Instantons and entanglement entropy

Bhattacharyya, Arpan; Hung, Ling-Yan; Melby-Thompson, Charles M.

doi:10.1007/jhep10(2017)081

Cited by 9 publications

(14 citation statements)

References 27 publications

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“…In fact, it is a famous observation in quantum quenches in 1 + 1 d CFT that linear terms do contribute [64], dictated by the so-called "light-cone" effect at early times. We note, however, that this result is highly reminiscent of our field theoretic result in [59], except that linear t terms beginning with single instanton contributions appear there.…”

Section: Setupsupporting

confidence: 69%

“…We will make more detailed comparison with a field theoretic instanton calculation in our other publication [59]. Let us note however that the exponentially-suppressed factors play exactly the same role as instantons and that at small t, the time dependence starts at t 2 ∆E 2 ∼ t 2 exp(−4α).…”

Section: Setupmentioning

confidence: 95%

“…For φ 4 theories, it is natural to work with bosonic excitations around different minima, each of them corresponds to a superconducting condensate [57,58]. Using this method, one could explicitly see that the area law is expected to be preserved, even with instanton corrections, as also observed using direct field theoretic computation employing the replica trick [59].…”

Section: Introductionmentioning

confidence: 92%

“…We will now investigate the situation where the potential has multiple minima, and so, there is tunneling between two square wells through a potential wall with a finite width. The exponential tail in the wavefunction is precisely equivalent to what we call the action of instantons, which we will discuss in closer detail in [59] to make a detailed comparison with the corresponding field theoretic studies. Here, we want to investigate the entropy dependence on the width of the wall and justify the approximations taken in the previous sections, up to this small exponentially suppressed correction.…”

Section: Tunneling and Entanglement Entropymentioning

confidence: 99%

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Inspecting Non-Perturbative Contributions to the Entanglement Entropy via Wavefunctions

Bhattacharyya

Hung

Lau

et al. 2017

Entropy

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Abstract:In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with a toy model of multiple particles whose interaction potential admits multiple minima. We study the entanglement of the true ground state after taking the tunneling effects into account and find some simple patterns. Notably, in the case of multiple particle interactions, entanglement entropy generically decreases with increasing number of minima. The knowledge of the subsystem actually increases with the number of minima. The reduced density matrix can also be seen to have close connections with graph spectra. In a more careful study of the two-well tunneling system, we also extract the exponentially-suppressed tail contribution, the analogue of instantons. To understand the effects of multiple minima in a field theory, we are inspired to inspect wavefunctions in a toy model of a bosonic field describing quasi-particles of two different condensates related by Bogoliubov transformations. We find that the area law is naturally preserved. This is probably a useful set of perspectives that promise wider applications.

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Section: Setupsupporting

confidence: 69%

Section: Setupmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 92%

Section: Tunneling and Entanglement Entropymentioning

confidence: 99%

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Inspecting Non-Perturbative Contributions to the Entanglement Entropy via Wavefunctions

Bhattacharyya

Hung

Lau

et al. 2017

Entropy

Self Cite

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“…Given that the locality of the network and covariance of space-time begs for the use of perfect tensors in the complete space-time network, a coherent picture of gravity, and perhaps black holes in particular being fast scramblers might emerge for free via the tensor network construction. Such construction is currently underway, and we will report them elsewhere [50].…”

Section: Jhep08(2016)086mentioning

confidence: 99%

Exploring the tensor networks/AdS correspondence

Bhattacharyya

Gao

Hung

et al. 2016

J. High Energ. Phys.

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In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

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Supersymmetry breaking, brane dynamics and Swampland conjectures

Basile

2021

J. High Energ. Phys.

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We investigate interactions between branes of various dimensions, both charged and uncharged, in three non-supersymmetric string models. These include the USp(32) and U(32) orientifold projections of the type IIB and type 0B strings, as well as the SO(16)×SO(16) projection of the exceptional heterotic string. The resulting ten-dimensional spectra are free of tachyons, and the combinations of branes that they contain give rise to rich and varied dynamics. We compute static potentials for parallel stacks of branes in three complementary regimes: the probe regime, in which one of the two stacks is parametrically heavier than the other, the string-amplitude regime, in which both stacks are light, and the holographic regime. Whenever comparisons are possible, we find qualitative agreement despite the absence of supersymmetry. For charged branes, our analysis reveals that the Weak Gravity Conjecture is satisfied in a novel way via a renormalization of the effective charge-to-tension ratio.

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Instantons and entanglement entropy

Cited by 9 publications

References 27 publications

Inspecting Non-Perturbative Contributions to the Entanglement Entropy via Wavefunctions

Inspecting Non-Perturbative Contributions to the Entanglement Entropy via Wavefunctions

Exploring the tensor networks/AdS correspondence

Supersymmetry breaking, brane dynamics and Swampland conjectures

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