteries came up as non-invasive and non-perturbing testing methods that can be used for research(Journal of The Electrochemical Society, 165 (11) A2557-A2562 (2018)) and a potential real-time monitoring tool (Denisov et.al. Fuel Cells 17,(2017),225-237).Metallic lithium anodes are currently commercially employed for non-rechargeable batteries (e.g LiSOCl2 or LiMnO2). The main hurdle along the way of implementation in rechargeable batteries is the dendrite formation during the charging process (Cheng, et.al. Chem. Rev. 2017, 117, 10403−10473). The formation of dendrites during charging can lead to catastrophic failure of the batteries including thermal runaway. Though studies on avoiding such failures through either modifying the surface of the electrode and/or the kinetics of deposition are underway, however, as indicated by the review: “more smartly designed in situ or operando techniques are urgently needed to track the process in a working cell”.We have been working on battery noise measurements for the past number of years (Turkish Journal of Chemistry, 42, (2018), 859-868). We have recently shown that the noise of primary Li/MnO2 batteries increase to measurable levels upon suffering a short circuit (Journal of the Electrochemical Society 165(11),(2018),A2557-A2562) and that this is due to the uneven discharge of the metallic lithium anode(Journal of the Electrochemical Society, submitted).In this contribution, we are going to be reporting electrochemical noise as a truly operando method to study dendrite formation. As the measurement requires no modification to the cell (i.e. no windows in the case or the current collectors, no geometry change, not a half cell) and no perturbation in the applied current or the voltage, it is the ultimate non-invasive and non-perturbing method that has the potential to be used as not only a research tool, but also a real-time implementable sensor that can be commercially deployed.As shown in the figure below, using a metallic lithium anode, the noise after a charging attempt with a high current does show an increased noise level due to the uneven formation of dendrites. Figure 1

Latest Results on Lattice Calculation Concerning K → π ℓ + ℓ − Decays

The K → π ℓ + ℓ − decay is a flavor changing neutral current process which is forbidden at tree level in the Standard Model. This suppression causes the decay to be sensitive to potential New Physics. The decay channels are dominated by long-distance contributions, which require non-perturbative methods of investigation. Previous lattice calculations by the RBC and UKQCD collaborations, at unphysical kaon/pion masses, have successfully extracted the matrix elements needed to describe the form factor of the decays. A new lattice calculation, on a gauge configuration with m π ≈ 140 MeV and m K ≈ 500 MeV, is underway and will be discussed here.

Spectral and transport properties of quark–gluon plasma in a nonperturbative approach

Nonperturbative methods play an important role in quantum many-body systems, especially in situations with an interplay of continuum and bound states and/or large coupling strengths between the constituents. Employing the Luttinger-Ward functional (LWF) we have computed the equation of state (EoS) of the quark-gluon plasma (QGP) using fully dressed selfconsistent 1- and 2-body propagators. We first give an alternative derivation of our previously reported results for resumming the ladder diagram series of the LWF using a "matrix log" technique which accounts for dynamically formed bound and resonant states. Two types of solutions were found in selfconsistent fits to lattice-QCD data for the EoS, heavy-quark free energy and quarkonium correlators: a strongly coupled scenario (SCS) with broad parton spectral functions and strong meson resonances near the transition temperature vs. a weakly coupled scenario (WCS) with well-defined parton quasiparticles and weak meson resonances. Here, we discuss how these solutions can be distinguished by analyzing the pertinent transport properties. We focus on the specific shear viscosity, $(4\pi )\eta/s$, and the heavy-quark diffusion coefficient, $(2\pi T) {\cal D}_s$, including its mass dependence. At low temperatures, in the SCS, they turn out to be a factor of 2 within their conjectured quantum lower bound, while they are a factor of 2-5 larger in the WCS. At higher temperatures, the transport parameters of the two scenarios approach each other. We propose the ratio $ (4\pi\eta/s)/(2\pi T {\cal D}_s )$ as a measure to distinguish the perturbative and strong-coupling limits of 5/2 and 1, respectively.

Localized rainbows in the QCD phase diagram

We study the phase diagram of strongly interacting matter with light quarks using a recently proposed, small parameter approach to infrared QCD in the Landau gauge. This is based on an expansion with respect to both the inverse number of colors and the pure Yang-Mills coupling in the presence of a Curci-Ferrari mass term. At leading order, this leads to the well-known rainbow equation for the quark propagator with a massive gluon propagator. We solve the latter at nonzero temperature and chemical potential using a simple semi-analytic approximation known to capture the essence of chiral symmetry breaking in the vacuum. In the chiral limit, we find a tricritical point which becomes a critical endpoint in the presence of a nonzero bare quark mass, in agreement with the results of nonperturbative functional methods and model calculations. This supports the view that the present approach allows for a systematic study of the QCD phase diagram in a controlled expansion scheme.

Entangled system-and-environment dynamics: Phase-space dissipaton theory.

Dissipaton-equation-of-motion (DEOM) theory [Y. J. Yan, J. Chem. Phys. 140, 054105 (2014)] is an exact and nonperturbative many-particle method for open quantum systems. The existing dissipaton algebra also treats the dynamics of hybrid bath solvation coordinates. The dynamics of conjugate momentums remain to be addressed within the DEOM framework. In this work, we establish this missing ingredient, the dissipaton algebra on solvation momentums, with rigorous validations against necessary and sufficient criteria. The resulted phase-space DEOM theory will serve as a solid ground for further developments of various practical methods toward a broad range of applications. We illustrate this novel dissipaton algebra with the phase-space DEOM-evaluation on heat current fluctuation.

Defect-limited thermal conductivity in MoS2

The wide measured range of thermal conductivities $(k)$ for monolayer ${\mathrm{MoS}}_{2}$ and the corresponding incongruent calculated values in the literature all suggest that extrinsic defect thermal resistance is significant and varied in synthesized samples of this material. Here we present defect-mediated thermal transport calculations of ${\mathrm{MoS}}_{2}$ using interatomic forces derived from density functional theory combined with Green's function methods to describe phonon-point-defect interactions and a Peierls-Boltzmann formalism for transport. Conductivity calculations for bulk and monolayer ${\mathrm{MoS}}_{2}$ using different density functional formalisms are compared. Nonperturbative first-principles methods are used to describe defect-mediated spectral functions, scattering rates, and phonon $k$, particularly from sulfur vacancies $({V}_{\mathrm{S}})$, and in the context of the plethora of measured and calculated literature values. We find that $k$ of monolayer ${\mathrm{MoS}}_{2}$ is sensitive to phonon-${V}_{\mathrm{S}}$ scattering in the range of experimentally observed densities, and that first-principles $k$ calculations using these densities can explain the range of measured values found in the literature. Furthermore, measured $k$ values for bulk ${\mathrm{MoS}}_{2}$ are more consistent because ${V}_{\mathrm{S}}$ defects are not as prevalent.

Seed and vacuum pair production in strong laser field

Researches on the electron-positron pair production in the presence of the intense laser field are reviewed, motivated by the theoretical importance of the nonperturbative QED problem and the worldwide development of high power laser facilities. According to the distinct experimental requirements and theoretical methods, two types of pair production are elaborated, which are, respectively, pair production in the combination of a seed particle and the strong laser, and vacuum pair production without a seed particle. The origin of the nonperturbative problem caused by the strong field is analyzed. The main ideas, realisation, achievements, validity, challenges and bottleneck problems of the nonperturbative methods developed for each type of the pair production problem are discussed.

Neutron star matter as a relativistic Fermi liquid

The equation of state (EoS) of neutron star matter, constrained by the existence of two-solar-mass stars and gravitational wave signals from neutron star mergers, is analysed using the Landau theory of relativistic Fermi liquids. While the phase diagram of dense and cold QCD matter is still open for scenarios ranging from hadronic to quark matter in the center of neutron stars, a Fermi-liquid treatment is motivated by a microscopic approach starting from a chiral nucleon-meson field theory combined with nonperturbative functional renormalization group methods. In this scheme effects of multipionic fluctuations and repulsive nuclear many-body correlations suggest that the transition to chiral symmetry restoration is shifted to densities above those typically encountered in the neutron star core. Under such conditions a Fermi-liquid description in terms of nucleon quasiparticles appears to be justified. The leading Landau parameters are derived and discussed. Our results are contrasted with a well-known Fermi liquid, namely liquid $^3$He.

Convergence of Nonperturbative Approximations to the Renormalization Group.

We provide analytical arguments showing that the "nonperturbative" approximation scheme to Wilson's renormalization group known as the derivative expansion has a finite radius of convergence. We also provide guidelines for choosing the regulator function at the heart of the procedure and propose empirical rules for selecting an optimal one, without prior knowledge of the problem at stake. Using the Ising model in three dimensions as a testing ground and the derivative expansion at order six, we find fast convergence of critical exponents to their exact values, irrespective of the well-behaved regulator used, in full agreement with our general arguments. We hope these findings will put an end to disputes regarding this type of nonperturbative methods.

Electronic Properties of α−RuCl3 in Proximity to Graphene

In the pursuit of developing routes to enhance magnetic Kitaev interactions in α-RuCl_{3}, as well as probing doping effects, we investigate the electronic properties of α-RuCl_{3} in proximity to graphene. We study α-RuCl_{3}/graphene heterostructures via abinitio density functional theory calculations, Wannier projection, and nonperturbative exact diagonalization methods. We show that α-RuCl_{3} becomes strained when placed on graphene and charge transfer occurs between the two layers, making α-RuCl_{3} (graphene) lightly electron doped (hole doped). This gives rise to an insulator-to-metal transition in α-RuCl_{3} with the Fermi energy located close to the bottom of the upper Hubbard band of the t_{2g} manifold. These results suggest the possibility of realizing metallic and even exotic superconducting states. Moreover, we show that in the strained α-RuCl_{3} monolayer the Kitaev interactions are enhanced by more than 50% compared to the unstrained bulk structure. Finally, we discuss scenarios related to transport experiments in α-RuCl_{3}/graphene heterostructures.