We study numerically, using a one-dimensional Heisenberg model, the spin-Peierls transition in the linear Cu 2+ spin-1/2 chains in the inorganic compound CuGeO 3 which has been recently observed experimentally. We suggest that the magnetic susceptibility, the temperature dependence of the spin gap and the spin-Peierls transition temperature of this material can be reasonably described by including nearest and next nearest neighbor antiferromagnetic interactions along the chain. We estimate that the nearest neighbor exchange parameter J is approximately 160 K, and that the next nearest neighbor exchange parameter is approximately 0.36 J.
The microscopic mechanism of the melting of a crystal is analyzed by the constant pressure Monte Carlo simulation of a Lennard-Jones fcc system. Beyond a temperature of the order of 0.8 of the melting temperature, we found that the relevant excitations are lines of defects. Each of these lines has the structure of a random walk of various lengths on an fcc defect lattice. We identify these lines with the dislocation ones proposed in recent phenomenological theories of melting. Near melting we find the appearance of long lines that cross the whole system. We suggest that these long lines are the precursor of the melting process. : 64.70.Dv, 61.72.Bd, Melting is one of the rare phase transitions that can be observed in real life, outside of laboratories. Being a common-life process, the melting mechanism has been of interest for centuries. However there is yet no complete understanding of the atomistic dynamics involved in the melting transition. This is due to several difficulties found both in the experimental and theoretical studies of this problem. Let us discuss some of these difficulties. PACSUpon a phase transition long-range order found in the low temperature phase (LTP) disappears at the transition temperature. In the simplest cases, such as a structural phase transition, order is associated with a geometrical quantity which distinguishes LTP from the high temperature phase (HTP). The dynamical collective structural deformation, namely phonons, converting LTP into HTP is already present in the higher-symmetry phase. It is therefore natural to assume that the softening of this phonon excitation is the essential mechanism of the phase transition capturing the most important dynamics of the particles near the transition point.However, at the melting temperature T m , both translational and rotational symmetries of a crystal are destroyed, and it is much more complicated to construct simple models including the relevant excitations on both sides of the transition temperature. Hence, one-phase models have been developed. Starting in the solid phase, the question is what kind of excitation could destroy crystalline order. It is easy to see [1] that phonons alone cannot convert a solid into a liquid, some kind of crystalline defects should be invoked. Kosterlitz and Thouless [2] proposed a fundamental theory of the thermal breakdown of long-range order in two dimensions (2D) by topological defects, and related it to transitions in 2D crystals, superfluids and magnets, the relevant topological defects in the case of melting being crystalline dislocations (which are point defects in 2D). Their theory was greatly extended and detailed by Halperin and Nelson [3] and Yound [4] who predicted that the complete transition from solid to liquid takes place in two steps: the dissociation of dislocation pairs drives a crystal into a liquid-crystal phase that retains finite-range orientational order, then a second transition at higher temperature completes the conversion to an isotropic liquid. This complete theory gave det...
We study the formation of antiferromagnetic correlations induced by impurity doping in anisotropic twodimensional spin-Peierls systems. Using a mean-field approximation to deal with the interchain magnetic coupling, the intrachain correlations are treated exactly by numerical techniques. The magnetic coupling between impurities is computed for both adiabatic and dynamical lattices and is shown to have an alternating sign as a function of the impurity-impurity distance, hence suppressing magnetic frustration. An effective model based on our numerical results supports the coexistence of antiferromagnetism and dimerization in this system.
Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1=2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U ¼ 0). Furthermore, at low enough temperatures, the system maps onto a spin-1=2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1=2 end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.
We analyze several properties of the lattice solitons in the incommensurate phase of spin-Peierls systems using exact diagonalization and quantum Monte Carlo. These systems are modelled by an antiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interactions coupled to the lattice in the adiabatic approximation. Several relations among features of the solitons and magnetic properties of the system have been determined and compared with analytical predictions. We have studied in particular the relation between the soliton width and the spin-Peierls gap. Although this relation has the form predicted by bosonized field theories, we have found some important quantitative differences which could be relevant to describe experimental studies of spin-Peierls materials.
We determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U>0 at half-filling. For large enough X
We present a novel mechanism for the appearance of magnetization plateaus in quasi-one-dimensional quantum spin systems, which is induced by the coupling to the underlying lattice. We investigate in detail a simple model of a frustrated spin-1/2 Heisenberg chain coupled to adiabatic phonons under an external magnetic field, but the present mechanism is expected to be more general. Using field theoretic methods complemented by extensive density matrix renormalization group techniques, we show that magnetization plateaus at nontrivial rational values of the magnetization can be stabilized by the lattice coupling. We suggest that such a scenario could be relevant for some low dimensional frustrated spin-Peierls compounds.
We investigate the groundstate properties of a recently proposed model for a topological Kondo insulator in one dimension (i.e., the p-wave Kondo-Heisenberg lattice model) by means of the Density Matrix Renormalization Group method. The non-standard Kondo interaction in this model is different from the usual (i.e., local) Kondo interaction in that the localized spins couple to the "p-wave" spin density of conduction electrons, inducing a topologically non-trivial insulating groundstate. Based on the analysis of the charge-and spin-excitation gaps, the string order parameter, and the spin profile in the groundstate, we show that, at half-filling and low energies, the system is in the Haldane phase and hosts topologically protected spin-1/2 end-states. Beyond its intrinsic interest as a useful "toy-model" to understand the effects of strong correlations on topological insulators, we show that the p-wave Kondo-Heisenberg model can be implemented in p−band optical lattices loaded with ultra-cold Fermi gases.
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