Diagonalizations on a correlated basis

Unsymmetrical quantum-dot systems are generally difficult to study using wave-function techniques, like quantum Monte Carlo (QMC) or exact diagonalization (ED) methods. The initial trial wave function for Monte Carlo methods is difficult to find, and the exact diagonalization method can only handle very few particles.In this article a two-dimensional semiconductor quantum dot containing a non-centered impurity ion is studied, using a new exact wave-function method. Results are analyzed and compared to density-functional-theory calculations. The computational method allows one to relax the commonly used lowest-Landau level (LLL) approximation, and it's effects are studied, e.g., on the charge and current density profiles.The method, which is a combination of QMC and ED methods, is described. It combines the scalability of Monte Carlo methods with the benefits of exact diagonalization, and allows one to accurately obtain the wave function for unsymmetrical quantum dots up to more than ten electrons. Also, excited states are accessible and are analyzed in this article.     

Mott-hubbard metal-insulator transition in paramagnetic V2O3: an LDA+DMFT(QMC) study

The electronic properties of paramagnetic V2O3 are investigated by the computational scheme LDA+DMFT(QMC). This approach merges the local density approximation (LDA) with dynamical mean-field theory (DMFT) and uses quantum Monte Carlo simulations (QMC) to solve the effective Anderson impurity model of DMFT. Starting with the crystal structure of metallic V2O3 and insulating (V0.962Cr0.038)2O3 we find a Mott-Hubbard transition at a Coulomb interaction U approximately 5 eV. The calculated spectrum is in very good agreement with experiment. Furthermore, the orbital occupation and the spin state S = 1 determined by us agree with recent polarization dependent x-ray-absorption experiments.     

Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene

We report an implementation of the momentum space quantum Monte Carlo(QMC) method on the interaction model for the twisted bilayer graphene(TBG). The long-range Coulomb repulsion is treated exactly with the flat bands, spin and valley degrees of freedom of electrons taking into account. We prove the absence of the minus sign problem for QMC simulation when either the two valleys or the two spin degrees of freedom are considered.By taking the realistic parameters of the twist angle and interlayer tunnelings into the simulation, we benchmark the QMC data with the exact band gap obtained at the chiral limit, to reveal the insulating ground states at the charge neutrality point(CNP). Then, with the exact Green's functions from QMC, we perform stochastic analytic continuation to obtain the first set of single-particle spectral function for the TBG model at CNP. Our momentum space QMC scheme therefore offers the controlled computation pathway for systematic investigation of the electronic states in realistic TBG model at various electron fillings.     

Calculation of photoemission spectra of the doped Mott insulator using LDA+DMFT(QMC)

The spectral properties of La_1–xSr_xTiO₃, a doped Mott insulator with strong Coulomb correlations, are calculated with the ab initio computational scheme LDA+DMFT(QMC). It starts from the non-interacting electronic band structure as calculated by the local density approximation (LDA), and introduces the missing correlations by the dynamical mean-field theory (DMFT), using numerically exact quantum Monte-Carlo (QMC) techniques to solve the resulting self-consistent multi-band single-impurity problem. The results of the LDA+DMFT(QMC) approach for the photoemission spectra of La_1–xSr_xTiO₃ are in good agreement with experiment and represent a considerable qualitative and quantitative improvement on standard LDA calculations. Received 20 May 2000 and Received in final form 27 July 2000     

Molecular physics and chemistry applications of quantum Monte Carlo

We discuss recent work with the diffusion quantum Monte Carlo (QMC) method in its application to molecular systems. The formal correspondence of the imaginary-time Schrödinger equation to a diffusion equation allows one to calculate quantum mechanical expectation values as Monte Carlo averages over an ensemble of random walks. We report work on atomic and molecular total energies, as well as properties including electron affinities, binding energies, reaction barriers, and moments of the electronic charge distribution. A brief discussion is given on how standard QMC must be modified for calculating properties. Calculated energies and properties are presented for a number of molecular systems, including He, F, F^?, H₂, N, and N₂. Recent progress in extending the basic QMC approach to the calculation of “analytic” (as opposed to finite-difference) derivatives of the energy is presented, together with an H₂ potential-energy curve obtained using analytic derivatives.     

A new approach to electron-electron interactions in strongly correlated systems at arbitrary spin-polarization and temperature

The uniform electron fluid is the reference model for density functional calculations. Even for this system, many-body perturbation theory, and related methods become questionable when the density parameter r_s exceeds unity. Hence, quantum Monte Carlo (QMC) simulation has been almost the only applicable method. We review a new approach, which uses a mapping of the quantum fluid to a classical Coulomb fluid, based on density-functional concepts. It is applicable at finite temperatures and arbitrary spin polarizations as well, and correctly recovers even the logarithmic terms in the exchange and correlations energies close to T=0. We show by detailed comparison with available QMC data that the method yields accurate pair-distribution functions, spin-dependent energies, static local-field factors, Landau parameter-based quantities like m∗ and g∗, for strongly coupled electron fluids.     

Non-Fermi-liquid phases in the two-band Hubbard model: finite-temperature exact diagonalization study of Hund's rule coupling

The two-band Hubbard model involving subbands of different widths is investigated via finite-temperature exact diagonalization (ED) and dynamical mean field theory (DMFT). In contrast to the quantum Monte Carlo (QMC) method which at low temperatures includes only Ising-like exchange interactions to avoid sign problems, ED permits a treatment of Hund's exchange and other onsite Coulomb interactions on the same footing. The role of finite-size effects caused by the limited number of bath levels in this scheme is studied by analyzing the low-frequency behavior of the subband self-energies as a function of temperature, and by comparing with numerical renormalization group (NRG) results for a simplified effective model. For half-filled, non-hybridizing bands, the metallic and insulating phases are separated by an intermediate mixed phase with an insulating narrow and a bad-metallic wide subband. The wide band in this phase exhibits different degrees of non-Fermi-liquid behavior, depending on the treatment of exchange interactions. Whereas for complete Hund's coupling, infinite lifetime is found at the Fermi level, in the absence of spin-flip and pair-exchange, this lifetime becomes finite. Excellent agreement is obtained both with new NRG and previous QMC/DMFT calculations. These results suggest that-finite temperature ED/DMFT might be a useful scheme for realistic multi-band materials.     

Simple classical mapping of the spin-polarized quantum electron gas: distribution functions and local-field corrections

We use the now well known spin unpolarized exchange-correlation energy E(xc) of the uniform electron gas as the basic "many-body" input to determine the temperature T(q) of a classical Coulomb fluid having the same correlation energy as the quantum system. It is shown that the spin-polarized pair distribution functions (SPDFs) of the classical fluid at T(q), obtained using the hypernetted chain equation, are in excellent agreement with those of the T = 0 quantum fluid obtained by quantum Monte Carlo (QMC) simulations. These methods are computationally simple and easily applied to problems which are currently beyond QMC simulations. Results are presented for the SPDFs and the local-field corrections to the response functions of the electron fluid at T = 0 and finite T.     

Traces of the evolution from Mott insulator to a band insulator in the pair excitation spectra

We inspect the fundamental difference between the correlated band insulators (BI) and the Mott insulators (MI) from the perspective of the dynamical pair excitations. To this end, we investigated the physics of the two-plane Hubbard model by employing the well-tested dynamical mean field theory (DMFT) together with the quantum Monte Carlo (QMC) method. At half-filling our results clearly indicate that while the spectral weight of the pair excitation becomes minimal at MI which corresponds to a diminishing of the double occupancy, the opposite occurs at BI. We then discuss the effect of doping and find that the correlated band insulator and the Mott insulator robust at low doping concentration and the metallic state emerges at larger doping. The pair spectral function demonstrates that the metallic state of doped MI is strongly different from that of doped BI and it is readily reflected in the lineshape of the spectra. We discuss the implication of our results in the context of the two-particle spectroscopy.     

Quantum Quenches with Random Matrix Hamiltonians and Disordered Potentials

We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists of sudden switching‐on the off‐diagonal elements of the Hamiltonian. In the latter case, it is sudden switching‐on of the hopping between adjacent lattice sites. The quench‐induced ensembles are compared with the so‐called “quantum micro‐canonical” (QMC) ensemble describing quantum superpositions with fixed energy expectation values. Our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the QMC ensemble. Away from the QMC condensation regime, the overall agreement with the QMC predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate.     

Asymmetry in the nuclear magnetic shielding tensor

The applicability of Green's function (GF) and Feynman path-integral quantum Monte Carlo (QMC) methods for the simulation of cyclic networks with (4n + 2) and 4n (n = 1, 2, 3, …) electrons is analysed. Both QMC techniques are employed in simulations on the basis of the simple Hückel Hamiltonian which is exclusively defined by nearest-neighbour hopping elements. In addition we have used the Pariser-Parr-Pople (PPP) Hamiltonian to perform GF QMC simulations. The electronic energies E derived by the QMC methods are compared either with Hückel molecular orbital (HMO) results or exact configuration interaction data where (π) electronic correlations are fully taken into account. A sign problem occurs in QMC simulations of 4n annulenes. This leads to an error in the total energy in the standard formulations of the employed QMC techniques, which is enhanced with decreasing ring size. A simple modification in the QMC formalisms is suggested to avoid the numerical uncertainties caused by the sign problem in 4n annulenes. Renormalization of the kinetic hopping integrals t by t cos (π/M) with M abbreviating the number of atomic sites leads to ground state energies as well as any other quantity close to the values derived by conventional diagonalization techniques. Substitution of t against t cos (π/M) conserves a common sign of all matrix elements containing the hopping. The occurrence of negative probabilities, which lead to numerical problems in the QMC simulations, is thereby prevented. The transformation suggested in 4n rings has a formal connection to so-called Möbius rings.     

Residue-specific NH exchange rates studied by NMR diffusion experiments

We present a novel approach to the investigation of rapid (>2s(-1)) NH exchange rates in proteins, based on residue-specific diffusion measurements. (1)H, (15)N-DOSY-HSQC spectra are recorded in order to observe resolved amide proton signals for most residues of the protein. Human ubiquitin was used to demonstrate the proposed method. Exchange rates are derived directly from the decay data of the diffusion experiment by applying a model deduced from the assumption of a two-site exchange with water and the "pure" diffusion coefficients of water and protein. The "pure" diffusion coefficient of the protein is determined in an experiment with selective excitation of the amide protons in order to suppress the influence of magnetization transfer from water to amide protons on the decay data. For rapidly exchanging residues a comparison of our results with the exchange rates obtained in a MEXICO experiment showed good agreement. Molecular dynamics (MD) and quantum mechanical calculations were performed to find molecular parameters correlating with the exchangeability of the NH protons. The RMS fluctuations of the amide protons, obtained from the MD simulations, together with the NH coupling constants provide a bilinear model which shows a good correlation with the experimental NH exchange rates.     

Magnetic properties of diluted magnetic semiconductors: Quantum Monte Carlo approach

The magnetic correlation between magnetic impurities in semiconductors is investigated by performing the quantum Monte Carlo (QMC) simulation. The Anderson Hamiltonian with the realistic parameters obtained by the local density approximation (LDA) calculation is employed. The LDA calculation gives a dispersion of the host (GaAs) electron and the mixing energy between host and magnetic impurity (Mn). The mixing between host and impurity electrons generates the impurity bound state in the energy gap of semiconductors. The long range ferromagnetic coupling is observed when the Fermi energy locates between the band edge and the impurity bound state. The ferromagnetic coupling is enhanced by decreasing temperature.     

Electron emission from diamondoids: a diffusion quantum Monte Carlo study

We present density-functional theory (DFT) and quantum Monte Carlo (QMC) calculations designed to resolve experimental and theoretical controversies over the optical properties of H-terminated C nanoparticles (diamondoids). The QMC results follow the trends of well-converged plane-wave DFT calculations for the size dependence of the optical gap, but they predict gaps that are 1-2 eV higher. They confirm that quantum confinement effects disappear in diamondoids larger than 1 nm, which have gaps below that of bulk diamond. Our QMC calculations predict a small exciton binding energy and a negative electron affinity (NEA) for diamondoids up to 1 nm, resulting from the delocalized nature of the lowest unoccupied molecular orbital. The NEA suggests a range of possible applications of diamondoids as low-voltage electron emitters.     

A novel approach to the simulation of nitroxide spin label EPR spectra from a single truncated dynamical trajectory

A simple effective method for calculation of EPR spectra from a single truncated dynamical trajectory of spin probe orientations is reported. It is shown that an accurate simulation can be achieved from the small initial fraction of a dynamical trajectory until the point when the autocorrelation function of re-orientational motion of spin label has relaxed. This substantially reduces the amount of time for spectra simulation compared to previous approaches, which require multiple full length trajectories (normally of several microseconds) to achieve the desired resolution of EPR spectra. Our method is applicable to trajectories generated from both Brownian dynamics and molecular dynamics (MD) calculations. Simulations of EPR spectra from Brownian dynamical trajectories under a variety of motional conditions including bi-modal dynamics with different hopping rates between the modes are compared to those performed by conventional method. Since the relatively short timescales of spin label motions are realistically accessible by modern MD computational methods, our approach, for the first time, opens the prospect of the simulation of EPR spectra entirely from MD trajectories of real proteins structures.     

交变电场驱动下三量子点中双电子的动力学

采用三点哈巴德模型及弗洛盖定理．研究了交变电场驱动下线形三量子点分子中双电子的动力学行为。由于系统哈密顿量中不包含自旋反转项,所以系统单态和三重态子空间是完全解耦的,可以分开进行讨论。研究表明,自旋三重态九维子空间还可以进一步分解成三个不相耦合的子空间,在每一个子空间中,动力学行为与交变电场驱动的双量子点中双电子的动力学行为相似。对自旋单态6维子空间,数值计算还表明,在合适的外加交变电场驱动下,电子在量子点之间的隧穿被抑制．初始局域在一个量子点中的两个电子能够在一定时间内保持其局域状态。     

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer–Büttiker scattering theory and the nonequilibrium Green’s function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.     

The effect of dilute nitrogen on nonlinear optical properties of the InGaAsN/GaAs single quantum wells

Employing the extended dynamical mean field theory (EDMFT) and the quantum Monte Carlo (QMC) method, we investigate the effect of the spatial fluctuations in the two-band Hubbard model with anisotropic bandwidth in the vicinity of the Mott metal-insulator transition. At half filling, we demonstrate that while the inclusion of the non-local spin-spin interaction amounts to enhancing the correlation and suppressing the metallic character, the orbitally selective Mott transition (OSMT) remains stable for various strengths of the non-local correlation. The same is true when the system is doped away from half filling. The OSMT phase is evidenced at low dopant concentration and the simultaneous metallic phase emerges at overdoped regime. From the analysis of the self energy, it follows that the nature of the metallic phase upon doping violates the Fermi liquid character and persists at considerably large doping. Our theory also offers a new perspective for the investigation of the non-local fluctuation in the multi-orbital system within the single-site scheme.     

Generalized effective-potential Landau theory for the two-dimensional extended Bose-Hubbard model

We analytically study the quantum phase diagrams of ultracold dipolar Bose gases in an optical square lattice at zero temperature by using the generalized effective-potential Landau theory (GEPLT). For a weak nearest-neighbor repulsion, our analytical results are better than the third-order strong-coupling expansion theory calculation. In contrast to a previous quantum Monte Carlo (QMC) simulation, we analytically calculate phase transition boundaries up to the third-order hopping, which are in excellent agreement with QMC simulations for second-order phase transition.     

Controlled dephasing of a quantum dot in the Kondo regime

Kondo correlation in a spin polarized quantum dot (QD) results from the dynamical formation of a spin singlet between the dot's net spin and a Kondo cloud of electrons in the leads, leading to enhanced coherent transport through the QD. We demonstrate here significant dephasing of such transport by coupling the QD and its leads to potential fluctuations in a nearby "potential detector." The qualitative dephasing is similar to that of a QD in the Coulomb blockade regime in spite of the fact that the mechanism of transport is quite different. A much stronger than expected suppression of coherent transport is measured, suggesting that dephasing is induced mostly in the "Kondo cloud" of electrons within the leads and not in the QD.