arXiv:1104.1004

Entanglement Entropy for Disjoint Subsystems in XX Spin Chain

Bai-Qi Jin, V. E. Korepin

Published Apr 6, 2011• 2 citations

Abstract

Fisher-Hartwig formula has been successful applied to describe the von Neumann and Rényi entropies of a block of spins in the ground state of XX spin chain. It was based on a determinant representation. In this paper, we generalize the free fermion method to obtain an exact formulation for the entropy of any finite subsystem in XX spin chain. Based on this, we derive a determinant representation of the entropy of multiple disjoint intervals in the ground state of $XX$ model.

DOI: 10.48550/arxiv.1104.1004

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arXiv:1104.1004

Entanglement Entropy for Disjoint Subsystems in XX Spin Chain

Bai-Qi Jin, V. E. Korepin

Published Apr 6, 2011• 2 citations

arXiv HTML PDF

Abstract

XX

model.

DOI: 10.48550/arxiv.1104.1004

Related papers

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L Brightmore, G P Gehér, Alexander Rudol'fovich Its +4 more

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Vanja Marić, Saverio Bocini, Maurizio Fagotti

A bstract We take the paradigm of interacting spin chains, the Heisenberg spin- $\frac{1}{2}$ 1 2 XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An example is the fermionic analogue of the gapless XXZ Hamiltonian, which, in a continuum scaling limit, is described by the massless Thirring model. We work out the Rényi- α entropies of disjoint blocks in the ground state and extract the universal scaling functions describing the Rényi- α tripartite information in the limit of infinite lengths. We consider also the von Neumann entropy, but only in the limit of large distance. We show how to use the entropies of spin blocks to unveil the spin structures of the underlying massless Thirring model. Finally, we speculate about the tripartite information after global quenches and conjecture its asymptotic behaviour in the limit of infinite time and small quench. The resulting conjecture for the “residual tripartite information”, which corresponds to the limit in which the intervals’ lengths are infinitely larger than their (large) distance, supports the claim of universality recently made studying noninteracting spin chains. Our mild assumptions imply that the residual tripartite information after a small quench of the anisotropy in the gapless phase of XXZ is equal to − log 2.A bstract We take the paradigm of interacting spin chains, the Heisenberg spin- $$ \frac{1}{2} $$ 1 2 XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An example is the fermionic analogue of the gapless XXZ Hamiltonian, which, in a continuum scaling limit, is described by the massless Thirring model. We work out the Rényi- α entropies of disjoint blocks in the ground state and extract the universal scaling functions describing the Rényi- α tripartite information in the limit of infinite lengths. We consider also the von Neumann entropy, but only in the limit of large distance. We show how to use the entropies of spin blocks to unveil the spin structures of the underlying massless Thirring model. Finally, we speculate about the tripartite information after global quenches and conjecture its asymptotic behaviour in the limit of infinite time and small quench. The resulting conjecture for the “residual tripartite information”, which corresponds to the limit in which the intervals’ lengths are infinitely larger than their (large) distance, supports the claim of universality recently made studying noninteracting spin chains. Our mild assumptions imply that the residual tripartite information after a small quench of the anisotropy in the gapless phase of XXZ is equal to − log 2.

arXiv:2312.10028Journal of High Energy PhysicsMar 7, 20241 citation

XX

model.

A bstract We take the paradigm of interacting spin chains, the Heisenberg spin-

\frac{1}{2}

1 2 XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An example is the fermionic analogue of the gapless XXZ Hamiltonian, which, in a continuum scaling limit, is described by the massless Thirring model. We work out the Rényi- α entropies of disjoint blocks in the ground state and extract the universal scaling functions describing the Rényi- α tripartite information in the limit of infinite lengths. We consider also the von Neumann entropy, but only in the limit of large distance. We show how to use the entropies of spin blocks to unveil the spin structures of the underlying massless Thirring model. Finally, we speculate about the tripartite information after global quenches and conjecture its asymptotic behaviour in the limit of infinite time and small quench. The resulting conjecture for the “residual tripartite information”, which corresponds to the limit in which the intervals’ lengths are infinitely larger than their (large) distance, supports the claim of universality recently made studying noninteracting spin chains. Our mild assumptions imply that the residual tripartite information after a small quench of the anisotropy in the gapless phase of XXZ is equal to − log 2.