Search

We study the entanglement content of a class of mesoscopic tunable magnetic systems. The systems are closed finite spin-1/2 chains with ferromagnetic nearest-neighbor interactions frustrated by antiferromagnetic next-nearest-neighbor interactions. The finite chains display a series of level crossings reflecting the incommensurate physics of the corresponding infinite-size chain. We present dramatic entanglement signatures characterizing these unusual level crossings. We focus on multi-spin and global measures of entanglement rather than only one-spin or two-spin entanglements. We compare and contrast the information obtained from these measures to that obtained from traditional condensed matter measures such as correlation functions., Comment: 6+ pages, 5 figures

Let F be a characteristic zero differential field with an algebraically closed field of constants, E be a no-new-constant extension of F by antiderivatives of F and let y1, ..., yn be antiderivatives of E. The antiderivatives y1, ..., yn of E are called J-I-E antiderivatives if the derivatives of yi in E satisfies certain conditions. We will discuss a new proof for the Kolchin-Ostrowski theorem and generalize this theorem for a tower of extensions by J-I-E antiderivatives and use this generalized version of the theorem to classify the finitely differentially generated subfields of this tower. In the process, we will show that the J-I-E antiderivatives are algebraically independent over the ground differential field. An example of a J-I-E tower is extensions by iterated logarithms. We will discuss the normality of extensions by iterated logarithms and produce an algorithm to compute its finitely differentially generated subfields., Comment: 66 pages, 1 figure

We study the locations of the gapless points which occur for quantum spin chains of finite length (with a twisted boundary condition) at particular values of the nearest neighbor dimerization, as a function of the spin S and the number of sites. For strong dimerization and large values of S, a tunneling calculation reproduces the same results as those obtained from more involved field theoretic methods using the non-linear sigma-model approach. A different analytical calculation of the matrix element between the two Neel states gives a set of gapless points; for strong dimerization, these differ significantly from the tunneling values. Finally, the exact diagonalization method for a finite number of sites yields a set of gapless points which are in good agreement with the Neel state calculations for all values of the dimerization, but the agreement with the tunneling values is not very good even for large S. This raises questions about possible corrections to the tunneling results., Comment: Revtex4, 10 pages including 5 figures

We study a system consisting of a junction of N quantum wires, where the junction is characterized by a scalar S-matrix, and an impurity spin is coupled to the electrons close to the junction. The wires are modeled as weakly interacting Tomonaga-Luttinger liquids. We derive the renormalization group equations for the Kondo couplings of the spin to the electronic modes on different wires, and analyze the renormalization group flows and fixed points for different values of the initial Kondo couplings and of the junction S-matrix (such as the decoupled S-matrix and the Griffiths S-matrix). We generally find that the Kondo couplings flow towards large and antiferromagnetic values in one of two possible ways. For the Griffiths S-matrix, we study one of the strong coupling flows by a perturbative expansion in the inverse of the Kondo coupling; we find that at large distances, the system approaches the ferromagnetic fixed point of the decoupled S-matrix. For the decoupled S-matrix with antiferromagnetic Kondo couplings and weak inter-electron interactions, the flows are to one of two strong coupling fixed points in which all the channels are strongly coupled to each other through the impurity spin. But strong inter-electron interactions, with K_\rho < N/(N+2), stabilize a multi-channel fixed point in which the coupling between different channels goes to zero. We have also studied the temperature dependence of the conductance at the decoupled and Griffiths S-matrices., Comment: Revtex4, 16 pages including 6 figures

The electronic properties of one-dimensional clusters of N atoms or molecules have been studied. The model used is similar to the Kronig-Penney model with the potential offered by each ion being approximated by an attractive delta function. The energy eigenvalues, the eigenstates and the density of states are calculated exactly for a linear cluster of N atoms or molecules. The dependence of these quantities on the various parameters of the problem show interesting behavior. Effects of random distribution of the positions of the atoms and random distribution of the strengths of the potential have also been studied. The results obtained in this paper can have direct applications for linear chain of atoms produced on metal surfaces or artificially created chain of atoms by using scanning tunneling microscope or in studying molecular conduction of electrons across one-dimensional barriers., Comment: A shorter version of this paper to be published in Physica B

We generalize a class of Heisenberg antiferromagnets in one, two and three dimensions, which have been shown to exhibit magnetization plateaus for spin-1/2. In a certain parameter range of the general model, which is formally defined in D dimensions, we obtain the exact ground state(s) in the presence of an external magnetic field for arbitrary values of spin. In this range, the magnetization remains a constant as a function of the external field, except at some special values of the field where there is a jump from one plateau to the next. The plateaus are formed at certain specific fractions of the full magnetization which are determined by the spin and the lattice. Our general spin-S result reproduces the known cases for spin-1/2 in various lattices. Furthermore, we argue that outside the exact regime, the mechanism for the plateau formation is different. This results in first order phase transitions along some of the plateaus as the coupling constant is varied. We rigorously show the existence of such transitions for some particular cases. Finally, we numerically analyze a spin-1 model in one dimension using exact diagonalization to obtain its complete phase diagram. It agrees with our analytic results., Comment: 10 pages, 5 figures, Revtex4

We study a system of an impurity spin coupled to a junction of several Tomonaga-Luttinger liquids using a renormalization group scheme. For the decoupled S-matrix at the junction, there is a range of Kondo couplings which flow to a multi-channel fixed point for repulsive inter-electron interactions; this is associated with a characteristic temperature dependence of the spin-flip scatterings. If the junction is governed by the Griffiths S-matrix, the Kondo couplings flow to a strong coupling fixed point where all the wires are decoupled., Comment: 7 pages including 3 figures; the RG equations have been corrected, and the discussion of the muti-channel fixed point has been suitably modified

We study a model which could explain some of the unusual magnetic properties observed for the one-dimensional helical spin system Co(hfac)_2 NITPhOMe. One of the properties observed is that the magnetization shows plateaus near zero and near one-third of the saturation value if a magnetic field is applied along the helical axis, but not if the field is applied in the plane perpendicular to that axis. The system consists of a spin-1/2 chain in which cobalt ions (which are highly anisotropic with an easy axis e_i) and organic radicals (which are isotropic) alternate with each other. The easy axis of the cobalts e_i lie at an angle theta_i with respect to the helical axis, while the projection of e_{i+1} - e_i on the plane perpendicular to the helical axis is given by 2 pi /3. For temperatures and magnetic fields which are much smaller than the coupling between the nearest-neighbor cobalts and radicals, one can integrate out the radicals to obtain an Ising model for the cobalts; this enables one to compute the thermodynamic properties of the system using the transfer matrix approach. We consider a model in which the tilt angles theta_i are allowed to vary with i with period three; we find that for certain patterns of theta_i, the system shows the magnetization plateaus mentioned above. At the ends of the plateaus, the entropy is finite even at very low temperatures, while the magnetic susceptibility and specific heat also show some interesting features., Comment: Revtex, 7 pages including 7 figures

Generalising recent studies on the sawtooth lattice, a two-spin variant of the model is considered. Numerical studies of the energy spectra and the relevant spin correlations in the problem are presented. Perturbation theory analysis of the model explaining some of the features of the numerical data is put forward and the spin wave spectra of the model corresponding to different phases are investigated., Comment: Latex, 37 pages including 14 figures; M. S. project report, Indian Institute of Science (March, 2003); this is one of the references of cond-mat/0307492

We study the low-energy properties of a sawtooth chain with spin-1's at the bases of the triangles and spin-1/2's at the vertices of the triangles. The spins have Heisenberg antiferromagnetic interactions between nearest neighbors, with a coupling J_2 between a spin-1 and a spin-1/2, and a coupling J_1 = 1 between two spin-1's. Analysis of the exact diagonalization data for periodic chains containing up to N=12 unit cells shows that the ground state is a singlet for exchange couplings up to approximately J_2 = 3.8, whereas for larger J_2, the system exhibits a ferrimagnetic ground state characterized by a net ferromagnetic moment per unit cell of 1/2. In the region of small interactions J_2, the mixed spin sawtooth chain maps on to an effective isotropic spin model representing two weakly interacting and frustrated spin-1/2 Heisenberg chains composed of spin-1/2 sites at odd and even vertices respectively. Finally, we study the phenomenon of a macroscopic magnetization jump which occurs if a magnetic field is applied with a value close to the saturation field for J_2 = 2., Comment: RevTeX, 28 pages including 11 figures