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

The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond

We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 $XXZ$ model in a $z$-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition which occurs at low temperatures.Comment: 6 figure

Entanglement and quantum phase transitions in matrix product spin one chains

We consider a one-parameter family of matrix product states of spin one particles on a periodic chain and study in detail the entanglement properties of such a state. In particular we calculate exactly the entanglement of one site with the rest of the chain, and the entanglement of two distant sites with each other and show that the derivative of both these properties diverge when the parameter $g$ of the states passes through a critical point. Such a point can be called a point of quantum phase transition, since at this point, the character of the matrix product state which is the ground state of a Hamiltonian, changes discontinuously. We also study the finite size effects and show how the entanglement depends on the size of the chain. This later part is relevant to the field of quantum computation where the problem of initial state preparation in finite arrays of qubits or qutrits is important. It is also shown that entanglement of two sites have scaling behavior near the critical point

Phase diagram of the asymmetric tetrahedral Ising-Heisenberg chain

The asymmetric tetrahedron is composed by all edges of tetrahedron represented by Ising interaction except one, which has a Heisenberg type interaction. This asymmetric tetrahedron is arranged connecting a vertex which edges are only Ising type interaction to another vertex with same structure of another tetrahedron. The process is replicated and this kind of lattice we call the asymmetric Ising-Heisenberg chain. We have studied the ground state phase diagram for this kind of models. Particularly we consider two situations in the Heisenberg-type interaction, (i) The asymmetric tetrahedral spin(1/2,1/2) Ising-XYZ chain, and (ii) the asymmetric tetrahedral spin-(1/2,1) Ising-XXZ chain, where we have found a rich phase diagram and a number of multicritical points. Additionally we have also studied their thermodynamics properties and the correlation function, using the decorated transformation. We have mapped the asymmetric tetrahedral Ising-Heisenberg chain in an effective Ising chain, and we have also concluded that it is possible to evaluate the partition function including a longitudinal external magnetic field.Comment: 14 pages, 8 figures. Accepted in Journal of Physics: Condensed Matte

Mixed Heisenberg Chains. I. The Ground State Problem

We consider a mechanism for competing interactions in alternating Heisenberg spin chains due to the formation of local spin-singlet pairs. The competition of spin-1 and spin-0 states reveals hidden Ising symmetry of such alternating chains.Comment: 7 pages, RevTeX, 4 embedded eps figures, final versio

Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem

The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and obtain recurrence relations for the traces. This is possible only if the rates satisfy certain compatibility conditions. These conditions are derived and the recurrence relations solved giving representations of the algebras.Comment: 12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.

A compact and light-weight refractive telescope for the observation of extensive air showers

A general purpose instrument for imaging of Cherenkov light or fluorescence light emitted by extensive air showers is presented. Its refractive optics allows for a compact and light-weight design with a wide field-of-view of 12{\deg}. The optical system features a 0.5 m diameter Fresnel lens and a camera with 61 pixels composed of Winston cones and large-sized 6x6 mm photo sensors. As photo sensors, semi conductor light sensors (SiPMs) are utilized. The camera provides a high photon detection efficiency together with robust operation. The enclosed optics permit operation in regions of harsh environmental conditions. The low price of the telescope allows the production of a large number of telescopes and the application of the instrument in various projects, such as FAMOUS for the Pierre Auger Observatory, HAWC's Eye for HAWC or IceAct for IceCube. In this paper the novel design of this telescope and first measurements are presented.Comment: Submitted to JINST, second (minor) revisio

Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics

We show in the example of a one-dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form. The corresponding algebra is quadratic and involves three different matrices. Using this formalism we prove previous conjectures for the equal-time correlation functions of the model.Comment: LaTeX, 8 pages, one postscript figur

Impact of brief prewarming on anesthesia-related core-temperature drop, hemodynamics, microperfusion and postoperative ventilation in cytoreductive surgery of ovarian cancer: a randomized trial

Background: General (GA)- and epidural-anesthesia may cause a drop in body-core-temperature (BCT(drop)), and hypothermia, which may alter tissue oxygenation (StO(2)) and microperfusion after cytoreductive surgery for ovarian cancer. Cell metabolism of subcutaneous fat- or skeletal muscle cells, measured in microdialysis, may be affected. We hypothesized that forced-air prewarming during epidural catheter placement and induction of GA maintains normothermia and improves microperfusion. Methods: After ethics approval 47 women scheduled for cytoreductive surgery were prospectively enrolled. Women in the study group were treated with a prewarming of 43 °C during epidural catheter placement. BCT (Spot on®, 3 M) was measured before (T(1)), after induction of GA (T(2)) at 15 min (T(3)) after start of surgery, and until 2 h after ICU admission (T(ICU2h)). Primary endpoint was BCT(drop) between T(1) and T(2). Microperfusion-, hemodynamic- and clinical outcomes were defined as secondary outcomes. Statistical analysis used the Mann-Whitney-U- and non-parametric-longitudinal tests. Results: BCT(drop) was 0.35 °C with prewarming and 0.9 °C without prewarming (p < 0.005) and BCT remained higher over the observation period (ΔT(4) = 0.9 °C up to ΔT(7) = 0.95 °C, p < 0.001). No significant differences in hemodynamic parameters, transfusion, arterial lactate and dCO(2) were measured. In microdialysis the ethanol ratio was temporarily, but not significantly, reduced after prewarming. Lactate, glucose and glycerol after PW tended to be more constant over the entire period. Postoperatively, six women without prewarming, but none after prewarming were mechanical ventilated (p < 0.001). Conclusion: Prewarming at 43 °C reduces the BCT(drop) and maintains normothermia without impeding the perioperative routine patient flow. Microdialysis indicate better preserved parameters of microperfusion. Trial registration: ClinicalTrials.gov; ID: NCT02364219; Date of registration: 18-febr-2015

Linear independence of localized magnon states

At the magnetic saturation field, certain frustrated lattices have a class of states known as "localized multi-magnon states" as exact ground states. The number of these states scales exponentially with the number $N$ of spins and hence they have a finite entropy also in the thermodynamic limit $N\to \infty$ provided they are sufficiently linearly independent. In this article we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices including what we called the orthogonal type and the isolated type as well as the kagom\'{e}, the checkerboard and the star lattice we have proven linear independence of all localized multi-magnon states. On the other hand the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence.Comment: 23 pages, 6 figure