Dynamic spin susceptibility of superconducting cuprates: A microscopic theory of the magnetic resonance mode

A microscopic theory of the dynamic spin susceptibility (DSS) in the superconducting state within the t-J model is presented. It is based on an exact representation for the DSS obtained by applying the Mori-type projection technique for the relaxation function in terms of Hubbard operators. The static spin susceptibility is evaluated by a sum-rule-conserving generalized mean-field approximation, while the self-energy is calculated in the mode-coupling approximation. The spectrum of spin excitations is studied in the underdoped and optimally doped regions. The DSS reveals a resonance mode (RM) at the antiferromagnetic wave vector Q = \pi(1,1) at low temperatures due to a strong suppression of the damping of spin excitations. This is explained by an involvement of spin excitations in the decay process besides the particle-hole continuum usually considered in random-phase-type approximations. The spin gap in the spin-excitation spectrum at Q plays a dominant role in limiting the decay in comparison with the superconducting gap which results in the observation of the RM even above $T_c$ in the underdoped region. A good agreement with inelastic neutron-scattering experiments on the RM in YBCO compounds is found.Comment: 15 pages, 20 figures, references adde

Superconductivity of strongly correlated electrons on the honeycomb lattice

A microscopic theory of the electronic spectrum and of superconductivity within the t-J model on the honeycomb lattice is developed. We derive the equations for the normal and anomalous Green functions in terms of the Hubbard operators by applying the projection technique. Superconducting pairing of d + id'-type mediated by the antiferromagnetic exchange is found. The superconducting Tc as a function of hole doping exhibits a two-peak structure related to the van Hove singularities of the density of states for the two-band t-J model. At half-filling and for large enough values of the exchange coupling, gapless superconductivity may occur. For small doping the coexistence of antiferromagnetic order and superconductivity is suggested. It is shown that the s-wave pairing is prohibited, since it violates the constraint of no-double-occupancy.Comment: 10 pages, 3 figures, to be published in Eur. Phys. J.

Spin excitations and thermodynamics of the t-J model on the honeycomb lattice

We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic t-J Heisenberg model on the honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures and hole dopings, the electronic spectrum of excitations, the spin-excitation spectrum and thermodynamic quantities (two-spin correlation functions, staggered magnetization, magnetic susceptibility, correlation length) are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature and doping dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. Our results on the doping dependencies of the magnetization and susceptibility are analyzed in comparison with previous results for the t_J model on the square lattice.Comment: 9 pages, 7 figures, submitted to European Physical Journal B. arXiv admin note: text overlap with arXiv:1703.0839

Kinetic Theory of Flocking: Derivation of Hydrodynamic Equations

It is shown how to explicitly coarse-grain the microscopic dynamics of the Vicsek model for self-propelled agents. The macroscopic transport equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport coefficients at large particle speed are given. The phase transition from a disordered to a flocking state is studied numerically and analytically.Comment: 4 pages, 1 figur

Thermodynamics of the frustrated J1J_1-J2J_2 Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

We use the spin-rotation-invariant Green's function method as well as the high-temperature expansion to discuss the thermodynamic properties of the frustrated spin-$S$ $J_{1}$-$J_{2}$ Heisenberg magnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighbor bonds $J_1 < 0$ and antiferromagnetic next-nearest-neighbor bonds $J_2 \ge 0$ and arbitrary spin $S$. We find that the transition point $J_2^c$ between the ferromagnetic ground state and the antiferromagnetic one is nearly independent of the spin $S$, i.e., it is very close to the classical transition point $J_2^{c,{\rm clas}}= \frac{2}{3}|J_1|$. At finite temperatures we focus on the parameter regime $J_2<J_2^c$ with a ferromagnetic ground-state. We calculate the Curie temperature $T_{C}(S,J_{2})$ and derive an empirical formula describing the influence of the frustration parameter $J_{2}$ and spin $S$ on $T_C$. We find that the Curie temperature monotonically decreases with increasing frustration $J_2$, where very close to $J_2^{c,{\rm clas}}$ the $T_C(J_2)$-curve exhibits a fast decay which is well described by a logarithmic term $1/\textrm{log}(\frac{2}{3}|J_1|-J_{2})$. To characterize the magnetic ordering below and above $T_C$, we calculate the spin-spin correlation functions $\langle {\bf S}_{\bf 0} {\bf S}_{\bf R} \rangle$, the spontaneous magnetization, the uniform static susceptibility $\chi_0$ as well as the correlation length $\xi$. Moreover, we discuss the specific heat $C_V$ and the temperature dependence of the excitation spectrum. As approaching the transition point $J_2^c$ some unusual features were found, such as negative spin-spin correlations at temperatures above $T_C$ even though the ground state is ferromagnetic or an increase of the spin stiffness with growing temperature.Comment: 19 pages, 10 figures, version as in EPJ

Transport coefficients of multi-particle collision algorithms with velocity-dependent collision rules

Detailed calculations of the transport coefficients of a recently introduced particle-based model for fluid dynamics with a non-ideal equation of state are presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are exactly conserved locally. A general scheme to derive transport coefficients for such biased, velocity dependent collision rules is developed. Analytic expressions for the self-diffusion coefficient and the shear viscosity are obtained, and very good agreement is found with numerical results at small and large mean free paths. The viscosity turns out to be proportional to the square root of temperature, as in a real gas. In addition, the theoretical framework is applied to a two-component version of the model, and expressions for the viscosity and the difference in diffusion of the two species are given.Comment: 31 pages, 8 figures, accepted by J. Phys. Cond. Matte

Quantum to classical crossover in the 2D easy-plane XXZ model

Ground-state and thermodynamical properties of the spin-1/2 two-dimensional easy-plane XXZ model are investigated by both a Green's-function approach and by Lanczos diagonalizations on lattices with up to 36 sites. We calculate the spatial and temperature dependences of various spin correlation functions, as well as the wave-vector dependence of the spin susceptibility for all anisotropy parameters $\Delta$. In the easy--plane ferromagnetic region $(-1< \Delta < 0)$, the longitudinal correlators of spins at distance $r$ change sign at a finite temperature $T_0(\Delta, {\bf r})$. This transition, observed in the 2D case for the first time, can be interpreted as a quantum to classical crossover.Comment: 4 pages, 6 figures, Contribution to the Ising Centennial Colloquium, ICM2000, Belo Horizonte, Brazil, August 200

Comment on ``Solidification of a Supercooled Liquid in a Narrow Channel''

Comment on PRL v. 86, p. 5084 (2001) [cond-mat/0101016]. We point out that the authors' simulations are consistent with the known theory of steady-state solutions in this system

Electron-hole pair condensation at the semimetal-semiconductor transition: a BCS-BEC crossover scenario

We act on the suggestion that an excitonic insulator state might separate---at very low temperatures---a semimetal from a semiconductor and ask for the nature of these transitions. Based on the analysis of electron-hole pairing in the extended Falicov-Kimball model, we show that tuning the Coulomb attraction between both species, a continuous crossover between a BCS-like transition of Cooper-type pairs and a Bose-Einstein condensation of preformed tightly-bound excitons might be achieved in a solid-state system. The precursor of this crossover in the normal state might cause the transport anomalies observed in several strongly correlated mixed-valence compounds.Comment: 5 pages, 5 figures, substantially revised versio