Spacetime entanglement entropy in 1 + 1 dimensions

Saravani, Mehdi; Sorkin, Rafael D.; Yazdi, Yasaman K.

doi:10.1088/0264-9381/31/21/214006

Cited by 28 publications

(77 citation statements)

References 17 publications

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“…From the definitions of the associated Legendre functions we have 18 : Let C k = D k = 0 for k = 0 19 , and A qk = B qk = 0 for k = 0 20 . We can then write A qk = δ qk cosh α k , B qk = δ qk sinh α k e iβ k , and (96)-(97) become…”

Section: Discussionmentioning

confidence: 99%

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Studies on the SJ vacuum in de Sitter spacetime

Surya

Nomaan

Yazdi

2019

J. High Energ. Phys.

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In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the O(4) Fock vacuum of Allen and Folacci nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find the causal set SJ vacuum for a range of masses m ≥ 0 of the free scalar field. While our simulations are limited to a finite volume slab of global de Sitter spacetime, they show good convergence as the volume is increased. We find that the 4d causal set SJ vacuum shows a significant departure from the continuum Mottola-Allen α-vacua. Moreover, the causal set SJ vacuum is well-defined for both the minimally coupled massless m = 0 and the conformally coupled massless m = m c cases. This is at odds with earlier work on the continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum is ill-defined for these masses. Our results hint at an important tension between the discrete and continuum behaviour of the SJ vacuum in de Sitter and suggest that the former cannot in general be identified with the Mottola-Allen α-vacua even for m > 0.

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Section: Discussionmentioning

confidence: 99%

“…Dimensional analysis tells us what are the right quantities to compare. 19 Justification for C k = D k = 0 when k = 0:…”

Section: Appendix A: De Sitter Spacetimementioning

confidence: 99%

Studies on the SJ vacuum in de Sitter spacetime

Surya

Nomaan

Yazdi

2019

J. High Energ. Phys.

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“…To this end we need to know the von Neumann entropy of an arbitrary Gaussian density matrix, which can be expressed in terms of the correlators (8). This relation has been addressed in detail in [55], and more recently in [39,[56][57][58], where it was demonstrated that the von Neumann entropy of a Gaussian density matrix can be expressed in terms of the so-called symplectic eigenvalues of the block matrix…”

Section: A Bosonic Matrix Modelmentioning

confidence: 99%

Quantum chaos, thermalization, and entanglement generation in real-time simulations of the Banks-Fischler-Shenker-Susskind matrix model

2019

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We study numerically the onset of chaos and thermalization in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model with and without fermions, considering Lyapunov exponents, entanglement generation, and quasinormal ringing. We approximate the real-time dynamics in terms of the most general Gaussian density matrices with parameters which obey self-consistent equations of motion, thus extending the applicability of real-time simulations beyond the classical limit. Initial values of these Gaussian density matrices are optimized to be as close as possible to the thermal equilibrium state of the system. Thus attempting to bridge between the low-energy regime with a calculable holographic description and the classical regime at high energies, we find that quantum corrections to classical dynamics tend to decrease the Lyapunov exponents, which is essential for consistency with the Maldacena-Shenker-Stanford (MSS) bound at low temperatures. The entanglement entropy is found to exhibit an expected "scrambling" behavior -rapid initial growth followed by saturation. At least at high temperatures the entanglement saturation time appears to be governed by classical Lyapunov exponents. Decay of quasinormal modes is found to be characterized by the shortest time scale of all. We also find that while the bosonic matrix model becomes nonchaotic in the low-temperature regime, for the full BFSS model with fermions the leading Lyapunov exponent, entanglement saturation time, and decay rate of quasinormal modes all remain finite and non-zero down to the lowest temperatures.

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“…Indeed, numerical simulations [17] strongly suggest that in these two cases the entanglement entropy will diverge in the absence of some sort of infrared regulator (the divergence being logarithmic in the regulator). In the analysis above, we have implicitly imposed such a regulator, for example Dirichlet conditions at one end of the spatial interval [0, L], or as in [18] the choice of "Sorkin-Johnston-vacuum" in some large "causal diamond" containing [0, L]. )…”

Section: Reasons For the Area Law And Departures From Itmentioning

confidence: 99%

“…For the purposes of condensed matter, this is not a problem, of course, but in the context of relativistic quantum field theory, or of black hole entropy, a more four-dimensional treatment would be desirable. Such a method was introduced in [20] and illustrated in [18] by a 1 + 1 dimensional calculation of entanglement entropy. Taking this as a point of reference, it would be interesting to ask whether the intuitive explanations offered above could also be cast into spatio-temporal form.…”

Section: Reasons For the Area Law And Departures From Itmentioning

confidence: 99%