Connecting Entanglement in Time and Space: Improving the Folding Algorithm

The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the temporal entanglement. We show that this temporal entanglement is, in many cases, equal to the spatial entanglement of a modified Hamiltonian. This inspires a modification to the folding algorithm, that we call the "hybrid algorithm". We find that this leads to improved accuracy for the same numerical effort. We then use these algorithms to study relaxation in a transverse plus parallel field Ising model, finding persistent quasi-periodic oscillations for certain choices of initial conditions.Comment: 16 pages, 11 figure

A S=1/2 vanadium-based geometrically frustrated spinel system Li2ZnV3O8

We report the synthesis and characterization of Li2ZnV3O8, which is a new Zn-doped LiV2O4 system containing only tetravalent vanadium. A Curie-Weiss susceptibility with a Curie-Weiss temperature of CW ~214 K suggests the presence of strong antiferromagnetic correlations in this system. We have observed a splitting between the zero-field cooled ZFC and field cooled FC susceptibility curves below 6 K. A peak is present in the ZFC curve around 3.5 K suggestive of spin-freezing . Similarly, a broad hump is also seen in the inferred magnetic heat capacity around 9 K. The consequent entropy change is only about 8% of the value expected for an ordered S = 1=2 system. This reduction indicates continued presence of large disorder in the system in spite of the large CW, which might result from strong geometric frustration in the system. We did not find any temperature T dependence in our 7Li nuclear magnetic resonance NMR shift down to 6 K (an abrupt change in the shift takes place below 6 K) though considerable T-dependence has been found in literature for LiV2O4- undoped or with other Zn/Ti contents. Consistent with the above observation, the 7Li nuclear spin-lattice relaxation rate 1/T1 is relatively small and nearly T-independent except a small increase close to the freezing temperature, once again, small compared to undoped or 10% Zn or 20% Ti-doped LiV2O4.Comment: 7 pages, 8 figures, accepted in JPCM (Journal of Physics condensed matter

Possible textures of the fermion mass matrices

Texture specific fermion mass matrices have played an important role in understanding several features of fermion masses and mixings. In the present work, we have given an overview of all possible cases of Fritzsch-like as well as non Fritzsch-like texture 6 and 5 zero fermion mass matrices. Further, for the case of texture 4 zero Fritzsch-like quark mass matrices, the issue of the hierarchy of the elements of the mass matrices and the role of their phases have been discussed. Furthermore, the case of texture 4 zero Fritzsch-like lepton mass matrices has also been discussed with an emphasis on the hierarchy of neutrino masses for both Majorana and Dirac neutrinos.Comment: 21 pages, 3 figure

Vortex Bubble Formation in Pair Plasmas

It is shown that delocalized vortex solitons in relativistic pair plasmas with small temperature asymmetries can be unstable for intermediate intensities of the background electromagnetic field. Instability leads to the generation of ever-expanding cavitating bubbles in which the electromagnetic fields are zero. The existence of such electromagnetic bubbles is demonstrated by qualitative arguments based on a hydrodynamic analogy, and by numerical solutions of the appropriate Nonlinear Schr\"odinger equation with a saturating nonlinearity.Comment: 4 pages of two-column text, 2 figure