Browsing by Author "Nevidomskyy, Andriy"
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Item Describing strong correlations with mean-field approximations(2012-09-05) Tsuchimochi, Takashi; Scuseria, Gustavo E.; Clementi, Cecilia; Nevidomskyy, AndriyStrong electron correlations in electronic structure theory are purely quantum effects arising as a result of degeneracies in molecules and materials, and exhibit significantly different yet interesting characters than do weak correlations. Although weak correlations have recently been able to be described very efficiently and accurately within single particle pictures, less known are good prescriptions for treating strong correlations efficiently. Brute-force calculations of strong correlations in wave function theories tend to be very computationally-intensive, and are usually limited to small molecules for applications. Breaking symmetry in a mean-field approximation is an efficient alternative to acquire strong correlations with, in many cases, qualitatively accurate results. The symmetry broken in quantum chemistry has been traditionally of spin, in so-called unrestricted methods, which typically break spatial symmetry as a consequence, and vice versa, in most situations. In this work, we present a novel approach to accurately describing strong correlations with a mean-field cost by means of Hartree- Fock-Bogoliubov (HFB) theory. We are inspired by the number-symmetry-breaking in HFB, which, with an attractive particle interaction, accounts for strong correlations, while maintaining spin and spatial symmetry. We show that this attractive interaction must be restricted to the chemically-relevant orbitals in an active space to obtain physically meaningful results. With such constraints, our constrained pairing mean-field theory (CPMFT) can accurately describe potential energy curves of various strongly-correlated molecular systems, by cleanly separating strong and weak correlations. To achieve the correct dissociation limits in hetero-atomic molecules, we have modified our CPMFT functional by adding asymptotic constraints. We also include weak correlations by combining CPMFT with density functional theory for chemically accurate results, and reveal the connection between CPMFT and traditional unrestricted methods. The similarity between CPMFT and unrestricted methods leads us to the idea of constrained active space unrestricted mean-field approaches. Motivated by CPMFT, we partially retrieve spin-symmetry that has been fully broken in unrestricted methods. We allow symmetry breaking only in an active space. This constrained unrestricted Hartree-Fock (CUHF) is an interpolation between two extrema: the fully broken-symmetry solution and the symmetry preserved solution. This thesis defines the theory behind and reports the results of CUHF. We first show that, if an active space is chosen to include only open-shell electrons, CUHF reduces to restricted open-shell Hartree-Fock (ROHF), and such CUHF proves in many ways significantlyItem Exploring aspects of nonequilibrium physics with quantum impurity problems(2014-04-22) Shashi, Aditya; Demler, Eugene; Si, Qimiao; Nevidomskyy, Andriy; Kono, JunichiroTraditionally the study of quantum mechanical ensembles was focused on the exploration of their equilibrium properties: the program has consisted of the classification of the quantum mechanical states of matter, and the identification of the striking phase transitions between them. On the other hand, questions about the out of equilibrium properties of quantum ensembles have largely remained academic until fairly recently. Particularly, the rapid technological progress in the field of atomic physics has enabled experimental demonstrations of nontrivial out of equilibrium phenomena which moreover are describable in terms of relatively simple theoretical models with a few parameters. Thus the time is ripe for a theoretical exploration of nonequilibrium physics. To this end, quantum impurity models offer a natural and simple starting point for studying nonequilibrium phenomena in the context of ultracold atoms, and pave the way toward the study of more complicated systems. I will discuss how the impurity-bath model offers a clean, simple realization of rich phenomenology including the dynamics of polaron formation as well as the orthogonality catastrophe, and can be engineered using dilute mixtures of cold atomic gases. Moreover I will demonstrate how impurity models are also embedded in the more complicated physics of the response of a one-dimensional system to an external perturbation, or a sudden local parameter change. Lastly, I will describe the approach to equilibrium of a more complicated system, the one dimensional Bose gas, following a sudden parameter change, and discuss some of the important questions which arise in this connection: does a quantum mechanical system thermalize? What is the appropriate asymptotic description of a nonequilibrium state? Does such a system retain a memory of its initial state?Item Magnetic Phases and Topological Excitations in Frustrated Magnetic Systems on Honeycomb Lattices(2022-12-02) Li, Shuyi; Nevidomskyy, AndriyIn recent years, there has been an explosion of interest in frustrated magnetic systems on the honeycomb lattice, a geometry well known to be associated with graphene. In this class of spin systems, different types of spin interactions such as Heisenberg exchange, bond-dependent anisotropic magnetic exchanges, and antisymmetric spin interactions may appear at the same time. The varying values of these parameters can greatly affect the magnetic phases and their properties. Understanding the role played by these interactions is significant and valuable for explaining the various experimental phenomena and for providing routes to potentially new honeycomb magnetic materials. In this thesis, I will present our study of three novel phenomena in spin systems on honeycomb lattices. In the first part, I will present our work on explaining the mechanism of an unusual noncollinear magnetic order of Ni$^{2+}$ $S=1$ moments with a nontrivial angle between adjacent spins appearing in a non-centrosymmetric honeycomb nickelate Ni$_2$Mo$_3$O$_8$. With the help of first principles electronic structure calculations and crystal field analysis, we construct an effective spin-1 bilinear-biquadratic model with estimated exchange parameters and single ion anisotropy. By performing the variational mean-field and linear spin-wave theory calculations, we find that the crucial key to explaining the observed noncollinear spin structure is the inclusion of the Dzyaloshinskii-Moriya interaction between the neighboring spins. In the second part, I will present our study of the topological properties and magnon Hall effect in a three-dimensional ferromagnet CrI$_3$ that crystallizes in the ABC stacked honeycomb layers. We find that the magnon band structure and Chern numbers of the magnon branches are significantly affected by the interlayer coupling $J_c$. Intriguingly, we find several Weyl magnon phases separating the non-equivalent Chern insulating phases, tuned by the ratio of the interlayer coupling $J_c$ and the third-neighbor Heisenberg interaction $J_3$. We further show that the topological character of the magnon bands results in non-zero thermal Hall conductivity, whose sign and magnitude depend on $J_c$ and the intra-layer couplings. Since the interlayer coupling strength $J_c$ can be easily tuned by applying pressure to the quasi-2D material, this provides a potential route to tuning the magnon thermal Hall effect in an experiment. In the last part, I will show our study of the possible magnon thermal Hall effect in a Kitaev model candidate material $\alpha$-RuCl$_3$. Because the model parameters of this system are uncertain, we investigate the behavior of the magnon thermal Hall conductivity $\kappa_{xy}/T$ in a wide parameter regime. Through the minimization of the classical energy and linear spin-wave theory, we determine the magnetic phases and compute $\kappa_{xy}/T$ in each set of parameters. We further compare the temperature and magnetic field dependence of $\kappa_{xy}/T$ to the experimental results, which shows that the magnon thermal Hall effect may not be enough to reproduce the experimental data.Item Occupancy Study of the CMS Pixel Subdetector for the Phase 1 Upgrade(2013-08-15) Zabel, James; Ecklund, Karl M; Corcoran, Marjorie D.; Nevidomskyy, AndriyThe Phase 1 Upgrade for CMS includes the installation of a new pixel subdetector, complete with newly designed readout chips as well as a new geometry. This upgrade is necessary to replace the existing irradiated pixel subdetector with one designed for higher instantaneous luminosities. It also provides an opportunity to improve the resolution of track reconstruction and vertex isolation. The new geometry and higher beam energies available after the upgrade increase the flux of ionizing radiation traveling through the pixel subdetector. Results of a simulation that estimate pixel hits, and thus provide an opportunity to estimate data rates and flux, will be shown. The simulation incorporates a variety of factors affecting the estimated data rates and flux, including various luminosities, bunch spacings, and beam spot locations. The simulation determines the number of data links per module necessary to maintain data rates within design limitations.Item Research on Dynamics and Thermodynamics near Quantum Critical Points(2014-08-15) Wu, Jianda; Si, Qimiao; Nevidomskyy, Andriy; Deem, MichaelQuantum phase transition arises in general as second order phase transition at zero temperature, tuned by a non-thermal parameter such as pressure, doping or a magnetic field. The point in the phase diagram of the material in which different phases meet is called a quantum critical point (QCP). Physics around QCPs are of extensive current interest because the critical quantum fluctuations influence the physical properties in a wide temperature range (quantum criticality), and are believed to be responsible for many emergent physical properties such as non-Fermi liquids and unconventional superconductivity. In this research we explore dynamics and thermodynamics near QCPs via investigating three classes of models, which all have real material correspondence. Specifically first, we study local dynamics in a perturbed quantum critical Ising chain with E8 symmetry, where we show the local dynamical spin susceptibility has a singular dependence on frequency, but differs from the diffusion form. The nuclear magnetic resonance (NMR) relaxation rate at low temperatures depends exponentially on the inverse temperature, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E8 description for CoNb2O6. Second, we investigate the thermodynamic properties of itinerant ferromagnets near quantum critical points, described by the quantum Landau-Ginzburg theory. We provide a regularized perturbative renormalization group procedure to calculate the free energy. We further carry out numerical calculations on thermodynamic quantities, capturing not only the leading critical behaviors, but also the subleading and nonsingular contributions. We demonstrate various thermodynamic signatures of quantum criticality, including the entropy accumulation effect and the divergence of the specific heat coefficient. A detailed comparison to the recent experimental results on an itinerant ferromagnet Sr3Ru2O7 is also presented. Third, we explore Ising-nematic and magnetic phases and their transitions in iso-electronically doped iron pnictides by carrying out a large-N study of an effective low-energy Ginzburg-Landau model for these systems. We demonstrate that the magnetic and Ising orders transitions are concurrent at zero temperature, and both transitions are weakly first-order, which is consistent with RG-based prediction and experimental observations.Item Variational approaches to the molecular electronic structure problem based on symmetry-projected Hartree--Fock configurations(2013-09-05) Jimenez-Hoyos, Carlos; Scuseria, Gustavo E.; Clementi, Cecilia; Kolomeisky, Anatoly B.; Nevidomskyy, AndriyApproximate wavefunctions such as Hartree--Fock (HF) states need not respect the symmetries of the molecular electronic Hamiltonian. In certain cases, the lowest-energy HF solution obtained by a variational scheme does not preserve the symmetries of the Hamiltonian. This broken symmetry HF solution captures some of the correlations associated with near-degeneracies in a symmetry-adapted construction. Broken symmetry HF solutions are, nevertheless, unphysical and cannot accurately represent the stationary states of a molecular system. By using projection operators, one can restore the physical character of the wavefunction while accessing the relevant correlations introduced by the broken symmetry mean field description. In this work, we consider a single symmetry-projected Slater determinant as a working wavefunction ansatz. Originally proposed by Löwdin in 1955, the idea was mostly abandoned in the quantum chemistry community after decades of work. By borrowing techniques successful in the nuclear physics community, we use a rigorous, yet efficient mathematical apparatus to perform the projection before the variation of broken symmetry wavefunctions. The wavefunctions thus obtained have a multi-determinantal character and can account for significantly more correlations than a broken symmetry HF state in finite systems. The symmetry-projected HF approach is, nonetheless, not free of vices. The approach is neither size-consistent nor size-extensive. In order to go beyond the symmetry projected HF wavefunction, we construct highly sophisticated multi-reference wavefunctions based on a small number of non-orthogonal Slater determinants. Chains of variational calculations are used to optimize wavefunctions suitable for an accurate description of ground and excited states, with well defined quantum numbers, which can account for both strong and weak correlation effects. Our results indicate that such expansions can produce fairly accurate results for small molecular systems. We hope our approach will eventually become yet another tool for the quantum chemist useful in situations where both strong and weak correlation effects are important.