Anomalous Spin and Charge Dynamics of the 2D t-J Model at low doping

We present an exact diagonalization study of the dynamical spin and density correlation function of the 2D t-J model for hole doping < 25%. Both correlation functions show a remarkably regular, but completely different scaling behaviour with both hole concentration and parameter values: the density correlation function is consistent with that of bosons corresponding to the doped holes and condensed into the lowest state of the noninteracting band of width 8t, the spin correlation function is consistent with Fermions in a band of width J. We show that the spin bag picture gives a natural explanation for this unusual behaviour.Comment: Revtex-file, 4 PRB pages + 5 figures attached as uu-encoded ps-files Hardcopies of figures (or the entire manuscript) can also be obtained by e-mailing to: [email protected]

Landau mapping and Fermi liquid parameters of the 2D t-J model

We study the momentum distribution function n(k) in the 2D t-J model on small clusters by exact diagonalization. We show that n(k) can be decomposed systematically into two components with Bosonic and Fermionic doping dependence. The Bosonic component originates from the incoherent motion of holes and has no significance for the low energy physics. For the Fermionic component we exlicitely perform the one-to-one Landau mapping between the low lying eigenstates of the t-J model clusters and those of an equivalent system of spin-1/2 quasiparticles. This mapping allows to extract the quasiparticle dispersion, statistics, and Landau parameters. The results show conclusively that the 2D t-J model for small doping is a Fermi liquid with a `small' Fermi surface and a moderately strong attractive interaction between the quasiparticles.Comment: Revtex file, 5 pages with 5 embedded eps-files, hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to: [email protected]

Dynamics of an SO(5) symmetric ladder model

We discuss properties of an exactly SO(5) symmetric ladder model. In the strong coupling limit we demonstrate how the SO(3)-symmetric description of spin ladders in terms of bond Bosons can be upgraded to an SO(5)-symmetric bond-Boson model, which provides a particularly simple example for the concept of SO(5) symmetry. Based on this representation we show that antiferro- magnetism on one hand and superconductivity on the other hand can be understood as condensation of either magnetic or charged Bosons into an RVB vacuum. We identify exact eigenstates of a finite cluster with general multiplets of the SO(5) group, and present numerical results for the single particle spectra and spin/charge correlation functions of the SO(5)-symmetric model and identify `fingerprints' of SO(5) symmetry in these. In particluar we show that SO(5) symmetry implies a `generalized rigid band behavior' of the photoemission spectrum, i.e. spectra for the doped case are rigorously identical to spectra for spin-polarized states at half-filling. We discuss the problem of adiabatic continuity between the SO(5) symmetric ladder and the actual t-J ladder and demonstrate the feasibility of a `Landau mapping' between the two models.Comment: Revtex-file, 16 pages with 15 eps-figures. Hardcopies of Figures (or the entire manuscript) obtainable by e-mail request to [email protected]

Validity of the rigid band picture for the t-J model

We present an exact diagonalization study of the doping dependence of the single particle Green's function in 16, 18 and 20 site clusters of t-J model. We find evidence for rigid-band behaviour starting from the half-filled case: upon doping, the topmost states of the quasiparticle band observed in the photoemisson spectrum at half-filling cross the chemical potential and reappear as the lowermost states of the inverse photoemission spectrum. Features in the inverse photoemission spectra which are inconsistent with rigid-band behaviour are shown to originate from the nontrivial point group symmetry of the ground state with two holes, which enforces different selection rules than at half-filling. Deviations from rigid band behaviour which lead to the formation of the `large Fermi surface' in the momentum distribution occur only at energies far from the chemical potential. A Luttinger Fermi surface and a nearest neighbor hopping band do not exist.Comment: Remarks: Revtex file + 7 figures attached as compressed postscript files Figures can also be obtained by ordinary mail on reques

Spin bags in the doped t-J model

We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to $1/8$, use of the composite operators leads to a drastic simplification of the single particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting Fermions corresponding to the doped holes. We conclude that for all doping levels under study, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin fluctuation picture and show that the dressing of the holes leads to formation of a bound state with d(x^2-y^2) symmetry.Comment: Remarks: Revtex file + 4 figures attached as compressed postscript files Figures can also be obtained by ordinary mail on reques

Ground state properties and dynamics of the bilayer t-J model

We present an exact diagonalization study of bilayer clusters of t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio J_perp/J between inter-layer and intra-layer exchange constants increases: for small J_perp/J the data suggest the development of 3D antiferromagnetic correlations without appreciable degradation of the intra-layer spin order and the d_(x2-y2) hole pairs within the planes persist. For larger values of J_perp/J local singlets along the inter-layer bonds dominate, leading to an almost complete suppression of the intra-layer spin correlation and the breaking of the intra-layer pairs. The ground state with two holes in this regime has s-like symmetry. The data suggest that the crossover may occur for values of J_perp/J as small as 0.2. We present data for static spin correlations, spin gap, and electron momentum distribution and spectral function of the `inter-layer RVB state' realized for large J_perp/J. The latter deviates from the single layer ground state, making it an implausible candidate for modelling high-temperature superconductors.Comment: Revtex-file, 6 PRB pages, figures appended as uu-encoded postscript. Hardcopies of figures (or the entire manuscript) can be obtained by e-mailing to: [email protected]

Tail-induced spin-orbit effect in the gravitational radiation of compact binaries

Gravitational waves contain tail effects which are due to the back-scattering of linear waves in the curved space-time geometry around the source. In this paper we improve the knowledge and accuracy of the two-body inspiraling post-Newtonian (PN) dynamics and gravitational-wave signal by computing the spin-orbit terms induced by tail effects. Notably, we derive those terms at 3PN order in the gravitational-wave energy flux, and 2.5PN and 3PN orders in the wave polarizations. This is then used to derive the spin-orbit tail effects in the phasing through 3PN order. Our results can be employed to carry out more accurate comparisons with numerical-relativity simulations and to improve the accuracy of analytical templates aimed at describing the whole process of inspiral, merger and ringdown.Comment: Minor corrections. To be published in Physical Review

Low energy states with different symmetries in the t-J model with two holes on a 32-site lattice

We study the low energy states of the t-J model with two holes on a 32-site lattice with periodic boundary conditions. In contrary to common belief, we find that the state with d_{x^2-y^2} symmetry is not always the ground state in the realistic parameter range 0.2\le J/t\le 0.4. There exist low-lying finite-momentum p-states whose energies are lower than the d_{x^2-y^2} state when J/t is small enough. We compare various properties of these low energy states at J/t=0.3 where they are almost degenerate, and find that those properties associated with the holes (such as the hole-hole correlation and the electron momentum distribution function) are very different between the d_{x^2-y^2} and p states, while their spin properties are very similar. Finally, we demonstrate that by adding ``realistic'' terms to the t-J model Hamiltonian, we can easily destroy the d_{x^2-y^2} ground state. This casts doubt on the robustness of the d_{x^2-y^2} state as the ground state in a microscopic model for the high temperature superconductors

Dynamics of spin ladders

We derive an approximate theory for Heisenberg spin ladders with two legs by mapping the spin dynamics onto the problem of hard-core `bond-Bosons'. The parameters of the Bosonic Hamiltonian are obtained by matching anomalous Green's functions to Lanczos results and we find evidence for a strong renormalization due to quantum fluctuations. Various dynamical spin correlation functions are calculated and found to be in good agreement with Lanczos results. We then enlarge the effective Hamiltonian to describe the coupling of the bond-Bosons to a single hole injected into the system and treat the hole-dynamics within the `rainbow-diagram' approximation by Schmidt-Rink et. al. Theoretical predictions for the single hole spectral function are obtained and found to be in good agreement with Lanczos results.Comment: RevTex-file, 10 PRB pages with 7 eps files. Hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to: [email protected]

Two-hole problem in the t-J model: A canonical transformation approach

The t-J model in the spinless-fermion representation is studied. An effective Hamiltonian for the quasiparticles is derived using canonical transformation approach. It is shown that the rather simple form of the transformation generator allows to take into account effect of hole interaction with the short-range spin waves and to describe the single-hole groundstate. Obtained results are very close to ones of the self-consistent Born approximation. Further accounting for the long-range spin-wave interaction is possible on the perturbative basis. Both spin-wave exchange and an effective interaction due to minimization of the number of broken antiferromagnetic bonds are included in the effective quasiparticle interaction. Two-hole bound state problem is solved using Bethe-Salpeter equation. The only d-wave bound state is found to exist in the region of 1< (t/J) <5. Combined effect of the pairing interactions of both types is important to its formation. Discussion of the possible relation of the obtained results to the problem of superconductivity in real systems is presented.Comment: 19 pages, RevTeX, 12 postscript figure