7,258 research outputs found
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
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