9,460 research outputs found
Entanglement entropy of two disjoint intervals in c=1 theories
We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure
Entanglement entropy of two disjoint intervals in conformal field theory
We study the entanglement of two disjoint intervals in the conformal field
theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any
integer n is calculated as the four-point function of a particular type of
twist fields and the final result is expressed in a compact form in terms of
the Riemann-Siegel theta functions. In the decompactification limit we provide
the analytic continuation valid for all model parameters and from this we
extract the entanglement entropy. These predictions are checked against
existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos
corrected and refs adde
Entanglement of excited states in critical spin chians
Renyi and von Neumann entropies quantifying the amount of entanglement in
ground states of critical spin chains are known to satisfy a universal law
which is given by the Conformal Field Theory (CFT) describing their scaling
regime. This law can be generalized to excitations described by primary fields
in CFT, as was done in reference (Alcaraz et. al., Phys. Rev. Lett. 106, 201601
(2011)), of which this work is a completion. An alternative derivation is
presented, together with numerical verifications of our results in different
models belonging to the c=1,1/2 universality classes. Oscillations of the Renyi
entropy in excited states and descendant fields are also discussed.Comment: 23 pages, 13 figure
Thermodynamic entropy of a many body energy eigenstate
It is argued that a typical many body energy eigenstate has a well defined
thermodynamic entropy and that individual eigenstates possess thermodynamic
characteristics analogous to those of generic isolated systems. We examine
large systems with eigenstate energies equivalent to finite temperatures. When
quasi-static evolution of a system is adiabatic (in the quantum mechanical
sense), two coupled subsystems can transfer heat from one subsystem to another
yet remain in an energy eigenstate. To explicitly construct the entropy from
the wave function, degrees of freedom are divided into two unequal parts. It is
argued that the entanglement entropy between these two subsystems is the
thermodynamic entropy per degree of freedom for the smaller subsystem. This is
done by tracing over the larger subsystem to obtain a density matrix, and
calculating the diagonal and off-diagonal contributions to the entanglement
entropy.Comment: 18 page
Entanglement properties of quantum spin chains
We investigate the entanglement properties of a finite size 1+1 dimensional
Ising spin chain, and show how these properties scale and can be utilized to
reconstruct the ground state wave function. Even at the critical point, few
terms in a Schmidt decomposition contribute to the exact ground state, and to
physical properties such as the entropy. Nevertheless the entanglement here is
prominent due to the lower-lying states in the Schmidt decomposition.Comment: 5 pages, 6 figure
Toward autonomous spacecraft
Ways in which autonomous behavior of spacecraft can be extended to treat situations wherein a closed loop control by a human may not be appropriate or even possible are explored. Predictive models that minimize mean least squared error and arbitrary cost functions are discussed. A methodology for extracting cyclic components for an arbitrary environment with respect to usual and arbitrary criteria is developed. An approach to prediction and control based on evolutionary programming is outlined. A computer program capable of predicting time series is presented. A design of a control system for a robotic dense with partially unknown physical properties is presented
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
We consider the Renyi entanglement entropies in the one-dimensional XX
spin-chains with open boundary conditions in the presence of a magnetic field.
In the case of a semi-infinite system and a block starting from the boundary,
we derive rigorously the asymptotic behavior for large block sizes on the basis
of a recent mathematical theorem for the determinant of Toeplitz plus Hankel
matrices. We conjecture a generalized Fisher-Hartwig form for the corrections
to the asymptotic behavior of this determinant that allows the exact
characterization of the corrections to the scaling at order o(1/l) for any n.
By combining these results with conformal field theory arguments, we derive
exact expressions also in finite chains with open boundary conditions and in
the case when the block is detached from the boundary.Comment: 24 pages, 9 figure
Field-theory results for three-dimensional transitions with complex symmetries
We discuss several examples of three-dimensional critical phenomena that can
be described by Landau-Ginzburg-Wilson theories. We present an
overview of field-theoretical results obtained from the analysis of high-order
perturbative series in the frameworks of the and of the
fixed-dimension d=3 expansions. In particular, we discuss the stability of the
O(N)-symmetric fixed point in a generic N-component theory, the critical
behaviors of randomly dilute Ising-like systems and frustrated spin systems
with noncollinear order, the multicritical behavior arising from the
competition of two distinct types of ordering with symmetry O() and
O() respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200
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