Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin Hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground-state configuration of all the members of the family on a periodic chain. The ground state is twofold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh Hamiltonian with a twofold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.

Simulation of the infrared spectra of thioacetamide by the extended molecular mechanics method

The infrared spectrum of the matrix-isolated species of thioacetamide has been simulated using the extended molecular mechanics method. The equilibrium structure, vibrational frequencies, dipole moment and infrared absorption intensities of thioacetamide have been calculated in good agreement with the experiment. The vibrational frequencies and infrared absorption intensities for the isotopic molecules (CH2CSNH2)-C-13, (CH3CSNH2)-N-15 and (CH2CSND2)-C-13 have also been calculated consistent with the experiment. The infrared spectra of the matrix isolated species of N- and C- deuterated isotopomers of thioacetamide, CH3CSND2 and CD3CSNH2 have also been simulated in satisfactory agreement with the experimental spectra.

Quantum phenomena in magnetic nano clusters

One of the fascinating fields of study in magnetism in recent years has been the study of quantum phenomena in nanosystems. While semiconductor structures have provided paradigms of nanosystems from the stand point of electronic phenomena the synthesis of high nuclearity transition metal complexes have provided examples of nano magnets. The range and diversity of the properties exhibited by these systems rivals its electronic counterparts. Qualitative understanding of these phenomena requires only a knowledge of basic physics, but quantitative study throws up many challenges that are similar to those encountered in the study of correlated electronic systems. In this article, a brief overview of the current trends in this area arc highlighted and some of the efforts of our group in developing a quantitative understanding of this field are outlined.

Simulation of the infrared spectra of N-methylformamide and N-methylacetamide by the extended molecular mechanics method

The infrared spectra of the matrix isolated species of N-methylformamide (NMF) and N-methylacetamide (NMA) and their N-deuterated molecules have been simulated by the extended molecular mechanics method using an empirical force field which includes charges and charge fluxes as coulombic potential parameters. The structural parameters and dipole. moments of NMF and NMA have. also been computed in satisfactory agreement with the experiment. Good agreement between experimental and calculated vibrational frequencies and infrared absorption band intensities for NMF and NMA and their deuterated molecules has been obtained. The vibrational assignments of NMF and NMA are-discussed taking also into account the infrared absorption intensities.

Quantum destruction of spiral order in two-dimensional frustrated magnets

We study the fate of spin-1/2 spiral-ordered two-dimensional quantum antiferromagnets that are disordered by quantum fluctuations. A crucial role is played by the topological point defects of the spiral phase, which are known to have a Z(2) character. Previous works established that a nontrivial quantum spin-liquid phase results when the spiral is disordered without proliferating the Z(2) vortices. Here, we show that when the spiral is disordered by proliferating and condensing these vortices, valence-bond solid ordering occurs due to quantum Berry phase effects. We develop a general theory for this latter phase transition and apply it to a lattice model. This transition potentially provides a new example of a Landau-forbidden deconfined quantum critical point.

Search on a Hypercubic Lattice using Quantum Random Walk

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d=2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article [ A. Patel and M. A. Rahaman Phys. Rev. A 82 032330 (2010)] provides an O(√NlnN) algorithm, which is not optimal. The scaling behavior can be improved to O(√NlnN) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78 012310 (2008). We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.