Topological Phase Transition and Phase Diagrams in a Two-Leg Kitaev Ladder System

A scheme to investigate the topological properties in a two-leg Kitaev ladder system composed of two Kitaev chains is proposed. In the case of two identical Kitaev chains, it is found that the interchain hopping amplitude plays a significant role in the separation of the energy spectrum and in inducing a topologically nontrivial phase, while the interchain pairing strength only affects the size of the energy gap. Moreover, another situation that the system consists of two non-identical Kitaev chains is also investigated and the corresponding phase diagram is calculated. It is found that two pairs of degenerate nonzero edge modes will, respectively, appear in the upper and lower energy gaps when the interchain hopping amplitude or the interchain pairing strength is large enough. Furthermore, it is pointed out that the winding number is quantitatively equivalent to half of the number of zero energy edge modes in our system.     

Absence of single-particle Bose-Einstein condensation at low densities for bosons with correlated hopping

Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two-dimensional model of bosons with correlated hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without single-particle Bose-Einstein condensation (BEC) at low densities for sufficiently strong correlated hopping, and of an Ising quantum phase transition towards a BEC phase at larger density. The physical arguments supporting the mean-field results and their implications for bosonic and quantum spin systems are discussed.     

Exactly solvable chain of interacting electrons with correlated hopping and pairing

A generalization of the Mattis-Nam model Mattis and Nam (1972) [7], which takes into account a correlated hopping and pairing of electrons, is proposed, its exact solution is obtained. In the framework of the model the stability of the zero energy Majorana fermions localized at the boundaries is studied in the chain in which electrons interact through both the on-site Hubbard interaction and the correlated hopping and pairing. The ground-state phase diagram of the model is calculated, the region of existence of topological states is determined. It is shown that low-energy excitations destroy bonds between electrons in the chain, leading to an insulator state.     

Exact Determination of the Phase Structure of a Multi-Species Asymmetric Exclusion Process

We consider a multi-species generalization of the Asymmetric Simple Exclusion Process on an open chain, in which particles hop with their characteristic hopping rates and fast particles can overtake slow ones. The number of species is arbitrary and the hopping rates can be selected from a discrete or continuous distribution. We determine exactly the phase structure of this model and show how the phase diagram of the 1-species ASEP is modified. Depending on the distribution of hopping rates, the system can exist in a three-phase regime or a two-phase regime. In the three-phase regime the phase structure is almost the same as in the one species case, that is, there are the low density, the high density and the maximal current phases, while in the two-phase regime there is no high-density phase.     

Non perturbative calculations for three particles in a linear chain within the generalized Hubbard model

A real-space method has been introduced to study the pairing problem within the generalized Hubbard Hamiltonian. This method includes the bond-charge interaction term as an extension of the previously proposed mapping method [1] for the Hubbard model. The generalization of the method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem can be solved exactly. In a one-dimensional lattice, we analyzed the three particle correlation by calculating the binding energy at the ground state, using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interactions. A pairing asymmetry is found between electrons and holes for the generalized hopping amplitude, where the hole pairing is not always easier than the electron case. For some special values of the hopping parameters and for all kinds of interactions in the Hubbard Hamiltonian, an analytical solution is obtained. Received 21 January 2000 and Received in final form 18 July 2000     

Triplet superconducting pairing and density-wave instabilities in organic conductors

Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations, and both intrachain and interchain repulsive interactions. We find a close proximity of spin-density- and charge-density-wave phases and singlet d-wave and triplet f-wave superconducting phases. There is a striking correspondence between our results and recent puzzling experimental findings in the Bechgaard salts, including the coexistence of spin-density-wave and charge-density-wave phases and the possibility of a triplet pairing in the superconducting phase.     

Trivial and non-trivial superconductivity in dsDNA

A double-stranded DNA (dsDNA) is modeled by two coupled one-dimensional Kitaev's chain and the topological superconductivity is studied. It is shown that the zero energy mode exists under some specific conditions. The wave function of zero mode is calculated and it is shown that the Majorana quasi-particles exist on the ends of each strand. By calculating the winding number, we show that the topological phase transition can happen if the hopping integral between two strands is very smaller than the pairing potential between the Cooper pairs. It means that the dsDNA behaves as a trivial superconductor, commonly, but single-stranded DNA (or two coupled ssDNA with very small hopping between them) may behave as a non-trivial superconductor. Finally, we suggest an experimental setup for probable detection of Majorana quasi-particle in DNA.     

交错跃迁Hofstadter梯子的量子流相

为玻色Hofstadter梯子模型引入交错跃迁,来扩展模型支持的量子流相.基于精确对角化和密度矩阵重整化群计算发现,无相互作用时,系统中包含横流相、涡旋相和纵流相;横流相来自均匀跃迁时Hofstadter梯子模型的Meissner相,纵流相是交错跃迁时才可见的流相.强相互作用极限下系统的超流区也包含横流相、纵流相和涡旋相,但存在更多的相变级数;超流区的横流相、纵流相之间存在相变但Mott区的不存在,把Mott区的"横、纵流相"称为Mott-均匀相,在Mott区只存在均匀相和涡旋相.跃迁的交错会压缩涡旋相存在的区域,使Mott区最终只剩下均匀相;跃迁的交错不仅能驱动Mott-超流相变,还使磁通的改变也能够驱动系统的Mott-超流相变.对这一系统的研究丰富了磁通系统中的量子流相,同时为研究拓扑流特性提供了模型支持.     

The ground state of the two-leg Hubbard ladder a density-matrix renormalization group study

We present density-matrix renormalization group results for the ground state properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an insulating spin-gapped system, exhibiting a crossover from a spin liquid to a band insulator as a function of the interchain hopping matrix element. When the system is doped, there is a parameter range in which the spin gap remains. In this phase, the doped holes from singlet pairs and the pair field and the “4k_F” density correlations associated with pair-density fluctuations decay as power laws, while the “2k_F” charge density wave correlations decay exponentially. We discuss the behavior of the exponents of the pairing and density correlations within this spin-gapped phase. Additional one-band Luttinger liquid phases which occur in the large interband hopping regime are also discussed.     

Unusual Destruction and Enhancement of Superfluidity of Atomic Fermi Gases by Population Imbalance in a One-Dimensional Optical Lattice

We study the superfluid behavior of a population imbalanced ultracold atomic Fermi gases with a short range attractive interaction in a one-dimensional(1 D) optical lattice,using a pairing fluctuation theory.We show that,besides widespread pseudogap phenomena and intermediate temperature superfluidity,the superfluid phase is readily destroyed except in a limited region of the parameter space.We find a new mechanism for pair hopping,assisted by the excessive majority fermions,in the presence of c...     

Effect of next-nearest-neighbour interaction on dx2?y2-wave superconducting phase in 2D t-J model

An exact diagonalization calculation of the t-J model on 2D square cluster has been studied for the ground state properties of HTSC. Effect of next-nearest-neighbour hopping and magnetic (both antiferromagnetic and ferromagnetic) interaction on d _x ²−y ²-wave pairing has been shown. Relative strength of the next-nearest-neighbour interaction with respect to that of near-neighbour interaction for the strongest d _x ²−y ²-wave pairing has been estimated. A schematic phase diagram is shown. It is shown that a two-sublattice model with antiferromagnetic interaction between them and a small intra-ferromagnetictype interaction in one sublattice favours d _x ²−y ²-wave superconductivity and moderate negative type NNN hopping adds flavours to this phase.     

Topological phase boundary in a generalized Kitaev model

We study the effects of the next-nearest-neighbor hopping and nearest-neighbor interactions on topological phases in a one-dimensional generalized Kitaev model. In the noninteracting case, we define a topological number and calculate exactly the phase diagram of the system. With addition of the next-nearest-neighbor hopping, the change of phase boundary between the topological and trivial regions can be described by an effective shift of the chemical potential. In the interacting case, we obtain the entanglement spectrum, the degeneracies of which correspond to the topological edge modes, by using the infinite time-evolving block decimation method. The results show that the interactions change the phase boundary as adding an effective chemical potential which can be explained by the change of the average number of particles.     

Self-organized criticality in 1D stochastic traffic flow model

Results of computer simulations of a 1D particle hopping model of traffic flow are presented. The model is characterized by parallel update and fully asymmetric stochastic hopping dynamics which allows unbounded series of jumps to empty neighbour sites on the right. The considered case of open boundary conditions can be used to model a “bottleneck” situation in traffic. Evidence for self-organized criticality is found in two aspects: the presence of long-range spatial correlations manifested in the shape of density profiles, and long-time temporal correlations showing up in the low-frequency behaviour of the spectral density of the total particle number and flow. A plausible conjecture is to interpret the observed qualitative changes in these features, as a function of the injection rate and the hopping probability, in terms of a nonequilibrium phase transition between a low-density phase and a maximal current phase. This conjecture is supported by the phase diagram obtained in mean-field approximation.     

Electronic phase transitions in the spinless falicov-kimball model with correlated hopping

The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. It is shown that in the half-filled band case the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional Falicov-Kimball model (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition. Outside half-filling correlated hopping stabilizes the segregated phase in the ground-state, however, the nature of the ground-state remains qualitatively unchanged.     

Rotonlike Fulde-Ferrell collective excitations of an imbalanced Fermi gas in a two-dimensional optical lattice

We address the question of whether superfluidity can survive in the case of fermion pairing between different species with mismatched Fermi surfaces using as an example a population-imbalanced mixture of 6Li atomic Fermi gas loaded in a two-dimensional optical lattice at nonzero temperatures. The collective mode is calculated from the Bethe-Salpeter equations in the general random phase approximation assuming a Fulde-Ferrell order parameter. The numerical solution shows that, in addition to low-energy (Goldstone) mode, two rotonlike minima exist, and therefore, the superfluidity can survive in this imbalanced system.     

Superconducting phase and pairing fluctuations in the half-filled two-dimensional Hubbard model

The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.     

Enhanced pairing in doped quantum magnets with frustrated hole motion

Evidence for strong pairing at arbitrarily small J/t is provided in a t-J model on the checkerboard lattice for a specific sign of the hopping amplitude. Destructive quantum interferences suppress Nagaoka ferromagnetism when J/t-->0 and drastically reduce coherent hole motion in the fluctuating singlet background. It is shown that, by pairing in various orbital symmetry channels, holes can benefit from a large gain of kinetic energy.     

Correlation mediated superconductivity in a Spin Peierls phase of the Hubbard model

We explore the consequences of a mapping of the Hubbard Hamiltonian with a view to finding possible superconducting phases. The transformation pairs up all the sites and is therfore a much more natural starting point for describing a Spin Peierls transition, generating enhanced singlet correlations for this pairing, than it is for describing the Resonating Valence Bond (RVB) state of Anderson. We show that in the less than half filling case, an effective non-linear hopping Hamiltonian is quite useful in describing half of the electrons. This effective Hamiltonian can show a form of superconducting instability when nearest neighbour hopping is introduced to stabilise it. This superconducting phase seems to be a very unlikely possibility for the standard Hubbard model.     

A model of hopping and band DC photoconduction in doped crystals

Expressions for the screening length and the ambipolar diffusion length are derived, for the first time, for the case where hopping conduction and band conduction coexist in semiconductors with hydrogen-like impurities. A method is proposed for calculating the diffusion coefficient of electrons (holes) hopping between impurity atoms from data on the Hall effect, in the case where the hopping and band conductivities are equal. An interpretation is given of available experimental data on hopping photoconduction between acceptors (Ga) and donors (As) in p-Ge at T=4.2 K doped by a transmutation method. It is shown that the relative magnitude of the mobilities of electrons hopping between donors and holes hopping between acceptors can be found from the hopping photoconductivity measured as a function of the intensity of band-to-band optical carrier excitation.     

Topological phase diagram of a Kitaev ladder

We investigate the topological properties of a Kitaev ladder, i.e., a system made of two Kitaev chains coupled together by transversal hopping and pairing term, t₁ and Δ₁, respectively. Using the Chern number invariant, we present the topological phase diagram of the system. It is shown that beyond a non-topological phase, the system exhibits a topological phase either with four or two Majorana (zero energy) modes. In particular, we find that for some critical values of the transversal hopping t₁, and at a given transversal paring Δ₁, the topological phase survives also when the Kitaev criterion for the single chain (Δ > 0,   |μ| < 2t) is violated. Using a tight-binding analysis for a finite-size system we numerically check the bulk-edge correspondence.