The theory for the dynamical spin susceptibility within the t-J model is developed, as relevant for the resonant magnetic peak and normal-state magnetic response in superconducting (SC) cuprates. The analysis is based on the equations of motion for spins and the memory-function presentation of magnetic response where the main damping of the low-energy spin collective mode comes from the decay into fermionic degrees of freedom. It is shown that the damping function at low doping is closely related to the c-axis optical conductivity. The analysis reproduces doping-dependent features of the resonant magnetic scattering. PACS numbers: 71.27.+a, Since its discovery in inelastic neutron scattering experiments in superconducting (SC) YBa 2 Cu 3 O 7 [1], the magnetic resonance peak has been the subject of numerous experimental investigations as well as theoretical analyses and interpretations. The magnetic peak has been systematically followed in YBa 2 Cu 3 O 6+x (YBCO) into the underdoped regime [2,3,4], where the resonant frequency ω r decreases while the peak intensity is increasing. Its pronounced appearance is still related to the onset of SC, although it could start appearing even at T > T c . More recent results confirm similar behavior in Bi2212 and Tl2201 cuprates [5].Several theoretical hypotheses have been considered for the origin of the resonant peak: that it is a bound state in the electron-hole excitation spectrum [6], a consequence of a novel symmetry between antiferromagnetism (AFM) and SC [7] and that it represents collective spin-wave-like mode induced by strong AFM correlations [8,9]. There is also an ongoing debate whether the resonant peak is intimately related to the mechanism of SC and whether it can account for anomalies in single-electron properties, as tested in angle resolved photoemission spectroscopy.The scenario of a resonant mode as a collective magnetic mode seems to correspond well to experimental facts, in particular the qualitative development of the resonant mode with doping and its onset for T < T c . Still the status of the theory of the resonant mode, and moreover of the magnetic response in cuprates in general, is not satisfactory, both from the point of understanding and of the appropriate analytical method. Relevant microscopic models, such as the Hubbard model and the t-J model have been so far studied in the weak coupling or random-phase approximation [6], neglecting strong correlations. The latter have been considered using a Hubbard-operator technique [10], and more recently within the self-consistent slave-boson approach [11], self-consistent spin-fluctuation method [12], as well as within the phenomenological spin-fermion model [8,9].Our aim is to develop a theory of the dynamical spin susceptibility χ q (ω) within the t-J model. The natural approach to analyse collective modes is the memory-function formalism [13]. In analogy to the previous study of spectral functions [14] we employ the method of equations of motion (EQM) to generate the spin dynamics and in particul...

A theory of the anomalous omega/T scaling of the dynamic magnetic response in cuprates at low doping is presented. It is based on the memory function representation of the dynamical spin susceptibility in a doped antiferromagnet where the damping of the collective mode is constant and large, whereas the equal-time spin correlations saturate at low T. Exact diagonalization results within the t-J model are shown to support assumptions. Consequences, for both the scaling function and the normalization amplitude, are well in agreement with neutron scattering results.

The e8'ective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the Cu02 layers in copper-oxide superconductors, is studied by the exact diagonalization of-a Gnite-size system with 16 cells. Single-and two-hole ground-state properties are calculated. Pair-binding-energy and hole-density correlation functions indicate that two holes bind for moderate exchange interactions, even in the case of the extreme anisotropic-Ising limit.

Several convenient formulae for the entanglement of two indistinguishable delocalised spin-1 2 particles are introduced. This generalizes the standard formula for concurrence, valid only in the limit of localised or distinguishable particles. Several illustrative examples are given.Entanglement is a well-defined quantity for two distinguishable qubits in a nonfactorizable quantum state, where it may be uniquely defined through von Neuman entropy and concurrence [1,2,3,4]. However, amongst the realistic systems of major physical interest, electronqubits have the potential for a much richer variety of entanglement measure choices due to both their charge and spin degrees of freedom. For example, in lattice fermion models such as the Hubbard dimer, entanglement is sensitive to the interplay between charge hopping and the avoidance of double occupancy due to Hubbard repulsion, which results in an effective Heisenberg interaction between adjacent spins [5]. In systems of identical particles the main challenge is to define an appropriate entanglement measure which adequately deals with multiple occupancy states [6,7,8,9,10,11]. In the case of fermions such a measure must also account for the effect of exchange [12] as well as of mutual electron repulsion.Entangled fermionic qubits can be created with electron-hole pairs in a Fermi sea [13] and in the scattering of two distinguishable particles [14]. A spinindependent scheme for detecting orbital entanglement of two-quasiparticle excitations of a mesoscopic normalsuperconductor system was also proposed recently [15].A consensus regarding the appropriate generalization of entanglement measure which would consider spin and orbital entanglement of electrons on the same footing has not, however, been reached yet. In any realistic solid-state device, spin entanglement is intimately related to the orbital degrees of freedom of the carriers, which cannot be ignored, even in otherwise pure spin entanglement observations. In this paper we introduce spinentanglement measure formulae valid for real electrons and show how, in general, spin-entanglement depends in an essential way on spatially delocalised orbitals.For two distinguishable particles A and B, each described with single spin-1 2 (or pseudo spin) states s =↑ or ↓ and in a pure state |Ψ AB = ss ′ α ss ′ |s A |s ′ B concurrence as a measure of entanglement is given by [2]Concurrence is related to the density matrix of a pair of spins [4] and can be expressed in terms of spinspin correlators Ψ AB |S λ A S µ B |Ψ AB and expectation values Ψ AB |S λ A(B) |Ψ AB , where S λ A(B) for λ = x, y, z are spin operators corresponding to spin A or B, respectively. This approach has proved to be efficient in the analysis of entanglement in various spin-chain systems with interaction [16,17,18,19].Consider now the general problem of two interacting electrons in a pure state. It is clear that in some circumstances this system reduces approximately to an equivalent system of two interacting spins, for which the above entanglement formula i...