2,285 research outputs found
Entanglement renormalization in fermionic systems
We demonstrate, in the context of quadratic fermion lattice models in one and
two spatial dimensions, the potential of entanglement renormalization (ER) to
define a proper real-space renormalization group transformation. Our results
show, for the first time, the validity of the multi-scale entanglement
renormalization ansatz (MERA) to describe ground states in two dimensions, even
at a quantum critical point. They also unveil a connection between the
performance of ER and the logarithmic violations of the boundary law for
entanglement in systems with a one-dimensional Fermi surface. ER is recast in
the language of creation/annihilation operators and correlation matrices.Comment: 5 pages, 4 figures Second appendix adde
Entanglement entropy in one-dimensional disordered interacting system: The role of localization
The properties of the entanglement entropy (EE) in one-dimensional disordered
interacting systems are studied. Anderson localization leaves a clear signature
on the average EE, as it saturates on length scale exceeding the localization
length. This is verified by numerically calculating the EE for an ensemble of
disordered realizations using density matrix renormalization group (DMRG). A
heuristic expression describing the dependence of the EE on the localization
length, which takes into account finite size effects, is proposed. This is used
to extract the localization length as function of the interaction strength. The
localization length dependence on the interaction fits nicely with the
expectations.Comment: 5 pages, 4 figures, accepted for publication in Physical Review
Letter
Boundary and impurity effects on entanglement of Heisenberg chains
We study entanglement of a pair of qubits and the bipartite entanglement
between the pair and the rest within open-ended Heisenberg and XY models.
The open boundary condition leads to strong oscillations of entanglements with
a two-site period, and the two kinds of entanglements are 180 degree out of
phase with each other. The mean pairwise entanglement and ground-state energy
per site in the model are found to be proportional to each other. We
study the effects of a single bulk impurity on entanglement, and find that
there exists threshold values of the relative coupling strength between the
impurity and its nearest neighbours, after which the impurity becomes pairwise
entangled with its nearest neighbours.Comment: 6 pages and 6 figure
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
Quantum Phase Transitions and Bipartite Entanglement
We develop a general theory of the relation between quantum phase transitions
(QPTs) characterized by nonanalyticities in the energy and bipartite
entanglement. We derive a functional relation between the matrix elements of
two-particle reduced density matrices and the eigenvalues of general two-body
Hamiltonians of -level systems. The ground state energy eigenvalue and its
derivatives, whose non-analyticity characterizes a QPT, are directly tied to
bipartite entanglement measures. We show that first-order QPTs are signalled by
density matrix elements themselves and second-order QPTs by the first
derivative of density matrix elements. Our general conclusions are illustrated
via several quantum spin models.Comment: 5 pages, incl. 2 figures. v3: The version published in PRL, including
a few extra comments and clarifications for which there was no space in the
PR
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Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench
We have studied quantum phase transition induced by a quench in different one
dimensional spin systems. Our analysis is based on the dynamical mechanism
which envisages nonadiabaticity in the vicinity of the critical point. This
causes spin fluctuation which leads to the random fluctuation of the Berry
phase factor acquired by a spin state when the ground state of the system
evolves in a closed path. The two-point correlation of this phase factor is
associated with the probability of the formation of defects. In this framework,
we have estimated the density of defects produced in several one dimensional
spin chains. At the critical region, the entanglement entropy of a block of
spins with the rest of the system is also estimated which is found to increase
logarithmically with . The dependence on the quench time puts a constraint
on the block size . It is also pointed out that the Lipkin-Meshkov-Glick
model in point-splitting regularized form appears as a combination of the XXX
model and Ising model with magnetic field in the negative z-axis. This unveils
the underlying conformal symmetry at criticality which is lost in the sharp
point limit. Our analysis shows that the density of defects as well as the
scaling behavior of the entanglement entropy follows a universal behavior in
all these systems.Comment: 4 figures, Accepted in Phys. Rev.
Neural network determination of the non-singlet quark distribution
We summarize the main features of our approach to parton fitting, and we show
a preliminary result for the non-singlet structure function. When comparing our
result to other PDF sets, we find a better description of large x data and
larger error bands in the extrapolation regions.Comment: 4 pages, 1 eps figure. Presented at the XIV International Workshop on
Deep Inelastic Scattering (DIS2006), Tsukuba, Japan, 20-24 April 200
Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
This work explores the use of a tree tensor network ansatz to simulate the
ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting
the entropic area law, the tree tensor network ansatz seems to produce
quasi-exact results in systems with sizes well beyond the reach of exact
diagonalisation techniques. We describe an algorithm to approximate the ground
state of a local Hamiltonian on a L times L lattice with the topology of a
torus. Accurate results are obtained for L={4,6,8}, whereas approximate results
are obtained for larger lattices. As an application of the approach, we analyse
the scaling of the ground state entanglement entropy at the quantum critical
point of the model. We confirm the presence of a positive additive constant to
the area law for half a torus. We also find a logarithmic additive correction
to the entropic area law for a square block. The single copy entanglement for
half a torus reveals similar corrections to the area law with a further term
proportional to 1/L.Comment: Major rewrite, new version published in Phys. Rev. B with highly
improved numerical results for the scaling of the entropies and several new
sections. The manuscript has now 19 pages and 30 Figure
Adiabatic quantum computation and quantum phase transitions
We analyze the ground state entanglement in a quantum adiabatic evolution
algorithm designed to solve the NP-complete Exact Cover problem. The entropy of
entanglement seems to obey linear and universal scaling at the point where the
mass gap becomes small, suggesting that the system passes near a quantum phase
transition. Such a large scaling of entanglement suggests that the effective
connectivity of the system diverges as the number of qubits goes to infinity
and that this algorithm cannot be efficiently simulated by classical means. On
the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR
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