Linear Density Matrix Research Articles

Loss of classicality in alternating spin-/spin-1 chain, in the presence of next-neighbor couplings and Dzyaloshinskii–Moriya interactions

We have considered and alternating spin-/spin-1 chain with nearest-neighbor (NN) (J 1), next-nearest neighbor (NNN) (J 2) antiferromagnetic (AFM) Heisenberg interactions along with z-component of the Dzyaloshinskii–Moriya (DM) (Dz ) interaction. The Hamiltonian has been studied using (a) linear spin-wave theory and (b) density matrix renormalization group. The system had been reported earlier as a classical ferrimagnet only when NN exchange interactions are present. Both the AFM NNN interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero J 2 introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of J 1 along with Dz introduces a short range order but develops long range order along the XY plane. J 1 along with J 2 induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the D z term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.

Spin liquid in twisted homobilayers of group-VI dichalcogenides

Twisted transition metal dichalcogenide (TMD) homobilayers have recently emerged as a powerful platform for studying correlated insulating states. In the strongly correlated limit, we construct an effective spin Hamiltonian on a honeycomb lattice that includes the Heisenberg interaction and nonsymmetric interactions such as a Dzyaloshinskii-Moriya interaction and a Kane-Mele coupling for the Mott-insulating phase at half-filling. For the twisted TMD homobilayers, the spin-orbit coupling in the Hubbard model, which is expected to induce the antisymmetric exchange couplings in the effective spin Hamiltonian, is a highly tunable and experimentally accessible quantity that can be tuned by an applied electric field. In this study, we investigate classical and quantum phase diagrams of the effective spin Hamiltonian using analytical and numerical methods. We show that the model exhibits a rich classical phase diagram including an antiferromagnetic (AFM) phase, a planar spiral ordered phase with high classical degeneracy, a $z$-AFM phase, a noncoplanar phase, a noncollinear phase, and a 120$^{\circ}$-AFM phase. In the quantum treatment, we calculate low-energy magnon excitation spectrum, ground state energy, and static spin structure factor using linear spin-wave theory and density matrix renormalization group methods to compose the quantum phase diagram of the effective spin Hamiltonian. Beyond the Heisenberg interaction, we find that the existence of these antisymmetric couplings is responsible for the quantum spin liquid, $z$-AFM, noncoplanar, and 120$^{\circ}$ phases. Twisted TMD homobilayers, therefore, offer rich platforms for realizing rich phases of matter such as quantum spin liquid, noncoplanar, and 120$^{\circ}$, resulting from the spin-orbit coupling.

Analysis of Mechanical Properties of Unidirectional Flax Roving and Sateen Weave Woven Fabric-Reinforced Composites

Abstract Natural fiber-reinforced composites are getting more attention from researchers and manufacturing companies to replace metals and synthetic materials that have dominated the manufacturing industries. In this study, the mechanical properties of unidirectional (UD) flax roving-reinforced composites and woven fabric-reinforced composites were investigated. Three different composites were prepared from flax rovings, which have the same linear density and epoxy resin matrix, with different reinforcement and composite preparation methods. The samples were subjected to experimental tests of flexural rigidity and tensile strength in a parallel and perpendicular direction to fiber orientation. The test results showed that flexural rigidity and tensile strength of flax fiber-reinforced composites are highly dependent on the direction of fiber orientation. The results also reveal that in a parallel direction to fiber orientation, UD composites have higher flexural rigidity and tensile strength than woven fabric-reinforced composite.

Nematic spin liquid phase in a frustrated spin-1 system on the square lattice

Frustration in quantum spin systems promote a variety of novel quantum phases. An important example is the frustrated spin-$1$ model on the square lattice with the nearest-neighbor bilinear ($J_1$) and biquadratic ($K_1$) interactions. We provide strong evidence for a nematic spin liquid phase in a range of $K_1/J_1$ near the SU(3)-symmetric point ($J_1 = K_1$), based on the linear flavor-wave theory and extensive density matrix renormalization group calculation. This phase displays no spin dipolar or quadrupolar order, preserves translational symmetry but spontaneously breaks $C_4$ lattice rotational symmetry, and possesses fluctuations peaked at the wavevector $(\pi, 2\pi/3)$. The spin excitation gap drops rapidly with system size and appears to be gapless, and the nematic order is attributed to the dominant $(\pi, 2\pi/3)$ fluctuations. Our results provide a novel mechanism for electronic nematic order and, more generally, open up a new avenue to explore frustration-induced exotic ground states.

On-the-Fly Computation of Frontal Orbitals in Density Matrix Expansions.

We propose a method for computation of frontal (homo and lumo) orbitals in recursive polynomial expansion algorithms for the density matrix. Such algorithms give a computational cost that increases only linearly with system size for sufficiently sparse systems, but a drawback compared to the traditional diagonalization approach is that molecular orbitals are not readily available. Our method is based on the idea to use the polynomial of the density matrix expansion as an eigenvalue filter giving large separation between eigenvalues around homo and lumo [ Rubensson et al. J. Chem. Phys. 2008 , 128 , 176101 ]. This filter is combined with a shift-and-square (folded spectrum) method to move the desired eigenvalue to the end of the spectrum. In this work we propose a transparent way to select recursive expansion iteration and shift for the eigenvector computation that results in a sharp eigenvalue filter. The filter is obtained as a byproduct of the density matrix expansion, and there is no significant additional cost associated either with its construction or with its application. This gives a clear-cut and efficient eigenvalue solver that can be used to compute homo and lumo orbitals with sufficient accuracy in a small fraction of the total recursive expansion time. Our algorithms make use of recent homo and lumo eigenvalue estimates that can be obtained at negligible cost [ Rubensson et al. SIAM J. Sci. Comput . 2014 , 36 , B147 ]. We illustrate our method by performing self-consistent field calculations for large scale systems.

Dynamics of linarite: Observations of magnetic excitations

Here we present inelastic neutron scattering measurements from the frustrated, quantum spin-1/2 chain material linarite, PbCuSO_4(OH)_2. Time of flight data, taken at 0.5K and zero applied magnetic field reveals low-energy dispersive spin wave excitations below 1.5meV both parallel and perpendicular to the Cu-chain direction. From this we confirm that the interchain couplings within linarite are around 10% of the nearest neighbour intrachain interactions. We analyse the data within both linear spin-wave theory and density matrix renormalisation group theories and establish the main magnetic exchange interactions and the simplest realistic Hamiltonian for this material.

The one-electron description of excited states: Natural excitation orbitals of density matrix theory and Kohn–Sham orbitals of density functional theory as ideal orbitals

Linear response density matrix functional theory has been shown to solve the main problems of time-dependent density functional theory (deficient in case of double, charge transfer and bond breaking excitations). However, the natural orbitals preclude the description of excitations as (approximately) simple orbital-to-orbital transitions: many weakly occupied ‘virtual’ natural orbitals are required to describe the excitations. Kohn–Sham orbitals on the other hand afford for many excitations such a simple orbital description. In this communication we show that a transformation of the set of weakly occupied NOs can be defined such that the resulting natural excitation orbitals (NEOs) restore the single orbital transition structure for excitations generated by the linear response DMFT formalism.

Diffusion and dissipation by linear momentum in spherical environment

An open quantum system is studied consisting of a particle moving in a spherical space with an infinite wall. With the theory of Lindblad the system is described by a density matrix which gets affected by operators with diffusive and dissipative properties depending on the linear momentum and density matrix only. It is shown that an infinite number of basis states leads to an infinite energy because of the infinite unsteadiness of the potential energy at the infinite wall. Therefore only a solution with a finite number of basis states can be performed. A slight approximation is introduced into the equation of motion in order that the trace of the density matrix remains constant in time. The equation of motion is solved by the method of searching eigenvalues. As a side-product two sums over the zeros of spherical Bessel functions are found.

Excitation energies with linear response density matrix functional theory along the dissociation coordinate of an electron-pair bond in N-electron systems

Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ωα and oscillator strengths fα for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ωα(R) curves along the bond dissociation coordinate R for the molecules LiH, Li2, and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate.

First-Principle Derivation of Entropy Production in Transport Phenomena

The linear response framework was established by Kubo a half century ago, but no clear explanation of irreversibility namely entropy production has been given in this scheme. This has been now solved. The serious puzzle up to now is the following. Even using the linear response density matrix ρlr = ρ0 + ρ1(t), it has been difficult to derive the entropy production.Surprisingly, the correct entropy production is given by the second-order term ρ2(t) as . It is shown to agree with the ordinary expression J·E/T = σE2/T in the case of electric conduction for a static electric field E, where σ denotes the electric conductivity expressed by the famous canonical current-current time correlation functions in equilibrium.The present article gives a review of the derivation of entropy production (M.S., Physica A 390(2011)1904-1916) based on the first-principle of using the projected density matrix ρ2(t) or more generally ρeven(t), while the previous standard argument is due to the thermodynamic energy balance. This new derivation clarifies conceptually the physics of irreversibility in transport phenomena. In general, the transport phenomena are described by the odd part ρodd(t) of the density matrix and the entropy production (namely irreversibility) is described by the even part ρeven(t). These are related to each other through the coupled equations as , where "q" denotes "even" (symmetric) or "odd" (antisymmetric), Pq is the projection operator to the "q" part of ρ(t), and ℋ1(t) denotes the partial Hamiltonian due to the external force such as in electric conduction.The concept of a stationary temperature Tst in steady states with current (say electric current) is also proposed by using the projected and symmetry-separated von Newmann equation introduced by the present author. The entropy production of the relevant steady state depends on this stationary temperature. A mechanical formulation of thermal conduction is given by introducing a thermal field ET and its conjugate "heat" operator for a local internal energy hj of the thermal particle j.

Linear scaling density matrix perturbation theory for basis-set-dependent quantum response calculations: An orthogonal formulation

Linear scaling density matrix perturbation theory [A. M. N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is extended to basis-set-dependent quantum response calculations for a nonorthogonal basis set representation. The generalization is achieved by a perturbation-dependent congruence transform, derived from the factorization of the inverse overlap matrix, which transforms the generalized eigenvalue problem to an orthogonal, standard form. With this orthogonalization transform the basis-set-dependent perturbation in the overlap matrix is included in the orthogonalized Hamiltonian, which is expanded in orders of the perturbation. In this way density matrix perturbation theory developed for an orthogonal representation can be applied also to basis-set-dependent response calculations. The method offers an alternative to the previous solution of the basis-set-dependent response problem, based on a nonorthogonal generalization of the density matrix perturbation theory, where the calculations are performed within a purely nonorthogonal setting [A. M. N. Niklasson et al., J. Chem. Phys. 123, 44107 (2005)].

Linear scaling density matrix search based on sign matrices

This paper presents a new approach to the linear scaling evaluation of density matrices in electronic structure theory. The new approach is based on the iterative computation of a special matrix function, the sign of the matrix and its performance is compared to that of some other methods developed for similar purpose. One particular variant of the sign approach turned out to be very competitive with other linear scaling density matrix evaluation algorithms, in terms of computational time and accuracy. It is also shown that a special damping technique greatly improves the stability of self-consistent field (SCF) calculations when using density matrix purification and sign methods.

Entropy in nonlinear quantum mechanics. II

For pt.I see ibid., vol.25, p.359 (1992). Regarding the discussion of Peres (1989) and Weinberg (1989) concerning a suitable definition of entropy in nonlinear quantum mechanics, two further observations are made. Firstly, by regarding the covariance matrix of the probability distribution over the phase space of wavefunctions as the nonlinear counterpart (pNL) of the (linear) density matrix (pL) and employing -Tr pNL In pNL, one obtains a limiting transition (as nonlinearities vanish), in which this entropy measure converges to the definition in ordinary quantum mechanics, -Tr pL In pL. Secondly, it is argued that Peres' contention that 'nonlinear variants of the Schrodinger equation violate the second law of thermodynamics' is flawed in that it relies upon the entropy of mixing of nonorthogonal states which as Dieks an van Dijk (1988) have indicated is an undefined concept. A proper approach to associating a quantum mechanical entropy with a mixture of a particle into two non-orthogonal states-by first estimating a suitable two-particle density matrix (p) and then employing -Tr p In p-is outlined.

Entropy in nonlinear quantum mechanics

For pt.I see ibid., vol.25, p.359 (1992). Regarding the discussion of Peres (1989) and Weinberg (1989) concerning a suitable definition of entropy in nonlinear quantum mechanics, two further observations are made. Firstly, by regarding the covariance matrix of the probability distribution over the phase space of wavefunctions as the nonlinear counterpart (pNL) of the (linear) density matrix (pL) and employing -Tr pNL In pNL, one obtains a limiting transition (as nonlinearities vanish), in which this entropy measure converges to the definition in ordinary quantum mechanics, -Tr pL In pL. Secondly, it is argued that Peres' contention that 'nonlinear variants of the Schrodinger equation violate the second law of thermodynamics' is flawed in that it relies upon the entropy of mixing of nonorthogonal states which as Dieks an van Dijk (1988) have indicated is an undefined concept. A proper approach to associating a quantum mechanical entropy with a mixture of a particle into two non-orthogonal states-by first estimating a suitable two-particle density matrix (p) and then employing -Tr p In p-is outlined.

NMR line shapes for exchanging systems at high rf field

A method is described by which NMR line shapes at high rf may be calculated for chemically exchanging systems. First order exchange results in a set of manifestly linear density matrix equations that are solved with standard methods. Second order exchanging systems, a model example of which is considered here, give rise to second order density matrix equations. Inspection of sample values of density matrix elements reveals that products of off-diagonal elements are small enough to drop from the equations, while products of off-diagonal and diagonal elements, respectively, may be linearized as ρi jAρk,kB=ρi jA/n B. This selective neglect of bilinear terms (SNOB) leads to a set of first order density matrix equations. Inspection of the calculated line shapes reveals that NMR at high rf in exchanging systems allows more precise determination of rate constants for exchange (compared to low power) in the slow, and, in a limited sense, in the fast exchange limits.