Finite Size Corrections to Entanglement in Quantum Critical Systems

Physical Review A (Impact Factor: 2.81). 09/2008; 78:032319. DOI: 10.1103/PhysRevA.78.032319
Source: arXiv


We analyze the finite size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system $L \to \infty$) exhibit a unique pattern of entanglement, which differ only at leading order $(1/L)^2$. In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length $L$ for both periodic and twisted boundary conditions.

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Available from: Marcelo S. Sarandy, Nov 16, 2013
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    • "Here c is the central charge of the underlying conformal field theory and C α a non universal constant that will be computed latter. However, less attention has been paid to the entropy when the system is in an excited state which can strongly change the behavior of the entropy [7] [8] [9] [10]. "
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    • "The entanglement entropy of disjoint intervals gives also information about other universal features of the conformal fixed point related to the full operator content of the theory [8]. Conversely, only little attention has been devoted to the entanglement properties of excited states (with the exception of few manuscripts [9] [10] [11] [12]), although it is a very natural problem. Here we consider two topical spin-chains [13] to address this issue. "
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