Results 1  10
of
16
Entanglement entropy and conformal field theory
, 2009
"... We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint ..."
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Cited by 92 (11 self)
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We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of nonequilibrium situations, are also considered.
Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with FisherHartwig singularities
 Ann. of Math
, 2011
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Universal corrections to scaling for block entanglement
 in spin1/2 XX chains
, 2010
"... Abstract. We consider the Rényi entropies Sn(`) in the one dimensional spin1/2 Heisenberg XX chain in a magnetic field. The case n = 1 corresponds to the von Neumann “entanglement ” entropy. Using a combination of methods based on the generalized FisherHartwig conjecture and a recurrence relation ..."
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Cited by 11 (6 self)
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Abstract. We consider the Rényi entropies Sn(`) in the one dimensional spin1/2 Heisenberg XX chain in a magnetic field. The case n = 1 corresponds to the von Neumann “entanglement ” entropy. Using a combination of methods based on the generalized FisherHartwig conjecture and a recurrence relation connected to the Painleve ́ VI differential equation we obtain the asymptotic behaviour, accurate to order O(`−3), of the Rényi entropies Sn(`) for large block lengths `. For n = 1, 2, 3, 10 this constitutes the 3, 6, 10, 48 leading terms respectively. The o(1) contributions are found to exhibit a rich structure of oscillatory behaviour, which we analyze in some detail both for finite n and in the limit n→∞. ar X iv
Entanglement, HaagDuality and Type Properties of Infinite Quantum Spin Chains
, 2008
"... We consider an infinite spin chain as a bipartite system consisting of the left and right halfchain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neum ..."
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Cited by 10 (5 self)
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We consider an infinite spin chain as a bipartite system consisting of the left and right halfchain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the halfchains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases the corresponding state is infinitely entangled in the sense that one copy of the system in such a state is sufficient to distill an infinite amount of maximally entangled qubit pairs. We apply this results to the critical XY model and show that its unique ground state ϕS provides a particular example for this type of entanglement.
Entanglement entropy of excited states
, 909
"... We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spinchain. For the latter, we developed a numerical application of algebraic Bethe Ansatz. We find two main classes of states with ..."
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Cited by 9 (6 self)
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We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spinchain. For the latter, we developed a numerical application of algebraic Bethe Ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as ground state. We also provide several details of the finite size scaling. Entanglement entropy of excited states 2 1.
Szegő limit theorem for operators with discontinuous symbols and applications to entanglement entropy
, 2006
"... Abstract. The main result in this paper is a one term Szegö type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are allowed to be nonsmooth or discontinuous in both position and momentum. The simplest example of ..."
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Cited by 8 (1 self)
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Abstract. The main result in this paper is a one term Szegö type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are allowed to be nonsmooth or discontinuous in both position and momentum. The simplest example of such symbol is the product of the characteristic functions of two compact sets, one in real space and the other in momentum space. The results of this paper are used in a study of the violation of the area entropy law for free fermions in [18]. This work also provides evidence towards a conjecture due to Harold Widom. 1.
TOEPLITZ AND HANKEL DETERMINANTS WITH SINGULARITIES: ANNOUNCEMENT OF RESULTS
, 809
"... Abstract. We obtain asymptotics for Toeplitz, Hankel, and Toeplitz+Hankel determinants whose symbols possess FisherHartwig singularities. Details of the proofs will be presented in another publication. Let f(z) be a complexvalued function integrable over the unit circle. Denote its Fourier coeffic ..."
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Cited by 3 (0 self)
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Abstract. We obtain asymptotics for Toeplitz, Hankel, and Toeplitz+Hankel determinants whose symbols possess FisherHartwig singularities. Details of the proofs will be presented in another publication. Let f(z) be a complexvalued function integrable over the unit circle. Denote its Fourier coefficients fj = 1
The FisherHartwig Formula and Generalized Entropies in XY Spin
, 2009
"... Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in exactly solvable models including spin chains. We use FisherHartwig formula to calculate entanglement entropy [as well as Rényi entropy] of large bloc ..."
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Cited by 1 (1 self)
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Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in exactly solvable models including spin chains. We use FisherHartwig formula to calculate entanglement entropy [as well as Rényi entropy] of large block of spins in the ground state of XY spin chain. In the end of the paper we announce our recent results [with F. Franchini and L. A. Takhtajan] on spectrum of density matrix of the block of spins.
FisherHartwig Formula and Entanglement Entropy
, 2009
"... Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use FisherHartwig formula, as well as the recent results concerning the asymptotics ..."
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Cited by 1 (0 self)
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Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use FisherHartwig formula, as well as the recent results concerning the asymptotics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.