Entanglement, replicas, and Thetas

Mukhi, Sunil; Murthy, Sameer; Wu, Jie-qiang

doi:10.1007/jhep01(2018)005

Cited by 16 publications

(43 citation statements)

References 37 publications

(137 reference statements)

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“…Restricting to replica surfaces, it is possible to write a more explicit form for the replica partition function in which the spin-structure-independent prefactor C is made precise. The result, as derived in [11], is:…”

Section: Twist Fields and The Conjecturementioning

confidence: 96%

“…1 For the odd Jacobi theta function we will often use the standard notation θ1(z|τ ) = −θ More details, including original references, can be found in [11].…”

Section: Rényi Entropy Computations and The Conjectured θ − θ Relationmentioning

confidence: 99%

“…In this note, we address all three points above. After a brief review of the results of [11], we argue that the twist-field prescription cannot be used for non-diagonal spin structures, for the simple reason that replica symmetry does not hold in this situation. Next we provide a rigorous proof of the conjectured identity of [11] for the case n = 2 (corresponding to the second Rényi).…”

Section: Introductionmentioning

confidence: 98%

“…After a brief review of the results of [11], we argue that the twist-field prescription cannot be used for non-diagonal spin structures, for the simple reason that replica symmetry does not hold in this situation. Next we provide a rigorous proof of the conjectured identity of [11] for the case n = 2 (corresponding to the second Rényi). In fact this identity is equivalent to a mathematical result of Fay [12] on doubly-branched covers, for which we also provide an elementary proof which relies on information about the zeros of the θ-functions that appear in the identity.…”

Section: Introductionmentioning

confidence: 98%

“…The plan of the paper is as follows. In Section 2 we start by reviewing the conjecture of [11] for what we call "diagonal" spin structures, and then go on to argue that analogous relations do not exist for non-diagonal spin structures. In Section 3 we give a proof of the Θ -θ identity for n = 2 using a result of Fay.…”

Section: Introductionmentioning

confidence: 99%

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Fermions on replica geometries and the $\Theta$ - $\theta$ relation

Mukhi

Murthy

2019

Communications in Number Theory and Physics

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In arXiv:1706:09426 we conjectured and provided evidence for an identity between Siegel Θ-constants for special Riemann surfaces of genus n and products of Jacobi θ-functions. This arises by comparing two different ways of computing the n th Rényi entropy of free fermions at finite temperature. Here we show that for n = 2 the identity is a consequence of an old result due to Fay for doubly branched Riemann surfaces. For n > 2 we provide a detailed matching of certain zeros on both sides of the identity. This amounts to an elementary proof of the identity for n = 2, while for n ≥ 3 it gives new evidence for it. We explain why the existence of additional zeros renders the general proof difficult.

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Section: Twist Fields and The Conjecturementioning

confidence: 96%

“…1 For the odd Jacobi theta function we will often use the standard notation θ1(z|τ ) = −θ More details, including original references, can be found in [11].…”

Section: Rényi Entropy Computations and The Conjectured θ − θ Relationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Fermions on replica geometries and the $\Theta$ - $\theta$ relation

Mukhi

Murthy

2019

Communications in Number Theory and Physics

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Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium

Marić,

Bocini,

Fagotti

2024

J. High Energ. Phys.

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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.

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Monodromy methods for torus conformal blocks and entanglement entropy at large central charge

Gerbershagen

2021

J. High Energ. Phys.

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We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick. We first generalize the known monodromy method for the calculation of conformal blocks on the plane to the torus. Then, we derive a monodromy method for the zero-point conformal blocks of the replica partition function. We explain the differences between the two monodromy methods before applying them to the calculation of the entanglement entropy. We find that the contribution of the vacuum exchange dominates the entanglement entropy for a large class of CFTs, leading to universal results in agreement with holographic predictions from the RT formula. Moreover, we determine in which regime the replica partition function agrees with a correlation function of local twist operators on the torus.

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Entanglement, replicas, and Thetas

Cited by 16 publications

References 37 publications

Fermions on replica geometries and the $\Theta$ - $\theta$ relation

Fermions on replica geometries and the $\Theta$ - $\theta$ relation

Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium

Monodromy methods for torus conformal blocks and entanglement entropy at large central charge

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