Bound states in the one-dimensional two-particle Hubbard model with an impurity (original) (raw)
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Physical Review Letters, 2012
We report a bound state, which is embedded in the continuum spectrum, of the one-dimensional two-particle (Bose or Fermion) Hubbard model with an impurity potential. The state has the Bethe-ansatz form, although this model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.
Bound States in the One-dimensional Hubbard Model
1998
The Bethe Ansatz equations for the one-dimensional Hubbard model are reexamined. A new procedure is introduced to properly include bound states. The corrected equations lead to new elementary excitations away from half-filling.
Emergent low-energy bound states in the two-orbital Hubbard model
Physical Review B, 2018
A repulsive Coulomb interaction between electrons in different orbitals in correlated materials can give rise to bound quasiparticle states. We study the non-hybridized two-orbital Hubbard model with intra (inter)-orbital interaction U (U12) and different band widths using an improved dynamical mean field theory numerical technique which leads to reliable spectra on the real energy axis directly at zero temperature. We find that a finite density of states at the Fermi energy in one band is correlated with the emergence of well defined quasiparticle states at excited energies ∆ = U − U12 in the other band. These excitations are inter-band holon-doublon bound states. At the symmetric point U = U12, the quasiparticle peaks are located at the Fermi energy, leading to a simultaneous and continuous Mott transition settling a long-standing controversy.
Scattering resonances and two-particle bound states of the extended Hubbard model
Journal of Physics B: Atomic, Molecular and Optical Physics, 2009
We present a complete derivation of two-particle states of the one-dimensional extended Bose-Hubbard model involving attractive or repulsive on-site and nearest-neighbour interactions. We find that this system possesses scattering resonances and two families of energy-dependent interactionbound states which are not present in the Hubbard model with the on-site interaction alone.
Even-odd and super-even effects in the attractive Hubbard model
Physical Review B, 1999
The canonical BCS wave function is tested for the attractive Hubbard model. Results are presented for one dimension, and are compared with the exact solutions by the Bethe ansatz and the results from the conventional grand canonical BCS approximation, for various chain lengths, electron densities, and coupling strengths. While the exact ground state energies are reproduced very well both by the canonical and grand canonical BCS approximations, the canonical method significantly improves the energy gaps for small systems and weak coupling. The "parity" effect due to the number of electrons being even or odd naturally emerges in our canonical results. Furthermore, we find a "super-even" effect: the energy gap oscillates as a function of even electron number, depending on whether the number of electrons is 4m or 4m + 2 (m integer). Such oscillations as a function of electron number should be observable with tunneling measurements in ultrasmall metallic grains.
Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetism
Physical Review A, 2009
We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the inter-site tunneling rate. An ensemble of such lattice-dimers is accurately described by an effective Hamiltonian of hard core bosons with strong nearest-neighbor repulsion which is equivalent to the XXZ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (anti-ferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the anti-ferromagnetic density profile and in density-density correlations. We derive a kink model which provides simple quantitative explanation of these features. To describe the longrange correlations of the system we employ the Luttinger liquid theory with the relevant Luttinger parameter K obtained exactly using the Bethe Ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density matrix renormalization group (DMRG) methods. We also present a perturbative treatment of the system in higher dimensions.
Physics Letters A, 2009
Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed for an open chain with L sites. Authors considered the case when the boundary site has a negative chemical potential-p and the Hubbard coupling U is positive. They have shown by an analytic method that when p is larger than the transfer integral some of the ground-state solutions of the Bethe ansatz equations become complex-valued. They have found that there is a surface phase transition at some critical value p c ; when p < p c all the charge excitations have the gap for this case, while there exists a massless charge mode when p > p c. To find whether this "surface phase transition" is of the first order or of the second order we have used the entanglement entropy concept. The entropy and its derivative has a discontinuity there, so this transition is of the first order.
A ug 2 00 4 Mixed phase and bound states in the phase diagram of the extended Hubbard model
The paper examines part of the ground state diagram of the extended Hubbard model, with the on-site attraction U < 0 and intersite repulsion W > 0 in the presence of charge density waves, superconducting and η-superconducting order parameters. We show the possibility of the stabilization of the mixed state, with all three nonzero order parameters, in the model with nearest neighbor interactions. The other result of the paper is application of the exact solution of the Schrodinger equation for the two-electron bound state, as an additional bound for the phase diagram of the model, resulting in the partial suppression of the superconducting state of the s-wave symmetry, in favor of the normal state phase.
Exact ground state of the two-dimensional Hubbard model at half-filling for U=0+
Solid State Communications, 2001
We solve analytically the N × N square lattice Hubbard model for even N at half filling and weak coupling by a new approach. The exact ground state wave function provides an intriguing and appealing picture of the antiferromagnetic order. Like at strong coupling, the ground state has total momentum Ktot = (0, 0) and transforms as an s wave for even N/2 and as a d wave otherwise.
Two-particle states in the Hubbard model
Journal of Physics B: Atomic, Molecular and Optical Physics, 2008
We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle states, which can be classified as (i) scattering states of asymptotically free particles, and (ii) interaction-bound dimer states. Our results provide a very transparent framework to understand the properties of interacting pairs of particles in a lattice.