A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices

e classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine the parent Hamiltonian and the points of possible quantum phase transitions. For two of the models, the interactions are three-body and for one the interaction is two-bodyComment: 17 pages, 3 figure

Exact ground states for two new spin-1 quantum chains, new features of matrix product states

We use the matrix product formalism to find exact ground states of two new spin-1 quantum chains with nearest neighbor interactions. One of the models, model I, describes a one-parameter family of quantum chains for which the ground state can be found exactly. In certain limit of the parameter, the Hamiltonian turns into the interesting case $H=\sum_i ({\bf S}_i\cdot {\bf S}_{i+1})^2$. The other model which we label as model II, corresponds to a family of solvable three-state vertex models on square two dimensional lattices. The ground state of this model is highly degenerate and the matrix product states is a generating state of such degenerate states. The simple structure of the matrix product state allows us to determine the properties of degenerate states which are otherwise difficult to determine. For both models we find exact expressions for correlation functions.Comment: 22 pages, references added, accepted for publication in European Physics Journal

Entanglement of bosonic modes in symmetric graphs

The ground and thermal states of a quadratic hamiltonian representing the interaction of bosonic modes or particles are always Gaussian states. We investigate the entanglement properties of these states for the case where the interactions are represented by harmonic forces acting along the edges of symmetric graphs, i.e. 1, 2, and 3 dimensional rectangular lattices, mean field clusters and platonic solids. We determine the Entanglement of Formation (EoF) as a function of the interaction strength, calculate the maximum EoF in each case and compare these values with the bounds found in \cite{wolf} which are valid for any quadratic hamiltonian.Comment: 15 pages, 8 figures, 3 tables, Latex, Accepted for publication in Physical Review

Elucidating mammalian cellular responses to the uptake of nanoparticles (NPs), pathogens, and lipoproteins: similarities and differences

Soft poly-ethylene-glycol (PEG)-based soft nanoparticles (NPs) including cylindrical (CNPs) micelles, spherical (SNPs) micelles, and lipid bilayer vesicles (LNPs) are thought to be treated as foreign objects by mammalian phagocytes. If this hypothesis is true, NPs should trigger a proinflammatory, autophagic phenotype that is similar to the one seen when macrophages phagocytose pathogens or when macrophage surface expressed proteins bind pathogen surface factors such as lipopolysaccharide (LPS). Here, we show that macrophage responses to the above NPs are almost completely unique from those triggered by group A streptococcus (GAS) pathogens (JRS4 cells) and LPS. Instead, macrophages treat these soft NPs more like high-density lipoprotein (HDL) and low-density lipoprotein (LDL). RNA sequencing of macrophage transcripts after hHDL, hLDL, JRS4 cell, LPS, and LNP incubation showed three diverse response clusters triggered by JRS4 cells (1), LPS (2), and hHDL-hLDL-LNP-PBS (3). Of these reagents, LNPs triggered the fewest post-incubation transcript changes from macrophages to which PBS was added (control). LNPs did not increased the transcription of factors associated with foreign object identification including Fc and complement receptors. LNPs did not increase transcripts whose translated proteins are involved in phagocytosis, autophagy, lysosome biogenesis, or inflammation. LNPs did not increase Tfeb transcripts, which is a master regulator of lysosome biogenesis and a necessary component of autophagy. To further determine the effects of these NPs on cells, we performed fluorescence microscopy and flow cytometry experiments. CNPs, SNPs, and LNPs lowered macrophage autophagosome levels that were raised by the canonical challenges: starvation, rapamycin, and LPS. CNPs, SNPs, and LNPs lowered reaction oxygen species (ROS) levels, did not increase lysosome acidification, and the reduced the secretion of proinflammatory cytokines compared to basal conditions and LPS addition to macrophage cultures. CNPs and SNPs triggered low lysosome acidification and LNPs did not increase Tfeb levels, the master regulator of lysosome biogenesis and a necessary component of autophagy. Thus, the terminology that macrophages clear NPs, which has been used over many decades, is most likely misleading. Our findings challenge the hypothesis that the main uptake mechanism of soft PEG-NPs by M1-polarized murine macrophages in vitro is phagocytosis

Quantum Phase Transitions and Matrix Product States in Spin Ladders

We investigate quantum phase transitions in ladders of spin 1/2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such models. We also study the behavior of entanglement of different neighboring sites near the transition point and show that quantum phase transitions in these systems are accompanied by divergences in derivatives of entanglement.Comment: 20 pages, 6 figures, essential changes (i.e derivation of the Hamiltonian), Revte

A new family of matrix product states with Dzyaloshinski-Moriya interactions

We define a new family of matrix product states which are exact ground states of spin 1/2 Hamiltonians on one dimensional lattices. This class of Hamiltonians contain both Heisenberg and Dzyaloshinskii-Moriya interactions but at specified and not arbitrary couplings. We also compute in closed forms the one and two-point functions and the explicit form of the ground state. The degeneracy structure of the ground state is also discussed.Comment: 15 pages, 1 figur