Piotr Wróbel

Theory of the lightly doped Mott insulator

A theory for the Hubbard model appropriate in the limit of large U/t, small doping away from half-filling and short-ranged antiferromagnetic spin correlations is presented. Despite the absence of any broken symmetry the Fermi surface takes the form of elliptical hole pockets centered near (pi/2,pi/2) with a volume proportional to the hole concentration. Short range antiferromagnetic correlations render the nearest neighbor hopping almost ineffective so that only second or third nearest neighbor hopping contributes appreciably to the dispersion relation.

Optical conductivity of strongly correlated electron systems

We present an exact-diagonalization study of the frequency- and wave-vector-dependent conductivity sigma(q,omega) in small clusters in the two-dimensional t-J model. Unlike the related dynamical density correlation function, sigma(q=0,omega) in the underdoped regime has the exchange constant J as its characteristic energy scale and is dominated by a resonancelike excitation with frequency similar to 1.7 J. We interpret this as transition to a p-like excited state of a spin-bag-type quasiparticle (or, alternatively, a tightly bound spinon-holon pair) and show that a simple calculation based on the string picture explains the numerical results semiquantitatively. For doping levels greater than or equal to 25% t remains the only energy scale of sigma(q=0,omega).

On the origin of the unconventional two-hole bound state in the t-J model

Abstract We present a description of the ground state and low-lying excited states of two holes in the 4 × 4 cluster t - J model in terms of a simple model for the motion of a single bipolaron. The existence of short-range antiferromagnetic correlations has been assumed. According to the suggested scenario, the formation of the bipolaron is mediated by the reduction of the magnetic energy in the case of two holes occupying nearest neighbor sites. The relevant part of the Hilbert space consists of wave functions corresponding to holes oscillating around pairs of nearest neighbor sites and trapped in a potential well due to strings of spin defects. Virtual processes which connect these states involve both the kinetic term and the transverse part of the Heisenberg Hamiltonian. Many properties of energy level schemes obtained by numerical diagonalizations such as the sequence of the lowest states for each irreducible representation of the k vector point groups can be reproduced satisfactorily. In agreement with numerical methods the ground state has nontrivial d x 2 − y 2 symmetry.

Coexistence of superconductivity and antiferromagnetism in the Hubbard model: A phase diagram for finite temperature

Abstract The normal paramagnetic, superconducting, antiferromagnetic and simultaneously superconducting and antiferromagnetic states of correlated electrons in the nearly half-filled band have been described by the mean field approach. The Hubbard model has been used as a starting point. A general form of the spin density wave (SDW) order parameter has been proposed. The possibility of coexistence of SDW and superconducting (SC) phases has been confirmed by comparison of free energies. It has been proved that near half-filling superconductivity is suppressed by antiferromagnetism. A finite temperature phase diagram has been presented. It has been shown that SDW cannot enhance the critical temperature of superconductivity. The possible relevance of these results in copper oxides, especially to those where this coexistence was observed, has been discussed.

ON ANTIFERROMAGNETIC INSTABILITY IN THE HUBBARD MODEL

A functional integral method applied to the Hubbard model has been used to construct the magnetic phase diagram (temperature versus doping) for large U/t. The antiferromagnetic order parameter has been represented in terms of fermion operators which correspond to neutral, spin one-half quasi-particles i.e. spinons. Static approximation has been applied. Numerical calculations have been performed for the two-dimensional square lattice. A stable antiferromagnetic phase for the half-filled band has been found below the critical temperature TN=J where J=4t2/U is the superexchange interaction. It has been shown that antiferromagnetism is destroyed by doping with about 15% of holes for t/J=10. The results are discussed in the light of recent experiments for high Tc oxides.

STRIPE STABILITY IN DOPED ANTIFERROMAGNETS

In the framework of the t-Jz we discuss localized spin polarons for various original hole arrangements in different spin backgrounds. According to the so-called string picture we assume that local destruction in the magnetic structure caused by hole motion tends to localize holes and acts on them as a kind of well potential. We concentrate on the case of the hole concentration 1/8 for which stripes are experimentally observed. We explicitly take into account interaction between holes and consider several possible configurations, that represent: holes homogeneously distributed in the antiferromagnetic background, hole pairs (which correspond to spin bipolarons) homogeneously distributed in the antiferromagnetic background, hole pairs which form the stripe structure in the perfect antiferromagnetic background, and eventually holes in stripes which separate antiferromagnetic domains with alternating direction of the staggered magnetization. Spin polarons are constructed by means of some computer algebra. It ...

BINDING OF SPIN POLARONS IN DOPED ANTIFERROMAGNETS

AbstractBy means of variational wave functions which construction is based on the spin polaron picture we calculate the energies of two hole states in the t–J model classified according to the momentum and the different irreducible representations of the

Hole pairing in the one-dimensional t-J model with staggered magnetic field

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