2,648 research outputs found
Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
Entanglement entropy obeys area law scaling for typical physical quantum
systems. This may naively be argued to follow from locality of interactions. We
show that this is not the case by constructing an explicit simple spin chain
Hamiltonian with nearest neighbor interactions that presents an entanglement
volume scaling law. This non-translational model is contrived to have couplings
that force the accumulation of singlet bonds across the half chain. Our result
is complementary to the known relation between non-translational invariant,
nearest neighbor interacting Hamiltonians and QMA complete problems.Comment: 9 pages, 4 figure
Superballistic Diffusion of Entanglement in Disordered Spin Chains
We study the dynamics of a single excitation in an infinite XXZ spin chain,
which is launched from the origin. We study the time evolution of the spread of
entanglement in the spin chain and obtain an expression for the second order
spatial moment of concurrence, about the origin, for both ordered and
disordered chains. In this way, we show that a finite central disordered region
can lead to sustained superballistic growth in the second order spatial moment
of entanglement within the chain.Comment: 5 pages, 1 figur
The Hidden Spatial Geometry of Non-Abelian Gauge Theories
The Gauss law constraint in the Hamiltonian form of the gauge theory
of gluons is satisfied by any functional of the gauge invariant tensor variable
. Arguments are given that the tensor is a more appropriate variable. When the Hamiltonian
is expressed in terms of or , the quantity appears.
The gauge field Bianchi and Ricci identities yield a set of partial
differential equations for in terms of . One can show that
is a metric-compatible connection for with torsion, and that the curvature
tensor of is that of an Einstein space. A curious 3-dimensional
spatial geometry thus underlies the gauge-invariant configuration space of the
theory, although the Hamiltonian is not invariant under spatial coordinate
transformations. Spatial derivative terms in the energy density are singular
when . These singularities are the analogue of the centrifugal
barrier of quantum mechanics, and physical wave-functionals are forced to
vanish in a certain manner near . It is argued that such barriers are
an inevitable result of the projection on the gauge-invariant subspace of the
Hilbert space, and that the barriers are a conspicuous way in which non-abelian
gauge theories differ from scalar field theories.Comment: 19 pages, TeX, CTP #223
Multi-party entanglement in graph states
Graph states are multi-particle entangled states that correspond to
mathematical graphs, where the vertices of the graph take the role of quantum
spin systems and edges represent Ising interactions. They are many-body spin
states of distributed quantum systems that play a significant role in quantum
error correction, multi-party quantum communication, and quantum computation
within the framework of the one-way quantum computer. We characterize and
quantify the genuine multi-particle entanglement of such graph states in terms
of the Schmidt measure, to which we provide upper and lower bounds in graph
theoretical terms. Several examples and classes of graphs will be discussed,
where these bounds coincide. These examples include trees, cluster states of
different dimension, graphs that occur in quantum error correction, such as the
concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier
transform in the one-way computer. We also present general transformation rules
for graphs when local Pauli measurements are applied, and give criteria for the
equivalence of two graphs up to local unitary transformations, employing the
stabilizer formalism. For graphs of up to seven vertices we provide complete
characterization modulo local unitary transformations and graph isomorphies.Comment: 22 pages, 15 figures, 2 tables, typos corrected (e.g. in measurement
rules), references added/update
Renormalization group transformations on quantum states
We construct a general renormalization group transformation on quantum
states, independent of any Hamiltonian dynamics of the system. We illustrate
this procedure for translational invariant matrix product states in one
dimension and show that product, GHZ, W and domain wall states are special
cases of an emerging classification of the fixed points of this
coarse--graining transformation.Comment: 5 pages, 2 figur
Zero dimensional area law in a gapless fermion system
The entanglement entropy of a gapless fermion subsystem coupled to a gapless
bulk by a "weak link" is considered. It is demonstrated numerically that each
independent weak link contributes an entropy proportional to lnL, where L is
linear dimension of the subsystem.Comment: 6 pages, 11 figures; added 3d computatio
Parity effects in the scaling of block entanglement in gapless spin chains
We consider the Renyi alpha-entropies for Luttinger liquids (LL). For large
block lengths l these are known to grow like ln l. We show that there are
subleading terms that oscillate with frequency 2k_F (the Fermi wave number of
the LL) and exhibit a universal power-law decay with l. The new critical
exponent is equal to K/(2 alpha), where K is the LL parameter. We present
numerical results for the anisotropic XXZ model and the full analytic solution
for the free fermion (XX) point.Comment: 4 pages, 5 figures. Final version accepted in PR
Entropy and Exact Matrix Product Representation of the Laughlin Wave Function
An analytical expression for the von Neumann entropy of the Laughlin wave
function is obtained for any possible bipartition between the particles
described by this wave function, for filling fraction nu=1. Also, for filling
fraction nu=1/m, where m is an odd integer, an upper bound on this entropy is
exhibited. These results yield a bound on the smallest possible size of the
matrices for an exact representation of the Laughlin ansatz in terms of a
matrix product state. An analytical matrix product state representation of this
state is proposed in terms of representations of the Clifford algebra. For
nu=1, this representation is shown to be asymptotically optimal in the limit of
a large number of particles
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