Competition between local potentials and attractive particle-particle interactions in superlattices

Naturally occuring or man-made systems displaying periodic spatial modulations of their properties on a nanoscale constitute superlattices. Such modulated structures are important both as prototypes of simple nanotechnological devices and as particular examples of emerging spatial inhomogeneity in interacting many-electron systems. Here we investigate the effect different types of modulation of the system parameters have on the ground-state energy and the charge-density distribution of the system. The superlattices are described by the inhomogeneous attractive Hubbard model, and the calculations are performed by density-functional and density-matrix renormalization group techniques. We find that modulations in local electric potentials are much more effective in shaping the system’s properties than modulations in the attractive on-site interaction. This is the same conclusion we previously [M.F. Silva, N.A. Lima, A.L. Malvezzi, K. Capelle, Phys. Rev. B 71 (2005) 125130.] obtained for repulsive interactions, suggesting that it is not an artifact of a specific state, but a general property of modulated structures.     

Analytic theory of correlation energy and spin polarization in the 2D electron gas

We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional (2D) electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering Schrödinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-Feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our results for the correlation energy show a quantum phase transition occurring at coupling strength r_s≈24 from the paramagnetic to the fully spin-polarized fluid.     

Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities

The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction U_c remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.     

Critically shielded potential in a three-dimensional electron gas: The induced charge density at the origin

The induced electron density at the position of a critically shielded single point charge embedded in a three-dimensional degenerate electron gas is studied at low densities, in a comparative manner. The partial-wave expansion method for scattering states and averaging over the occupied Fermi sphere are used for an attractive potential energy of Hulthen form. The third-order differential equation of March and Murray [N.H. March, A.M. Murray, Phys. Rev. 120 (1960) 830] for the diagonal of the one-particle density matrix is also investigated, for the same continuous set of energy eigenvalues. The comparative study, performed for the s-type component of the total electron density, explicitly demonstrates the equivalence of the two methods.     

Thomas-Fermi model for quasi one-dimensional finite crystals

The model presented here applies a self-consistent method to electrons in crystals, thus enabling the calculation of the effective inner potential field. For this purpose, a Thomas-Fermi (TF) type model was developed, using a “qausi” one-dimensional finite crystal—a set of equidistant infinite thin plates representing the ionic planes, spread perpendicularly to a length axis. The model is applied to a finite crystal with no external fields. This application of a “multi-centered” TF model to an entire crystal is carried out for the first time in this work; the TF model was widely used in the past for atomic and molecular calculations, but in crystals it was limited to local use such as impurities. Poisson's (non-linear) differential equation describing the problem is solved using the highly efficient Relaxation Method. A pattern of almost periodical peaks (except near the boundaries) residing at the ionic sites is obtained for the potential, as well as for the electronic local density (indicating the electrons' tendency to pack mainly near the ions).     

From quantum mechanics to classical statistical physics: Generalized Rokhsar-Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition

Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar-Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave functions are intimately related to the partition functions of combinatorial problems of classical statistical physics. We show that all the known examples of quantum Hamiltonians, when fine-tuned to their RK points, belong to a larger class of real, symmetric, and irreducible matrices that admit what we dub a Stochastic Matrix Form (SMF) decomposition. Matrices that are SMF decomposable are shown to be in one-to-one correspondence with stochastic classical systems described by a Master equation of the matrix type, hence their name. It then follows that the equilibrium partition function of the stochastic classical system partly controls the zero-temperature quantum phase diagram, while the relaxation rates of the stochastic classical system coincide with the excitation spectrum of the quantum problem. Given a generic quantum Hamiltonian construed as an abstract operator defined on some Hilbert space, we prove that there exists a continuous manifold of bases in which the representation of the quantum Hamiltonian is SMF decomposable, i.e., there is a (continuous) manifold of distinct stochastic classical systems related to the same quantum problem. Finally, we illustrate with three examples of Hamiltonians fine-tuned to their RK points, the triangular quantum dimer model, the quantum eight-vertex model, and the quantum three-coloring model on the honeycomb lattice, how they can be understood within our framework, and how this allows for immediate generalizations, e.g., by adding non-trivial interactions to these models.     

Quantum critical phenomena, entanglement entropy and Hubbard model in 1d with the boundary site with a negative chemical potential −p and the Hubbard coupling U positive

Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed exactly for an open chain with L sites. The case when the boundary site has the chemical potential −p and the Hubbard coupling U is positive was considered. We model CeAl₂ nanoparticles, in which a valence of 4f electron number changes on surface Ce atoms, by this Hubbard model. A surface phase transition exists at some critical value pc3 of chemical potential (its absolute value) p in the model; when p<pc3 all the charge excitations have the gap, while there exists a massless charge mode when p>pc3. The aim of this Letter is to find whether this surface phase transition is of the first order or of the second order. We have found that the entanglement entropy and its derivative has a discontinuity at pc3 in general and thus this transition is of the first order (with exception of two points for the probability w₂ of occurrence of two electrons with opposites spins on the same site). There is a divergence in the difference of entanglement entropy for points w₂=0 and . The first point w₂=0 corresponds to ferro- (antiferro-) magnetic state at half-filled case. The second point does not correspond to any state for halffilled case. In the first case there is present the surface phase transition of the second order type.     

Compressibility of a two-dimensional electron gas in a parallel magnetic field

The thermodynamic compressibility of a two-dimensional electron system in the presence of an in-plane magnetic field is calculated. We use accurate correlation energy results from quantum Monte Carlo simulations to construct the ground state energy and obtain the critical magnetic field B_c required to fully spin polarize the system. Inverse compressibility as a function of density shows a kink-like behavior in the presence of an applied magnetic field, which can be identified as B_c. Our calculations suggest an alternative approach to transport measurements of determining full spin polarization.     

Rotating electrons in quantum dots: Classical limit

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of a quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.     

Second quantized reduced Bloch equations and the exact solutions for pairing Hamiltonian

In this article, we present a set of hierarchy Bloch equations for the reduced density operators in either canonical or grand canonical ensembles in the occupation number representation. They provide a convenient tool for studying the equilibrium quantum statistical mechanics for some model systems. As an example of their applications, we solve the equations for the model system with a pairing Hamiltonian. With the aid of its symplectic group symmetry, we obtain the statistical reduced density matrices with different orders. As a special instance for the solutions, we also get the reduced density matrices of the ground state for a superconductor.     

Topological order and conformal quantum critical points

We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as quantum critical points separating these phases. All of the ground-state equal-time correlators of these theories are equal to correlation functions of a local two-dimensional classical model. The critical points therefore exhibit a time-independent form of conformal invariance. These theories characterize the universality classes of two-dimensional quantum dimer models and of quantum generalizations of the eight-vertex model, as well as and non-abelian gauge theories. The conformal quantum critical points are relatives of the Lifshitz points of three-dimensional anisotropic classical systems such as smectic liquid crystals. In particular, the ground-state wave functional of these quantum Lifshitz points is just the statistical (Gibbs) weight of the ordinary two-dimensional free boson, the two-dimensional Gaussian model. The full phase diagram for the quantum eight-vertex model exhibits quantum critical lines with continuously varying critical exponents separating phases with long-range order from a deconfined topologically ordered liquid phase. We show how similar ideas also apply to a well-known field theory with non-Abelian symmetry, the strong-coupling limit of 2+1-dimensional Yang–Mills gauge theory with a Chern–Simons term. The ground state of this theory is relevant for recent theories of topological quantum computation.     

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping δ away from half-filling, finite-system density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/δ and 1/δ, respectively, corresponding to ordering wavevectors 2k_F and 4k_F for the currents and densities, where 2k_F = π (1 − δ). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/δ, the DMRG results are consistent with a true long-range order scenario for the currents and densities.     

On the visibility of electron-electron interaction effects in field emission spectra

One of the most convenient methods to obtain information about the energy distribution function of electrons in conducting materials is the measurement of the energy resolved current j(ω) in field emission (FE) experiments. Its high energy tail j_>(ω) (above the Fermi edge) contains invaluable information about the nature of the electron-electron interactions inside the emitter. Thus far, j_>(ω) has been calculated to second order in the tunnelling probability, and it turns out to be divergent toward the Fermi edge for a wide variety of emitters. The extraction of the correlation properties from real experiments can potentially be obscured by the eventually more divergent contributions of higher orders as well as by thermal smearing around E_F. We present an analysis of both factors and make predictions for the energy window where only the second order tunnelling events dominate the behaviour of j_>(ω). We apply our results to the FE from Luttinger liquids and single-wall carbon nanotubes.     

Energetics of a strongly correlated Fermi gas

The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution:

     

A Chiral Macroscopic Force between Liquid of Butyl Alcohol and Copper Block

A non-zero macroscopic chirality-dependent force between a copper block and a vessel of homochiral molecules （butyl alcohol） is calculated quantitatively with the central field approximation. The magnitude of the force is estimated with the published limits of the scalar and pseudo-scalar coupling constants.     

A planar model for interacting fermions

One-particle Green function in the paramagnetic phase of a model of interacting fermions is obtained in the planar approximation. The model is zero-dimensional, in that thermal fluctuations are the only source of kinetic energy.     

Pseudopotentials, correlations, and hierarchy states in quantum hall systems: When the composite Fermion picture works and why

A system of Fermions in a shell of angular momentum l can form a set of multiplets of total angular momentum L. The composite Fermion (CF) picture picks out the lowest lying energy multiplets by selecting from this set a subset that is “Laughlin correlated”, i.e. which maximally avoids pair orbits with the largest pair angular momentum L^′ (or smallest relative angular momentum R=2l−L^′). We demonstrate that Laughlin correlations occur only when the pseudopotential V(L^′) (the interaction energy of a pair as a function of L^′) increases with L^′ more rapidly, than the eigenvalue of L^′2 at the value of L^′ (or R) avoided in the Laughlin correlated state. This requirement is not satisfied for QEs and QHs of the Laughlin ν=1/3 and ν=1/5 states at R=1 and R=3 respectively. At and , clustering of QPs gives lower energy than Laughlin correlations. Novel spin polarized incompressible states at ν=4/11 and ν=4/13 cannot be explained as a second generation in the CF hierarchy.     

Study of the order–disorder transition and martensitic transformation in a Cu–Al–Be alloy by EELS

Changes in 3d states occupancy associated with order–disorder transition and martensitic transformation in a Cu–Al–Be alloy was investigated by electron energy loss spectroscopy (EELS) in both high energy and low energy loss regions. From the high energy loss region, the Cu L_2,3 white-line intensities, which reflect the unoccupied density of states in 3d bands, was measured for three states of the alloy: disordered austenite, ordered austenite and martensite. It was found that the white-line intensity remains the same during order–disorder transition but appears slightly smaller in martensite, indicating that some electrons left Cu 3d bands or some hybridization took place during phase transformation. From the low energy loss region, the optical joint density of states (OJDS) was obtained by Kramers–Kronig analysis. As maxima observed in the OJDS spectra are assigned to interband transitions, these spectra can be used to probe changes in the electronic band structure. The analysis shows that during the martensitic transformation, the peaks positions and relative intensities in the OJDS spectra undergoes noticeable changes, which are associated with interband transitions.     

Large momentum part of a strongly correlated Fermi gas

It is well known that the momentum distribution of the two-component Fermi gas with large scattering length has a tail proportional to 1/k⁴ at large k. We show that the magnitude of this tail is equal to the adiabatic derivative of the energy with respect to the reciprocal of the scattering length, multiplied by a simple constant. This result holds at any temperature (as long as the effective interaction radius is negligible) and any large scattering length; it also applies to few-body cases. We then show some more connections between the 1/k⁴ tail and various physical quantities, including the pressure at thermal equilibrium and the rate of change of energy in a dynamic sweep of the inverse scattering length.