Local Density Matrix Research Articles

Entanglement spectrum as a marker for phase transitions in the density embedding theory for interacting spinless fermionic models

Entanglement related properties work as nice fingerprint of the quantum many-body wave function. However, those of fermionic models are hard to evaluate in standard numerical methods because they suffer from finite size effects. We show that a so-called density embedding theory (DET) can evaluate them without size scaling analysis in comparably high quality with those obtained by the large-size density matrix renormalization group analysis. This method projects the large scale original many-body Hamiltonian to the small number of basis sets defined on a local cluster, and optimizes the choice of these bases by tuning the local density matrix. The DET entanglement spectrum of one-dimensional interacting fermions perfectly reproduces the exact ones and works as a marker of the phase transition point. It is further shown that the phase transitions in two-dimension could be determined by the entanglement entropy and the fidelity that reflects the change of the structure of the wave function.

Gradient-based stochastic estimation of the density matrix

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S−(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory

We introduce density matrix embedding theory (DMET), a quantum embedding theory for computing frequency-independent quantities, such as ground-state properties, of infinite systems. Like dynamical mean-field theory, DMET maps the bulk interacting system to a simpler impurity model and is exact in the noninteracting and atomic limits. Unlike dynamical mean-field theory, DMET is formulated in terms of the frequency-independent local density matrix, rather than the local Green's function. In addition, it features a finite, algebraically constructible bath of only one bath site per impurity site, with no bath discretization error. Frequency independence and the minimal bath make DMET a computationally simple and efficient method. We test the theory in the one-dimensional and two-dimensional Hubbard models at and away from half filling, and we find that compared to benchmark data, total energies, correlation functions, and metal-insulator transitions are well reproduced, at a tiny computational cost.

Theoretical investigation of electronic structure, electric field gradients, and photoemission of PuCoGa5and PuRhGa5superconductors

We report electronic structure calculations of PuCoGa${}_{5}$ and PuRhGa${}_{5}$ superconductors. The band structure, electric field gradients, and Fermi surface topologies were investigated using two methods of correlated band theory, namely the conventional static mean-field LDA$+$$U$ and the local density matrix approximation (LDMA). The latter is based on the Hubbard-I approximation and includes intra-atomic dynamical correlations in a self-consistent manner. Our results show that although LDA$+$$U$ and LDMA calculations do not significantly modify the Fermi surface topologies compared to LDA, they do lead to a substantial reduction of the $f$ character of the electronic states at the Fermi energy. The calculations indicate presence of a pseudogap in the electronic spectrum. We achieve a good agreement between calculated and experimental nuclear quadrupolar resonance frequencies and a fairly good agreement between calculated and experimental photoemission spectra. Our findings can be important for the theory of superconductivity in PuCoGa${}_{5}$ and related compounds.

Local quenches in frustrated quantum spin chains: Global versus subsystem equilibration

We study the equilibration behavior following local quenches, using frustrated quantum spin chains as an example of interacting closed quantum systems. Specifically, we examine the statistics of the time series of the Loschmidt echo, the trace distance of the time-evolved local density matrix to its average state, and the local magnetization. Depending on the quench parameters, the equilibration statistics of these quantities show features of good or poor equilibration, indicated by Gaussian, exponential or bistable distribution functions. These universal functions provide valuable tools to characterize the various time-evolution responses and give insight into the plethora of equilibration phenomena in complex quantum systems.

Exchange effects in nuclear rainbow scattering

Abstract A simple microscopic approach to the calculation of the exchange part of the real nucleus-nucleus optical potential based on a generalization of the double-folding model and the local density matrix formalism has been proposed. The model successfully reproduces the nuclear rainbow scattering data for α-particles, 6 Li and 9 Be. The role of knock-on exchange effects in these processes is considered in detail.

Dipole-phonon coupling and dielectric relaxation

Equations of motion for the average polarisation are derived from a microscopic approach by use of the local density matrix. A specific form of the dipole-phonon coupling in the memory kernel is investigated and the necessary conditions for the generation of a non-Debye form of response examined. It is shown that these conditions can only be fulfilled by allowing for dipole-induced distortion with the lifetime of the “phonons” determined by the lifetime of the dipole correlation.

Quantum Theory of Kinetic Equations for Electrons in Phonon Fields

A method is presented which yields a kinetic equation for the time development of the one-electron density matrix for dynamically independent electrons in phonon and other arbitrary static fields of force under the influence of a weak but otherwise general external dynamical disturbance. The exclusion principle, the finiteness of the phonon energies, and the quantum mechanical nature of the processes involved are taken into account rigorously. The effects of the electron-phonon interaction are described only in the Born approximation. A kinetic equation for the steady state is also derived in an arbitrary oneelectron representation. An iterative solution of the kinetic equation is discussed and the power absorption due to direct and indirect transitions is derived from the general kinetic equation. The case of a uniform but oscillating electric field is considered in detail for free, Landau, and Bloch electrons, for which special kinetic equations are derived. A local density matrix, useful in the calculation of space-varying densities of various physical observables, is introduced and a kinetic equation for it is obtained from the general theory. Applications of it are made to the case of free and Landau electrons for disturbances of arbitrary space-time variation. The applicability of the method tomore » more general situations is indicated. (auth)« less