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Fermions and Bosons in a Double-Well Potential

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vol. 126
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issue 4a
A-118-A-123
EN
The boson-fermion model, describing a mixture of fermions and bosons is analyzed on a small, two-site lattice. The model includes all the on-site Coulomb-type interactions between bosons, between fermions and between fermions and bosons. Additionally, the Hamiltonian includes a term that describes a conversion of a pair of opposite-spin fermions into a boson and vice versa. We show how this conversion depends on the model parameters.
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Results of Monte Carlo simulations for the spinless Falicov-Kimball model with the next-nearest-neighbor hopping are presented. We find the critical value of the next-nearest-neighbor hopping integral, below which the low temperature configuration of the localized particles is the same as in the presence of only the nearest-neighbor hopping. Beyond this critical value the localized particles form horizontal or vertical stripes.
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The origin of the pseudogap is one of the most puzzling features of the high-temperature superconductors. There are two main scenarios: the first one assumes the presence of a hidden order competing or coexisting with superconductivity; within the framework of the second one the pseudogap is a precursor of the superconducting gap. In this paper we present some aspects of the hidden order pseudogap scenario. In particular, we discuss how the competing order modifies the structure of vortices in high-temperature superconductors. We demonstrate that the presence of the hidden order can explain some features of vortices observed in scanning tunneling microscopy experiments.
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We present exact diagonalization studies of two-dimensional electron gas on hexagonal lattice. Using Lanczös method we analyze the influence of the Coulomb correlations on the density of states and spectral functions. Choosing appropriate boundary conditions we simulate the geometry of a single wall carbon nanotube. In particular, integration over the boundary condition in one direction and summation in the other one allows us to perform cluster calculations for a tube-like system with a finite diameter and infinite length.
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Spontaneous Currents in a Bosonic Ring

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EN
Nonequilibrium dynamics of non-interacting bosons in a one-dimensional ring-shaped lattice is studied by means of the kinetic Monte Carlo method. The system is approximated by the classical XY model (the kinetic term is neglected) and then the simulations are performed for the planar classical spins. We study the dynamics that follows a finite-time quench to zero temperature. If the quench is slow enough the system can equilibrate and finally reaches the ground state with uniform spin alignment. However, we show that if the quench is faster than the relaxation rate, the system can get locked in a current-carrying metastable state characterized by a nonzero winding number. We analyze how the zero-temperature state depends on the quench rate.
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We investigate the vortex structure in the Penson-Kolb model with and without impurities. We focus on the consequences arising from the non-local field-dependent pairing interaction for the vortex profile, current distribution, and the local density of states.
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Motivated by the recent discovery of the cobalt oxide superconductors, we calculate the temperature dependence of the upper critical field on a triangular lattice. Using the lattice version of the Gor'kov equations we investigate how the applied magnetic field affects singlet and triplet types of superconductivity. We show that in a wide range of model parameters not only Zeeman coupling, but also the diamagnetic pair breaking mechanism favors the triplet pairing. In the cobalt oxide superconductors the symmetry of the order parameter remains an open problem and both singlet and triplet superconductivity should be taken into account. We show that in such a case, an external magnetic field may induce a transition from singlet to triplet superconductivity. We discuss experimental results which may confirm this tempting hypothesis.
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Experimental results concerning persistent currents in small rings threaded by a magnetic flux do not agree with theoretical predictions, especially for experiments performed in diffusive regime. This suggests important role of disorder in these experiments. In this paper we demonstrate how impurities present in ring modify the persistent current by generating or enhancing charge density waves. The electronic correlations are taken into account for both repulsive as well as attractive electron-electron interaction. The calculations are carried out for one-dimensional rings consisting of up to 12 lattice sites using Lanczös exact diagonalization approach, and for finite-width much larger rings using the Bogolyubov-de Gennes equations.
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We derive a doped carrier representation of the t-J model Hamiltonian. Within this approach the t-J model is described in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator. This representation of the t-J Hamiltonian is very convenient for underdoped systems since close to half-filling it allows for a controlled treatment of the crucial constraint of no doubly occupied sites. When neglecting the transverse spin-spin interaction, the effective Hamiltonian can be investigated with classical Monte Carlo simulations. We discuss the results obtained for systems consisting of several hundred lattice sites.
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issue 2
379-382
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We study thermodynamic properties of the two-dimensional (2D) Falicov-Kimball model in the presence of external magnetic field perpendicular to the lattice. The field is taken into account by the Peierls substitution in the hopping term. We show how the Hofstadter butterfly is affected by electronic correlations. In the non-interacting case the field dependent energy spectrum forms the famous Hofstadter butterfly. Our results indicate that for arbitrary nonzero interaction strength and arbitrary magnetic field there is a gap in the energy spectrum at sufficiently low temperature. The gap vanishes with increase of temperature for weak coupling, however, it persists at high temperatures if the coupling is strong enough. Numerical results have been obtained with the help of Monte Carlo technique based on a modified Metropolis algorithm.
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Spin related phenomena in quantum nanostructures have attracted recently much interest due to fast growing field of spintronics. In particular complex nanostructures are important as they provide a versatile system to manipulate spin and the electronic states. Such systems can be used as spin memory devices or scalable quantum bits. We investigate the spin relaxation for an electron in a complex structure composed of a quantum dot surrounded by a quantum ring. We shown that modifications of the confinement potential result in the substantial increase of the spin relaxation time.
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Transport properties of a two-dimensional nanostructure composed of a quantum dot surrounded by a quantum ring (dot-ring nanostructure), are discussed. This complex system is a highly controllable object. Conduction through dot-ring nanostructure depends crucially on the coupling strength of its states to the electrodes, which is related to the spatial distribution of the electron's wave functions in dot-ring nanostructure. This distribution can be strongly modified, e.g., by the electrical gating so that the ground and excited states move between the inner dot and the outer ring. In this paper we show that this property can be used to control single-electron DC current through dot-ring nanostructure in the Coulomb blockade regime so that it can be used as a single electron transistor.
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