Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry

We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time evolution in an SU(2) invariant system. The resulting algorithm is tested in a critical quantum spin chain and shown to be significantly more efficient than the standard TEBD.Comment: 5 pages, 4 figure

Ground state fidelity from tensor network representations

For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well-defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields.Comment: 4 pages, 2 figures. Published version in Physical Review Letter

The iTEBD algorithm beyond unitary evolution

The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit. Here we extend the algorithm to tackle a much broader class of problems, namely the simulation of arbitrary one-dimensional evolution operators that can be expressed as a (translationally invariant) tensor network. Relatedly, we also address the problem of finding the dominant eigenvalue and eigenvector of a one-dimensional transfer matrix that can be expressed in the same way. New applications include the simulation, in the thermodynamic limit, of open (i.e. master equation) dynamics and thermal states in 1D quantum systems, as well as calculations with partition functions in 2D classical systems, on which we elaborate. The present extension of the algorithm also plays a prominent role in the infinite projected entangled-pair states (iPEPS) approach to infinite 2D quantum lattice systems.Comment: 11 pages, 16 figures, 1 appendix with algorithms for specific types of evolution. A typo in the appendix figures has been corrected. Accepted in PR

Eternity and the cosmological constant

The purpose of this paper is to analyze the stability of interacting matter in the presence of a cosmological constant. Using an approach based on the heat equation, no imaginary part is found for the effective potential in the presence of a fixed background, which is the n-dimensional sphere or else an analytical continuation thereof, which is explored in some detail.Comment: 45 pages, 6 figure

Social media in cardiology: Reasons to learn how to use it

Social media has changed the way we learn, educate, and interact with our peers. The dynamic nature of social media and their immediate availability through our portable devices (smartphones, tablets, smartwatches, etc.) is quickly transforming the way we participate in society. The scope of these digital tools is broad as they deal with many different aspects: Teaching and learning, case discussion, congresses coverage, peer to peer interaction, research are examples worth mentioning. The scientific societies considered more innovative, are promoting these tools between their members. These new concepts need to be known by the cardiologists to stay updated, as countless information is moving rapidly through these channels. We summarize the main reasons why learning how to use these tools to be part of the conversation is essential for the cardiologist in training or fully stablished

Quantifying Quantum Correlations in Fermionic Systems using Witness Operators

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of problems known as semidefinite programs (SDPs), which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robust- ness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann con- currence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.Comment: 7 pages, 6 figures, Accepted for publication in Quantum Information Processin

Tensor network states and geometry

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D=1 systems is seen to be determined by the structure of geodesics in the physical and holographic geometries, respectively; whereas the asymptotic scaling of entanglement entropy is seen to always obey a simple boundary law -- that is, again in the relevant geometry. This geometrical interpretation offers a simple and unifying framework to understand the structural properties of, and helps clarify the relation between, different tensor network states. In addition, it has recently motivated the branching MERA, a generalization of the MERA capable of reproducing violations of the entropic boundary law in D>1 dimensions.Comment: 18 pages, 18 figure

Association of patients' geographic origins with viral hepatitis co-infection patterns, Spain

To determine if hepatitis C virus seropositivity and active hepatitis B virus infection in HIV-positive patients vary with patients' geographic origins, we studied co-infections in HIV-seropositive adults. Active hepatitis B infection was more prevalent in persons from Africa, and hepatitis C seropositivity was more common in persons from eastern Europe.Ministerio de Sanidad. Instituto de Salud Carlos II