Exact relationship between the entanglement entropies of XY and quantum Ising chains

Iglói, Ferenc; Juhász, Róbert

doi:10.1209/0295-5075/81/57003

Cited by 78 publications

(121 citation statements)

References 32 publications

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“…This method was used for deriving the entropy asymptotics of the critical Ising model from that of the critical XY chain [29], our result generalizes this.…”

Section: The Generalized Xy -Ising Correspondencesupporting

confidence: 64%

Entanglement entropy in quantum spin chains with broken reflection symmetry

Kadar

Zimborás

2010

Phys. Rev. A

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We investigate the entanglement entropy of a block of L sites in quasifree translation-invariant spin chains concentrating on the effect of reflection-symmetry breaking. The Majorana two-point functions corresponding to the Jordan-Wigner transformed fermionic modes are determined in the most general case; from these, it follows that reflection symmetry in the ground state can only be broken if the model is quantum critical. The large L asymptotics of the entropy are calculated analytically for general gauge-invariant models, which have, until now, been done only for the reflection-symmetric sector. Analytical results are also derived for certain nongauge-invariant models (e.g., for the Ising model with Dzyaloshinskii-Moriya interaction). We also study numerically finite chains of length N with a nonreflection-symmetric Hamiltonian and report that the reflection symmetry of the entropy of the first L spins is violated but the reflection-symmetric Calabrese-Cardy formula is recovered asymptotically. Furthermore, for noncritical reflection-symmetry-breaking Hamiltonians, we find an anomaly in the behavior of the saturation entropy as we approach the critical line. The paper also provides a concise but extensive review of the block-entropy asymptotics in translation-invariant quasifree spin chains with an analysis of the nearest-neighbor case and the enumeration of the yet unsolved parts of the quasifree landscape.

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“…This method was used for deriving the entropy asymptotics of the critical Ising model from that of the critical XY chain [29], our result generalizes this.…”

Section: The Generalized Xy -Ising Correspondencesupporting

confidence: 64%

Entanglement entropy in quantum spin chains with broken reflection symmetry

Kadar

Zimborás

2010

Phys. Rev. A

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“…In complete analogy with the result for the bipartite entanglement[53], one finds  ℓ ℓ = (2 ) 2 ( ) XX o o TI…”

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confidence: 78%

On the partial transpose of fermionic Gaussian states

2015

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We consider Gaussian states of fermionic systems and study the action of the partial transposition on the density matrix. It is shown that, with a suitable choice of basis, these states are transformed into a linear combination of two Gaussian operators that are uniquely defined in terms of the covariance matrix of the original state. In case of a reflection symmetric geometry, this result can be used to efficiently calculate a lower bound for a well-known entanglement measure, the logarithmic negativity. Furthermore, exact expressions can be derived for traces involving integer powers of the partial transpose. The method can also be applied to the quantum Ising chain and the results show perfect agreement with the predictions of conformal field theory.

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“…It was shown in [15] that the XX system with 2L sites in the subsystem and the combined TI systems with L sites have the same set of eigenvalues ε l . This holds even in the inhomogeneous case and can easily be checked numerically.…”

Section: Chain Problemmentioning

confidence: 99%

Entanglement in fermionic chains with interface defects

Eisler

Peschel

2010

Annalen der Physik

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We study the ground-state entanglement of two halves of a critical transverse Ising chain, separated by an interface defect. From the relation to a two-dimensional Ising model with a defect line we obtain an exact expression for the continuously varying effective central charge which governs the asymptotic behaviour of the entanglement entropy. The result is relevant also for other fermionic chains.

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Exact relationship between the entanglement entropies of XY and quantum Ising chains

Cited by 78 publications

References 32 publications

Entanglement entropy in quantum spin chains with broken reflection symmetry

Entanglement entropy in quantum spin chains with broken reflection symmetry

On the partial transpose of fermionic Gaussian states

Entanglement in fermionic chains with interface defects

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