Form factors and correlation functions of an interacting spinless fermion model

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green's function and the density–density correlation function both for any interaction strength and for arbitrary particle densities. In particular for the free fermion model, our formulae reproduce the known exact results. Form factors of local fermion operators are also calculated for a finite system.     

Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media

By use of the time dependent theory for random lasers, we make a comprehensive calculation on the spectrum intensity as well as the pump rate dependence of the peak intensity and the spectral width of localized modes in two-dimensional random media for both transverse electric and transverse magnetic polarization fashions. For any mode, there is a jump in the curve of the spectral width vs the pump rate. A method based on the trailing edge of the jump to determine the pump threshold of a mode is confirmed to be available and effective.     

Time evolution of power spectra from two-dimensional passive random media with different shapes

For a set of two-dimensional passive random media that have the same randomness and different shapes, the effects of morphology on the time evolution of the power spectrum of the localized modes supported by the media are investigated. The results demonstrate that the evolving process of the spectrum, the lifetime of short-lived modes and the amount of long-lived modes are morphological-dependent, while the lifetime of long-lived modes is morphological-independent. The denser the medium is, the quicker the evolving process and the shorter the lifetime of the short-lived modes are. Single-mode operation is more possible and occurs more early for a denser medium, which is of practical importance for proposing a mode-selecting technique for random lasers.     

Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses

Pulsing random lasing property has been investigated in both one- and two-dimensional random medium by numerically solving Maxwell’s equations and rate equations in which the pumping rate is described by a time function with duration of 10s or 100s of femtoseconds. The peak intensity, width and delay time of a random lasing pulse are traced with the variation of the peak intensity, duration, shape and numbers of a pumping pulse. Results show that the behavior of random lasing depends strongly on the pumping process, some of which are in agreement with previously reported experiments pumped by femtosecond-lasing pulses. The present work enriches the knowledge about random lasers, especially in temporal regime, and could offer more guidance for relevant experiments.     

Nonadiabatic Geometric Phase and Induced Persistent Current in Mesoscopic Square Circuit with Tilted Magnetic Field at Edges

We investigate the geometric phase produced by nonadiabatic transition of spin states at corners of mesoscopic square circuit with tilted magnetic field at its edges, From the Schrodlnger equation, the transitions of electron spin state at corners are described by the transfer matrices. The eigenenergies and eigenstates are obtained from the cyclic condition and the multiplying of the transfer matrices. We show that there exist persistent charge and spin currents in such a system due to the lift of degeneracy between the opposite moving directions in the presence of the tilted magnetic field. The dependences of eigenenergies, geometric phase, charge and spin persistent currents on the tilting angles of magnetic field are analysed.     

Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

We present calculations of the localisation length, , for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength U and system size. is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates are obtained by finite-size scaling. For U=0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite U, we find that with varying between and . We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction. Received 19 June 1998 and Received in final form 29 October 1998     

Scaling of decay lengths for surface states in the gaps of one-dimensional semi-infinite superlattices

We look at some one-dimensional semi-infinite superlattices with an underlying Hamiltonian that is of the nearest neighbour, tight binding type. A real space rescaling procedure which is exact in one dimension is applied to obtain the location of the subbands. It has been found that these subbands never overlap in 1D, and we interpret this as a band repulsion effect. Relevance in the case of a disordered system where this band repulsion crosses over to the well-known level repulsion is discussed. Then with a proper matching at the boundary we solve for the sets of denumerably infinite number of decaying solutions (the surface states) in the gaps. These types of states have been proposed quite some time ago. We look at detail theirexact analytical solutions in 1D and find that their decay lengths near the band edges diverge as |E–E _b|^–v, wherev=1/2 andE _b is the nearest band edge. The decay lengths and their divergence exponent match extremely well with those obtained from transfer matrix method. Some recent experiments on quantum well structures seem to have observed such states.     

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.     

Visibility graph approach to exchange rate series

By means of a visibility graph, we investigate six important exchange rate series. It is found that the series convert into scale-free and hierarchically structured networks. The relationship between the scaling exponents of the degree distributions and the Hurst exponents obeys the analytical prediction for fractal Brownian motions. The visibility graph can be used to obtain reliable values of Hurst exponents of the series. The characteristics are explained by using the multifractal structures of the series. The exchange rate of EURO to Japanese Yen is widely used to evaluate risk and to estimate trends in speculative investments. Interestingly, the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series.     

Universal correlations of one-dimensional interacting electrons in the gas phase

We consider dynamical correlation functions of short range interacting electrons in one dimension at finite temperature. Below a critical value of the chemical potential there is no Fermi surface anymore, and the system can no longer be described as a Luttinger liquid. Its low temperature thermodynamics is that of an ideal gas. We identify the impenetrable electron gas model as a universal model for the gas phase and present exact and explicit expressions for the asymptotics of correlation functions at small temperatures, in the presence of a magnetic field.     

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.     

Phase diagram of electron-hole systems: Interplay between exciton Mott transition and quantum pair condensation

Quasi-thermal-equilibrium states of electron-hole (e-h) systems in photoexcited insulators are studied from a theoretical viewpoint, stressing the exciton Bose-Einstein condensation (BEC), the e-h BCS-type pair-condensed state, and the exciton Mott transition between an insulating exciton/biexciton gas phase and a metallic e-h plasma phase. We determine the quasi-equilibrium phase diagram of the e-h system at zero and finite temperatures with applying the dynamical mean-field theory (DMFT) to the e-h Hubbard model with both repulsive and attractive on-site interactions. Effects of inter-site interactions on the exciton Mott transition are also clarified with applying the extended DMFT to the extended e-h Hubbard model.     

Effective Hamiltonians for holes in antiferromagnets: a new approach to implement forbidden double occupancy

A coherent state representation for the electrons of ordered antiferromagnets is used to derive effective Hamiltonians for the dynamics of holes in such systems. By an appropriate choice of these states, the constraint of forbidden double occupancy can be implemented rigorously. Using these coherent states, one arrives at a path integral representation of the partition function of the systems, from which the effective Hamiltonians can be read off. We apply this method to the t-J model on the square lattice and on the triangular lattice. In the former case, we reproduce the well-known fermion-boson Hamiltonian for a hole in a collinear antiferromagnet. We demonstrate that our method also works for non-collinear antiferromagnets by calculating the spectrum of a hole in the triangular antiferromagnet in the self-consistent Born approximation and by comparing it with numerically exact results. Received: 23 December 1997 / Accepted: 17 March 1998     

Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism

We describe a new formulation of the functional renormalization group (RG) for interacting fermions within a Wilsonian momentum-shell approach. We show that the Luttinger-Ward functional is invariant under the RG transformation, and derive the infinite hierarchy of flow equations satisfied by the two-particle-irreducible (2PI) vertices. In the one-loop approximation, this hierarchy reduces to two equations that determine the self-energy and the 2PI two-particle vertex Φ⁽²⁾. Susceptibilities are calculated from the Bethe-Salpeter equation that relates them to Φ⁽²⁾. While the one-loop approximation breaks down at low energy in one-dimensional systems (for reasons that we discuss), it reproduces the exact results both in the normal and ordered phases in single-channel (i.e. mean-field) theories, as shown on the example of BCS theory. The possibility to continue the RG flow into broken-symmetry phases is an essential feature of the 2PI RG scheme and is due to the fact that the 2PI two-particle vertex, contrary to its 1PI counterpart, is not singular at a phase transition. Moreover, the normal phase RG equations can be directly used to derive the Ginzburg-Landau expansion of the thermodynamic potential near a phase transition. We discuss the implementation of the 2PI RG scheme to interacting fermion systems beyond the examples (one-dimensional systems and BCS superconductors) considered in this paper.     

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.     

Wigner time delay and related concepts: Application to transport in coherent conductors

The concepts of Wigner time delay and Wigner–Smith matrix allow us to characterise temporal aspects of a quantum scattering process. The paper reviews the statistical properties of the Wigner time delay for disordered systems; the case of disorder in 1D with a chiral symmetry is discussed and the relation with exponential functionals of the Brownian motion is underlined. Another approach for the analysis of time delay statistics is the random matrix approach, from which we review few results. As a practical illustration, we briefly outline a theory of non-linear transport and AC transport developed by Büttiker and coworkers, where the concept of Wigner–Smith time delay matrix is a central piece allowing us to describe screening properties in out-of-equilibrium coherent conductors.