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Register a new userEstimating the central charge from the Renyi entanglement entropy
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We calculate the von Neumann and Renyi bipartite entanglement entropy of the $O(2)$ model with a chemical potential on a 1+1 dimensional Euclidean lattice with open and periodic boundary conditions. We show that the Calabrese-Cardy conformal field theory predictions for the leading logarithmic scaling with the spatial size of these entropies are consistent with a central charge $c=1$. This scaling survives the time continuum limit and truncations of the microscopic degrees of freedom, modifications which allow us to connect the Lagrangian formulation to quantum Hamiltonians. At half-filling, the forms of the subleading corrections imposed by conformal field theory allow the determination of the central charge with an accuracy better than two percent for moderately sized lattices. We briefly discuss the possibility of estimating the central charge using quantum simulators.
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We use entanglement entropy to define a central charge associated to a two-dimensional defect or boundary in a conformal field theory (CFT). We present holographic calculations of this central charge for several maximally supersymmetric CFTs dual to eleven-dimensional supergravity in Anti-de Sitter space, namely the M5-brane theory with a Wilson surface defect and three-dimensional CFTs related to the M2-brane theory with a boundary. Our results for the central charge depend on a partition of the number of M2-branes, $N$, ending on the number of M5-branes, $M$. For the Wilson surface, the partition specifies a representation of the gauge algebra, and we write our result for the central charge in a compact form in terms of the algebras Weyl vector and the representations highest weight vector. We explore how the central charge scales with $N$ and $M$ for some examples of partitions. In general the central charge does not scale as $M^3$ or $N^{3/2}$, the number of degrees of freedom of the M5- or M2-brane theory at large $M$ or $N$, respectively.
We study the entanglement R{e}nyi $alpha$-entropy (ER$alpha $E) as the measure of entanglement. Instead of a single quantity in standard entanglement quantification for a quantum state by using the von Neumann entropy for the well-accepted entanglement of formation (EoF), the ER$alpha $E gives a continuous spectrum parametrized by variable $alpha $ as the entanglement measure, and it reduces to the standard EoF in the special case $alpha rightarrow 1$. The ER$alpha $E provides more information in entanglement quantification, and can be used such as in determining the convertibility of entangled states by local operations and classical communication. A series of new results are obtained: (i) we can show that ER$alpha $E of two states, which can be mixed or pure, may be incomparable, in contrast to the fact that there always exists an order for EoF of two states; (ii) similar as the case of EoF, we study in a fully analytical way the ER$alpha $E for arbitrary two-qubit states, the Werner states and isotropic states in general d-dimension; (iii) we provide a proof of the previous conjecture for the analytical functional form of EoF of isotropic states in arbitrary d-dimension.
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Renyi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operational entanglement that is both computationally and experimentally accessible. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most, a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to $10^5$ particles.
We explore an asymptotic behavior of Renyi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.
We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed of a central spin coupled and initially uncorrelated with 15 other spins. Due to the spin-spin interactions, information flows from the central spin to the surrounding ones forming clusters of multi-spin correlations that grow in time. We design a nuclear magnetic resonance experiment that directly measures the amplitudes of the multi-spin correlations and use them to compute the evolution of what we call correlation Renyi entropy. This entropy keeps growing even after the equilibration of the entanglement entropy. We also analyze how the saturation point and the timescale for the equilibration of the correlation Renyi entropy depend on the system size.
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