684 research outputs found
Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
We consider the tensors generating matrix product states and density
operators in a spin chain. For pure states, we revise the renormalization
procedure introduced by F. Verstraete et al. in 2005 and characterize the
tensors corresponding to the fixed points. We relate them to the states
possessing zero correlation length, saturation of the area law, as well as to
those which generate ground states of local and commuting Hamiltonians. For
mixed states, we introduce the concept of renormalization fixed points and
characterize the corresponding tensors. We also relate them to concepts like
finite correlation length, saturation of the area law, as well as to those
which generate Gibbs states of local and commuting Hamiltonians. One of the
main result of this work is that the resulting fixed points can be associated
to the boundary theories of two-dimensional topological states, through the
bulk-boundary correspondence introduced by Cirac et al. in 2011.Comment: 63 pages, Annals of Physics (2016). Accepted versio
Projected entangled-pair states can describe chiral topological states
We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions
can describe chiral topological states by explicitly constructing a family of
such states with a non-trivial Chern number. They are ground states of two
different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii)
gapped, but with hopping amplitudes that decay according to a power law. We
derive general conditions on topological free fermionic PEPS which show that
they cannot correspond to exact ground states of gapped, local parent
Hamiltonians, and provide numerical evidence demonstrating that they can
nevertheless approximate well the physical properties of topological insulators
with local Hamiltonians at arbitrary temperatures.Comment: v2: minor changes, references added. v3: accepted version,
Journal-Ref adde
Nonlocal resources in the presence of Superselection Rules
Superselection rules severely alter the possible operations that can be
implemented on a distributed quantum system. Whereas the restriction to local
operations imposed by a bipartite setting gives rise to the notion of
entanglement as a nonlocal resource, the superselection rule associated with
particle number conservation leads to a new resource, the \emph{superselection
induced variance} of local particle number. We show that, in the case of pure
quantum states, one can quantify the nonlocal properties by only two additive
measures, and that all states with the same measures can be asymptotically
interconverted into each other by local operations and classical communication.
Furthermore we discuss how superselection rules affect the concepts of
majorization, teleportation and mixed state entanglement.Comment: 4 page
Edge theories in Projected Entangled Pair State models
We study the edge physics of gapped quantum systems in the framework of
Projected Entangled Pair State (PEPS) models. We show that the effective
low-energy model for any region acts on the entanglement degrees of freedom at
the boundary, corresponding to physical excitations located at the edge. This
allows us to determine the edge Hamiltonian in the vicinity of PEPS models, and
we demonstrate that by choosing the appropriate bulk perturbation, the edge
Hamiltonian can exhibit a rich phase diagram and phase transitions. While for
models in the trivial phase any Hamiltonian can be realized at the edge, we
show that for topological models, the edge Hamiltonian is constrained by the
topological order in the bulk which can e.g. protect a ferromagnetic Ising
chain at the edge against spontaneous symmetry breaking.Comment: 5 pages, 4 figure
Transfer Matrices and Excitations with Matrix Product States
We investigate the relation between static correlation functions in the
ground state of local quantum many-body Hamiltonians and the dispersion
relations of the corresponding low energy excitations using the formalism of
tensor network states. In particular, we show that the Matrix Product State
Transfer Matrix (MPS-TM) - a central object in the computation of static
correlation functions - provides important information about the location and
magnitude of the minima of the low energy dispersion relation(s) and present
supporting numerical data for one-dimensional lattice and continuum models as
well as two-dimensional lattice models on a cylinder. We elaborate on the
peculiar structure of the MPS-TM's eigenspectrum and give several arguments for
the close relation between the structure of the low energy spectrum of the
system and the form of static correlation functions. Finally, we discuss how
the MPS-TM connects to the exact Quantum Transfer Matrix (QTM) of the model at
zero temperature. We present a renormalization group argument for obtaining
finite bond dimension approximations of MPS, which allows to reinterpret
variational MPS techniques (such as the Density Matrix Renormalization Group)
as an application of Wilson's Numerical Renormalization Group along the virtual
(imaginary time) dimension of the system.Comment: 39 pages (+8 pages appendix), 14 figure
Projection, Spatial Correlations, and Anisotropies in a Large and Complete Sample of Abell Clusters
An analysis of R >= 1 Abell clusters is presented for samples containing
recent redshifts from the MX Northern Abell Cluster Survey. The newly obtained
redshifts from the MX Survey as well as those from the ESO Nearby Abell Cluster
Survey (ENACS) provide the necessary data for the largest magnitude-limited
correlation analysis of rich clusters in the entire sky (excluding the galactic
plane) to date. We find 19.4 <= r_0 <= 23.3 h^-1Mpc, -1.92 <= gamma <= -1.83
for four different subsets of Abell/ACO clusters, including a large sample
(N=104) of cD clusters. We have used this dataset to look for line-of-sight
anisotropies within the Abell/ACO catalogs. We show that the strong
anisotropies present in previously studied Abell cluster datasets are not
present in our R >= 1 samples. There are, however, indications of residual
anisotropies which we show are the result of two elongated superclusters, Ursa
Majoris and Corona Borealis, whose axes lie near the line-of-sight. After
rotating these superclusters so that their semi-major axes are prependicular to
the line-of-sight, we find no anisotropies as indicated by the correlation
function. The amplitude and slope of the two-point correlation function remain
the same before and after these rotations. We also remove a subset of R = 1
Abell/ACO clusters that show sizable foreground/background galaxy contamination
and again find no change in the amplitude or slope of the correlation function.
We conclude that the correlation length of R >= 1 Abell clusters is not
artificially enhanced by line-of-sight anisotropies.Comment: 37 pages, 8 figures, AASTeX Accepted for publication in Ap
The Bose-Hubbard model is QMA-complete
The Bose-Hubbard model is a system of interacting bosons that live on the
vertices of a graph. The particles can move between adjacent vertices and
experience a repulsive on-site interaction. The Hamiltonian is determined by a
choice of graph that specifies the geometry in which the particles move and
interact. We prove that approximating the ground energy of the Bose-Hubbard
model on a graph at fixed particle number is QMA-complete. In our QMA-hardness
proof, we encode the history of an n-qubit computation in the subspace with at
most one particle per site (i.e., hard-core bosons). This feature, along with
the well-known mapping between hard-core bosons and spin systems, lets us prove
a related result for a class of 2-local Hamiltonians defined by graphs that
generalizes the XY model. By avoiding the use of perturbation theory in our
analysis, we circumvent the need to multiply terms in the Hamiltonian by large
coefficients
The impact of computer simulations on the teaching and learning of electromagnetism in grade 11 : a case study of a school in the Mpumalanga Province
The study investigated the impact of computer simulations on the teaching and learning of electromagnetism in grade 11. Electromagnetism is a section of the Physical Science curriculum. Two grade 11 classes in the Mgwenya circuit in Mpumalanga province of South Africa were used as a case study. Using a pre-test, post-test non-equivalent control group design, it was found that learners in the experimental group (n = 30) who were taught using the simulations achieved significantly higher scores on the post-test than learners in the control group (n = 35) who were taught using traditional teacher-centred teaching method; (t statistic = 3.582, df = 56, p = 0.32 compared to = 0.18 for the control group confirmed conceptual improvement. Both teachers and learners indicated that they accept the use of computer simulations in teaching and learning of electromagnetism.Science and Technology EducationM. Sc. (Mathematics, Science and Technology Education
Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
In this paper, we do a complete classification of valence-bond crystals
(VBCs) on the kagome lattice based on general arguments of symmetry only and
thus identify many new VBCs for different unit cell sizes. For the spin-1/2
Heisenberg antiferromagnet, we study the relative energetics of competing
gapless spin liquids (SLs) and VBC phases within the class of
Gutzwiller-projected fermionic wave functions using variational Monte Carlo
techniques, hence implementing exactly the constraint of one fermion per site.
By using a state-of-the-art optimization method, we conclusively show that the
U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and
36-site unit cell VBCs. This stability is also preserved on addition of a
next-nearest-neighbor super-exchange coupling of both antiferromagnetic and
ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is
stabilized on addition of a very small next-nearest-neighbor FM super-exchange
coupling, i.e. |J2|~0.045, and this VBC is the same in terms of space-group
symmetry as that obtained in an effective quantum dimer model study. It breaks
reflection symmetry, has a nontrivial flux pattern and is a strong dimerization
of the uniform RVB SL.Comment: 16 pages, 25 figures. Invited paper for Focus issue on "Quantum Spin
Liquids" of the New Journal of Physic
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