Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States

We explain how to implement, in the context of projected entangled-pair states (PEPS), the general procedure of fermionization of a tensor network introduced in [P. Corboz, G. Vidal, Phys. Rev. B 80, 165129 (2009)]. The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the t-J model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.Comment: 25 pages, 35 figures (revised version

Monte Carlo study of fermionic trions in a square lattice with harmonic confinement

We investigate the strong-coupling limit of a three-component Fermi mixture in an optical lattice with attractive interactions. In this limit bound states (trions) of the three components are formed. We derive an effective Hamiltonian for these composite fermions and show that it is asymptotically equivalent to an antiferromagnetic Ising model. By using Monte-Carlo simulations, we investigate the spatial arrangement of the trions and the formation of a trionic density wave (CDW), both in a homogeneous lattice and in the presence of an additional harmonic confinement. Depending on the strength of the confinement and on the temperature, we found several scenarios for the trionic distribution, including coexistence of disordered trions with CDW and band insulator phases. Our results show that, due to a proximity effect, staggered density modulations are induced in regions of the trap where they would not otherwise be present according to the local density approximation.Comment: 10 pages, 8 figure

SUPERFLUID CHARACTERISTICS OF INDUCED-PAIRING MODEL

We study the electromagnetic and thermodynamic properties of a model of coexisting local electron pairs and itinerant carriers coupled via the intersubsystem charge exchange. The calculations of the London penetration depth, the energy gap, the magnetic critical fields and the coherence length in the superconducting phase are performed. The effects of reduced binding energy of local pairs are discussed. The 'considered effective Hamiltonian of coexisting localized d-electrons and itinerant c-electrons can be written as where E0 measures the relative position of d-level with respect to the bottom of the c-electron band εk in the absence of interactions, is the chemical potential which ensures that a total number of particles is constant, i.e. n = n, -I-n a = (Σkσ (ck ckσ) + Σi σ (n ó)) /N, U is the effective on-site density interaction between d-electrons, t is the hopping integral for c-electrons and I0 is the intersubsystem charge exchange coupling. The Peierls factor in Eq. (1) account for the coupling of electrons to the magnetic field via its vector potential A(r). Φij = -fi g f' drA(r), and e is the electron charge. In analysis we used the variational approach which treats the on-site interaction term U exactl

Phase separation in a lattice model of a superconductor with pair hopping

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d=1) in the ground state. Moreover, at T=0 some results derived within the random phase approximation (and the spin-wave approximation) for d=2 and d=3 lattices and within the low density expansions for d=3 lattices are presented. Our investigation of the general case (as a function of the electron concentration and as a function of the chemical potential) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases: superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.Comment: 15 pages, 9 figures; pdf-ReVTeX, final version, corrected typos; submitted to Journal of Physics: Condensed Matte

Superconductivity of the Two-Dimensional Penson-Kolb Model

Two-dimensional (d=2) Penson-Kolb model, i.e. the tight-binding model with the pair-hopping (intersite charge exchange) interaction, is considered and the effects of phase fluctuations on the s-wave superconductivity of this system are discussed within the Kosterlitz-Thouless scenario. The London penetration depth λ at T=0, the Kosterlitz-Thouless critical temperature T$\text{}_{c}$, and the Hartree-Fock approximation critical temperature T$\text{}_{p}$ are determined as a function of particle concentration and interaction. The Uemura type plots (T$\text{}_{c}$ vs.λ$\text{}^{-2}$(0)) are derived. Beyond weak coupling and for low concentrations they show the existence of universal scaling: T$\text{}_{c}$ ~1/λ$\text{}^{2}$(0), as it was previously found for the attractive Hubbard model and for the models with intersite electron pairing

Electron Orderings of Half-Filled Extended Hubbard Models with Spin- and Charge-Exchange Interaction

The electron orderings of the half-filled extended Hubbard models (i) with anisotropic spin-exchange interactions (the t-U-J$\text{}_{ǁ}$-J$\text{}_{⊥}$ model) and (ii) with charge-exchange interaction (the t-U-I model) are discussed. In particular, we present new results concerning the phase diagrams of the model (i) in the case of uniaxial spin exchange (J$\text{}_{ǁ}$≢0) for d-dimensional hypercubic lattices (1≤d≤∞) and conclude about the basic effects of the particular spin- and charge-exchange interaction terms (J$\text{}_{ǁ}$, J$\text{}_{⊥}$, and I) in both models

Ground State Phase Diagrams of the Extended Hubbard Model with Repulsive Pair-Hopping Interaction for Nonfrustrated 2D Lattice

We analyze the extended Hubbard model with pairhopping interaction J, i.e. the PensonKolbHubbard model, in the case of repulsive J (J < 0) within the (broken symmetry) HartreeFock approximation. We fo-cus our study on the effects of on-site U interaction on the mutual stability of magnetic, charge-ordered, and superconducting states including the eta-pairing phase, i.e. the state with the Cooper-pair center-of-mass momen-tum q = Q. The ground state phase diagrams are obtained for arbitrary particle concentration n on nonfrustrated d = 2 square lattice

Superconducting Properties of theη-Pairing State in the Penson-Kolb-Hubbard Model

The Penson-Kolb-Hubbard model, i.e. the Hubbard model with the pair-hopping interaction J is studied. We focus on the properties of the superconducting state with the Cooper-pair center-of-mass momentum q= Q (η-phase). The transition into theη-phase, which is favorized by the repulsive J (J<0) is found to occur only above some critical value |J$\text{}_{c}$|, dependent on band filling, on-site interaction U and band structure, and the system never exhibits standard BCS-like features. This is in obvious contrast with the properties of the isotropic s-wave state, stabilized by the attractive J and attractive U, which exhibit at T=0 a smooth crossover from the BCS-like limit to that of tightly bound pairs with increasing pairing strength

Influence of Coulomb Interactions on the Properties of Induced Pairing Model

We study the superconducting properties of a model of coexisting itinerant carriers and local pairs with finite binding energy, taking into account the effects of Coulomb (density-density) and direct pair hopping interactions. The evolution of the phase diagrams and superfluid characteristics with electron concentration, interaction parameters and the relative position of the bands is examined. The model is found to exhibit several kinds of superconducting behaviors ranging from the BCS-like to the local-pair-like. The relevance of the obtained results to the interpretation of experimental data for the doped bismuthates (Ba$\text{}_{1-x}$K$\text{}_{x}$BiO$\text{}_{3}$ and BaPb$\text{}_{1-x}$BiO$\text{}_{3}$) is pointed out