Ladder states formed by the superposition of short-range dimer coverings, also known as short-range resonating valence bond (RVB) states, can be simulated by using atoms in optical lattices and, as shown recently, by using interacting photons . The properties of such systems have also been tested experimentally in several systems and proposals thereof have been presented, including in compounds and cold gases . On the other hand, concepts such as entanglement and other quantum correlations have been applied to understand quantum critical phenomena in spin systems , including in spin ladders. The characteristic pseudo 2D structure of ladders has generated considerable interest in several other areas of condensed matter physics and quantum information . The possibility of relating doped even-legged quantum spin ladders to high-temperature superconductivity makes such quantum systems extremely important. The quantum spin ladder is an interesting platform to investigate quantum many-body systems in the intermediate sector between one-dimensional (1D) and two-dimensional (2D) lattice structures . The parameter on the vertical axes is dimensionless, while that on the horizontal ones is in the units of number of rungs. GGM decreases for even and increases for odd ladders. The figures show the generalized geometric measure (GGM), on the vertical axes, with increasing number of rungs, on the horizontal axes, of even- (right) and odd-legged (left) ladders. The formalism can be extended to study properties of quantum states of other spin lattices, and may prove useful in studying their potentiality for quantum computation.įigure. The DMRM is an efficient exact method to calculate physical properties in quantum spin-ladders. We quantify the genuine multisite entanglement by using the generalized geometric measure. We find that the well-known and intriguing disparity between even- and odd-legged ladders show up very distinctly in the behavior of genuine multiparty entanglement with increasing system size. To demonstrate the efficiency of the method, we calculate the genuine multipartite entanglement content in such systems. The method works by using a recursion of states and parameters that generates larger ladder states out of smaller ones. We introduce a technique, which we call the density matrix recursion method (DMRM) that is an efficient exact method to calculate bipartite and multipartite physical properties of large spin-ladders, in the case when the state is a superposition of lattice coverings of singlets. However, exact calculation of the physical properties of the quantum spin-ladders is difficult as for typical states on such lattices, the number of terms in the superposition scales exponentially with the increase in system size. Interestingly, such spin-ladder states are now being implemented in the laboratories in several physical systems, including atoms in optical lattices and interacting photons. Spin-ladder states are potentially associated with high-temperature superconductors and quantum computers. A configuration of quantum spin-1/2 particles arranged in the form of a ladder is an important system in many body physics. Clearly a line of length \(n\) units takes the same time to articulate regardless of how it is composed.GENERAL SCIENTIFIC SUMMARY Introduction and background. A line of length \(n\) contains \(n\) units where each short syllable is one unit and each long syllable is two units. Suppose also that each long syllable takes twice as long to articulate as a short syllable. Suppose we assume that lines are composed of syllables which are either short or long. In particular, about fifty years before Fibonacci introduced his sequence, Acharya Hemachandra (1089 – 1173) considered the following problem, which is from the biography of Hemachandra in the MacTutor History of Mathematics Archive: Historically, it is interesting to note that Indian mathematicians were studying these types of numerical sequences well before Fibonacci.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |