Limit Of Large Interaction Research Articles

Charge dynamics in magnetically disordered Mott insulators

With the aid of both a semianalytical and a numerically exact method, we investigate the charge dynamics in the vicinity of half-filling in the one- and two-dimensional $t\text{\ensuremath{-}}J$ model derived from a Fermi-Hubbard model in the limit of large interaction $U$ and hence small exchange coupling $J$. The spin degrees of freedom are taken to be disordered. So we consider the limit $0<J\ensuremath{\ll}T\ensuremath{\ll}W$, where $W$ is the bandwidth. We focus on evaluating the local spectral density of a single hole excitation and the charge gap that separates the upper and the lower Hubbard band. We find indications that no band edges exist if the magnetic exchange is taken into account; instead of band edges, Gaussian tails seem to appear. A discussion of the underlying physics is provided.

Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case

We analyze the top Lyapunov exponent of the product of sequences of two by two matrices that appears in the analysis of several statistical mechanics models with disorder: for example these matrices are the transfer matrices for the nearest neighbor Ising chain with random external field, and the free energy density of this Ising chain is the Lyapunov exponent we consider. We obtain the sharp behavior of this exponent in the large interaction limit when the external field is centered: this balanced case turns out to be critical in many respects. From a mathematical standpoint we precisely identify the behavior of the top Lyapunov exponent of a product of two dimensional random matrices close to a diagonal random matrix for which top and bottom Lyapunov exponents coincide. In particular, the Lyapunov exponent is only $\log$-H\"older continuous.

Enhanced performance of a quantum-dot-based nanomotor due to Coulomb interactions

We study the relation between quantum pumping of charge and the work exchanged with the driving potentials in a strongly interacting ac-driven quantum dot. We work in the large-interaction limit and in the adiabatic pumping regime, and we develop a treatment that combines the time-dependent slave-boson approximation with linear response in the rate of change of the ac-potentials. We find that the time evolution of the system can be described in terms of equilibrium solutions at every time. We analyze the effect of the electronic interactions on the performance of the dot when operating as a quantum motor. The main two effects of the interactions are a shift of the resonance and an enhancement of the efficiency with respect to a non-interacting dot. This is due to the appearance of additional ac-parameters accounting for the interactions that increase the pumping of particles while decreasing the conductance.

Multihole edge states in Su-Schrieffer-Heeger chains with interactions

We address the effect of nearest-neighbor (NN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) chain, with alternating hopping amplitudes t1 and t2. Both numerically and analytically, we show that the presence of interactions induces phase transitions between topologically different regimes. In the particular case of one-hole excitations in a half-filled SSH chain, the V=t2 vs. t1=t2 phase diagram has topological phases at diagonal regions of the phase plane. The interaction acts in this case as a passivation potential. For general filling of the SSH chain, different eigensubspaces of the SSH Hamiltonian may be classified as topologically trivial and non-trivial. The two-hole case is studied in detail in the large interaction limit, and we show that a mapping can be constructed of the two-hole SSH eigensubspaces into one-particle states of a non-interacting one-dimensional (1D) tight-binding model, with interfaces between regions with different hopping constants and local potentials. The presence of topological edge states in the equivalent chain can be readily identifed, as well as their correspondence to the original two-hole states. Furthermore, we found that the presence of the NN interaction generates a state where two holes occupy two consecutive edge states. Such many-body states should also occur for arbitrary filling leading to the possibility of a macroscopic hole gathering at the surface (at consecutive edge states).

Magnetism, transport, and thermodynamics in two-dimensional half-filled Hubbard superlattices

We study magnetic, transport and thermodynamic properties of the half-filled two-dimensional ($2D$) Hubbard model with layered distributed repulsive interactions using unbiased finite temperature quantum Monte Carlo simulations. Antiferromagnetic long-ranged correlations at $T=0$ are confirmed by means of the magnetic structure factor and the onset of short-ranged ones is at a minimum temperature which can be obtained by peaks in susceptibility and specific heat following an RPA prediction. We also show that transport is affected in the large interaction limit and is enhanced in the non-repulsive layers suggesting a change of dimensionality induced by increased interactions. Lastly, we show that by adiabatically switching the interactions in layered distributed patterns reduces the overall temperature of the system with a potential application in cooling protocols in cold atoms systems.

Phase diagram and entanglement of two interacting topological Kitaev chains

A superconducting wire described by a $p$-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb-type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising-type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultracold atoms and Josephson junctions.

Dynamic phase diagram for the quantum phase model

We address the stability of superfluid currents in a system of interacting lattice bosons. We consider various Gutzwiller trial states for the quantum phase model which provides a good approximation for the Bose-Hubbard model in the limit of large interactions and boson populations. We thoroughly analyze the current-carrying stationary states of the dynamics ensuing from a Gaussian ansatz, and derive analytical results for the critical lines signaling their modulational and energetic instability, as well as the maximum of the carried current. We show that these analytical results are in good qualitative agreement with those obtained numerically in previous works on the Bose-Hubbard model, and in the present work for the quantum phase model.

Correlated Dirac particles and superconductivity on the honeycomb lattice

We investigate the properties of the nearest-neighbor singlet pairing and the emergence of d-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t-J_1-J_2$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott insulating state, we confirm the emergence of d-wave superconductivity in agreement with earlier works. We show that a small but finite $J_2$ spin coupling between next-nearest neighbors stabilizes d-wave symmetry compared to the extended s-wave scenario. At small hole doping, to minimize energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a $d+id$ singlet pairing assigned to one valley and a $d-id$ singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral $d+id$ symmetry and breaking time-reversal symmetry. Then, we apply the functional Renormalization Group and we study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half-filling. We discuss possible applications to strongly-correlated compounds with Copper hexagonal planes such as In$_3$Cu$_{2}$VO$_9$. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.

Scaling behavior and phase diagram of a [formula omitted]-symmetric non-Hermitian Bose–Hubbard system

We study scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose–Hubbard model. In the free interaction case, using both analytical and numerical approaches, the metric operator for many-particle is constructed. The derived properties of the metric operator, similarity matrix and equivalent Hamiltonian reflect the fact that all the matrix elements change dramatically with diverging derivatives near the exceptional point. In the nonzero interaction case, it is found that even small on-site interaction can break the PT symmetry drastically. It is demonstrated that the scaling law can be established for the exceptional point in both small and large interaction limit. Based on perturbation and numerical methods, we also find that the phase diagram shows rich structure: there exist multiple regions of unbroken PT symmetry.

Variational Monte Carlo study of Anderson localization in the Hubbard model

We have studied the effects of interactions on persistent currents in half-filled and quarter-filled Hubbard models with weak and intermediate strength disorder. Calculations are performed using a variational Gutzwiller ansatz that describes short-range correlations near the Mott transition. We apply an Aharonov-Bohm magnetic flux, which generates a persistent current that can be related to the Thouless conductance. The magnitude of the current depends on both the strength of the screened disorder potential and the strength of electron-electron correlations, and the Anderson localization length can be extracted from the scaling of the current with system size. At half-filling, the persistent current is reduced by strong correlations when the interaction strength is large. Surprisingly, we find that the disorder potential is strongly screened in the large interaction limit, so that the localization length grows with increasing interaction strength even as the magnitude of the current is suppressed. This supports earlier dynamical mean-field-theory predictions that the elastic scattering rate is suppressed near the Mott transition.

Phase separation of trapped spin-imbalanced Fermi gases in one-dimensional optical lattices

We calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local density approximation (LDA) and density matrix renormalization group (DMRG) simulations. Based on the exact equation of state obtained by Bethe ansatz, LDA predicts that the gas phase-separates into shells with a partially polarized core and fully paired wings, where the latter occurs below a critical spin polarization. This behavior is also seen in numerically exact DMRG calculations at sufficiently large particle numbers. Unlike the continuum case, we show that the critical polarization is a non monotonic function of the interaction strength and vanishes in the limit of large interactions.

Spin glass behaviors compatible with a Zhang–Rice singlet within an effective model forcuprate superconductors

To address the incompatibility of Zhang–Rice singlet formation and the observedspin glass behavior, an effective model is proposed for the electronic behavior ofcuprate materials. The model includes an antiferromagnetic interaction betweenthe spin of the hole in a Zhang–Rice orbital and the spin of the hole on thecorresponding copper site. While in the large interaction limit this recovers thet–J model, in the low energy limit the Zhang–Rice singlets are deformed. It is also shown thatsuch deformation can induce random defect ferromagnetic (FM) bonds between adjacentlocal spins, an effect herein referred to as unusual double exchange, and then spin glassbehavior shall result in the case of localized holes. A derivation of the model is alsopresented.

Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit

In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any positive U to the limit of large interaction is also shown. This continuity property, when combined with the proof that the wavefunction obtained with the generalized Bethe Ansatz is normalizable, is relevant to the question of whether or not the solution gives us the ground state of the finite system, as suggested by Lieb and Wu. Lastly, for the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the well known solution of the 1D Hubbard model.

Dynamical systems with time-dependent coupling: clustering and critical behaviour

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with autonomous dynamics. The system exhibits different dynamical regimes, with various forms of collective organization, controlled by the range of interactions and the dispersion of time scales in the evolution of the internal variables. In the limit of large interaction ranges, it reduces to an ensemble of coupled identical phase oscillators and, to some extent, admits to be treated analytically. We find and characterize a transition between ordered and disordered states, mediated by a regime of dynamical clustering.

Hubbard model for intermediate-dimensional excitons.

A Hubbard model is solved exactly to characterize confined, intermediate-dimensional excitons for the full range of electron and hole hopping and interaction strengths. Finite systems with periodic boundary conditions model unconfined excitons. Finite systems with terminated ends model confined excitons. Exciton energies, oscillator strengths, and electron and hole distributions are determined. Oscillator strengths and electron-hole distributions of confined intermediate-dimensional excitons exhibit anomalous, nonmonotonic, nonuniversal dependences on the electron-hole interaction strength and hopping that are counter to the conventional behavior for quantum-confined excitons and free excitons. Perturbation theory is used to clarify the weak and large interaction limits. In the large-interaction limit, an exciton dead layer occurs near the boundary of the system because electron-hole correlation is suppressed near the boundary. Second-order perturbation theory determines the surface potential barrier caused by the suppression of pair correlation near the surface and determines the hopping rate for tunneling into this barrier. In the weak-interaction limit, on-site correlation of a confined electron-hole pair is suppressed by asymmetry in the electron and hole hopping. For large asymmetry in the electron and hole hopping, the oscillation strength of the confined intermediate-dimensional exciton can be less than the oscillator strength of an uncorrelated, noninteracting pair.

Impurity band states in SI(P)

A comparison is made between calculated impurity band densities of state in Si(P) for donor concentrations below that of the semiconductor-to-metal transition and experimental results obtained from photoluminescence spectra after subtracting an electron-hole droplet line. The theoretical results were obtained within the large interaction limit of the Hubbard model, assuming the impurities to be randomly distributed. The density of states was computed from cumulants appropriate to the low and high impurity density limit.

Electrical conductivity in narrow-band materials

The dc conductivity of a system of strongly interacting electrons in narrow-band materials is calculated using the large-interaction limit of the Hubbard model with impurities. A generalized-moment method allows for the calculation of the conductivity for arbitrary electron and impurity concentrations as a function of magnetization. The conductivity vanishes for a half-filled band, and in the absence of impurities it increases approximately linearly with the number of empty or doubly occupied sites. In the absence of electron-electron scattering the impurity-limited conductivity varies linearly as the product of the hole and electron concentrations. Numerical results indicate that to within 3% a generalized Matthiessen's rule holds; the resistivities due to impurities and electron-electron interactions are additive. An upper bound on the conductivities of strongly interacting electrons in narrow-band materials is obtained. The model of a planar antiferromagnet is used to explain the anisotropic conductivity of nickel sulfide below the N\'eel temperature.

Electron-Magnon Bound States

Interactions between strongly correlated electrons (or holes) and spin waves are investigated with the aid of a simple physical model. The model is the large-interaction limit of the Hubbard model with an additional ferromagnetic Heisenberg interaction between nearest-neighbor singly occupied sites. We find that even though there is no obvious electron-magnon attraction in the model, electron-magnon bound states exist for some crystal structures.