2,542 research outputs found
A Generic Renormalization Method in Curved Spaces and at Finite Temperature
Based only on simple principles of renormalization in coordinate space, we
derive closed renormalized amplitudes and renormalization group constants at 1-
and 2-loop orders for scalar field theories in general backgrounds. This is
achieved through a generic renormalization procedure we develop exploiting the
central idea behind differential renormalization, which needs as only inputs
the propagator and the appropriate laplacian for the backgrounds in question.
We work out this generic coordinate space renormalization in some detail, and
subsequently back it up with specific calculations for scalar theories both on
curved backgrounds, manifestly preserving diffeomorphism invariance, and at
finite temperature.Comment: 15pp., REVTeX, UB-ECM-PF 94/1
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
Simulation of many-qubit quantum computation with matrix product states
Matrix product states provide a natural entanglement basis to represent a
quantum register and operate quantum gates on it. This scheme can be
materialized to simulate a quantum adiabatic algorithm solving hard instances
of a NP-Complete problem. Errors inherent to truncations of the exact action of
interacting gates are controlled by the size of the matrices in the
representation. The property of finding the right solution for an instance and
the expected value of the energy are found to be remarkably robust against
these errors. As a symbolic example, we simulate the algorithm solving a
100-qubit hard instance, that is, finding the correct product state out of ~
10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow
growth of the average minimum time to solve hard instances with
highly-truncated simulations of adiabatic quantum evolution.Comment: 5 pages, 4 figures, final versio
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
Half the entanglement in critical systems is distillable from a single specimen
We establish that the leading critical scaling of the single-copy
entanglement is exactly one half of the entropy of entanglement of a block in
critical infinite spin chains in a general setting, using methods of conformal
field theory. Conformal symmetry imposes that the single-copy entanglement for
critical many-body systems scales as E_1(\rho_L)=(c/6) \log L- (c/6)
(\pi^2/\log L) + O(1/L), where L is the number of constituents in a block of an
infinite chain and c corresponds to the central charge. This proves that from a
single specimen of a critical chain, already half the entanglement can be
distilled compared to the rate that is asymptotically available. The result is
substantiated by a quantitative analysis for all translationally invariant
quantum spin chains corresponding to general isotropic quasi-free fermionic
models. An analytic example of the XY model shows that away from criticality
the above simple relation is only maintained near the quantum phase transition
point.Comment: 4 pages RevTeX, 1 figure, final versio
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
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
Concurrence in collective models
We review the entanglement properties in collective models and their
relationship with quantum phase transitions. Focusing on the concurrence which
characterizes the two-spin entanglement, we show that for first-order
transition, this quantity is singular but continuous at the transition point,
contrary to the common belief. We also propose a conjecture for the concurrence
of arbitrary symmetric states which connects it with a recently proposed
criterion for bipartite entanglement.Comment: 8 pages, 2 figures, published versio
Entanglement negativity in quantum field theory
We develop a systematic method to extract the negativity in the ground state
of a 1+1 dimensional relativistic quantum field theory, using a path integral
formalism to construct the partial transpose rho_A^{T_2} of the reduced density
matrix of a subsystem A=A1 U A2, and introducing a replica approach to obtain
its trace norm which gives the logarithmic negativity E=ln||\rho_A^{T_2}||.
This is shown to reproduce standard results for a pure state. We then apply
this method to conformal field theories, deriving the result E\sim(c/4) ln(L1
L2/(L1+L2)) for the case of two adjacent intervals of lengths L1, L2 in an
infinite system, where c is the central charge. For two disjoint intervals it
depends only on the harmonic ratio of the four end points and so is manifestly
scale invariant. We check our findings against exact numerical results in the
harmonic chain.Comment: 4 pages, 5 figure
- âŠ