Distance between Quantum States and Gauge-Gravity Duality

Miyaji, Masamichi; Numasawa, Tokiro; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento

doi:10.1103/physrevlett.115.261602

Cited by 183 publications

(318 citation statements)

References 25 publications

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“…In fact we recover the same leading behavior as the case of a CFT living in flat space [1,5,6]. What makes the configuration of the cylinder more interesting is the existence of a physical universal contribution.…”

Section: Jhep09(2017)086supporting

confidence: 58%

“…We will use the same formalism and arguments used in [1]. In particular we focus on the quantum information metric for a CFT ground state deformed by a scalar primary operator.…”

Section: Jhep09(2017)086mentioning

confidence: 99%

“…Prime examples of the correspondence [1,[5][6][7] involve a d dimensional CFT perturbed by a scalar primary operator of dimension ∆ and its gravity dual described by the d+1 dimensional Euclidean Janus geometry [8,9]. The overlap | Ψ(λ + δλ)|Ψ(λ) | and the corresponding quantum information metric can be realized by a path integral of the CFT on R × M d−1 (M d−1 being the spatial manifold where the CFT lives) with an operator O turned on whose coupling jumps from λ to λ+δλ though the interface at τ = 0 where τ is the Euclidean time coordinate ranged from [−∞, ∞].…”

Section: Jhep09(2017)086mentioning

confidence: 99%

“…1 One can now perform an expansion of | Ψ 1 |Ψ 0 | for small δλ. The regularized quantum information metric is defined as minus the coefficient of the δλ 2 term…”

Section: Jhep09(2017)086mentioning

confidence: 99%

“…It has been proposed [1] that, based on the AdS/CFT correspondence [2], the quantum information metric may serve as a new tool to probe the bulk gravity. This proposed correspondence requires an interesting new dictionary, which may shed a new light on the issue of bulk decoding from the view point of field theories.…”

Section: Introductionmentioning

confidence: 99%

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Quantum information metric on ℝ × S d − 1

Bak

Trivella²

2017

J. High Energ. Phys.

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We present a formula for the information metric on R × S d−1 for a scalar primary operator of integral dimension ∆ ( > d+12 ). This formula is checked for various space-time dimensions d and ∆ in the field theory side. We check the formula in the gravity side using the holographic setup. We clarify the regularization and renormalization involved in these computations. We also show that the quantum information metric of an exactly marginal operator agrees with the leading order of the interface free energy of the conformal Janus on Euclidean S d , which is checked for d = 2, 3.

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Section: Jhep09(2017)086supporting

confidence: 58%

“…We will use the same formalism and arguments used in [1]. In particular we focus on the quantum information metric for a CFT ground state deformed by a scalar primary operator.…”

Section: Jhep09(2017)086mentioning

confidence: 99%

Section: Jhep09(2017)086mentioning

confidence: 99%

“…1 One can now perform an expansion of | Ψ 1 |Ψ 0 | for small δλ. The regularized quantum information metric is defined as minus the coefficient of the δλ 2 term…”

Section: Jhep09(2017)086mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum information metric on ℝ × S d − 1

Bak

Trivella²

2017

J. High Energ. Phys.

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Geometry of the Parameter Space of a Quantum System: Classical Point of View

Alvarez‐Jimenez¹,

González²,

Gutiérrez‐Ruiz³

et al. 2019

Annalen der Physik

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The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed matter physics. Classical integrable systems are considered and a new approach is reported to obtain the classical analogs of the quantum metric tensor and the Berry curvature. An advantage of this approach is that it can be applied to a wide variety of classical systems corresponding to quantum systems with bosonic and fermionic degrees of freedom. The approach used arises from the semiclassical approximation of the Berry curvature and the quantum metric tensor in the Lagrangian formalism. This semiclassical approximation is exploited to establish, for the first time, the relation between the quantum metric tensor and its classical counterpart. The approach described is illustrated and validated by applying it to five systems: the generalized harmonic oscillator, the symmetric and linearly coupled harmonic oscillators, the singular Euclidean oscillator, and a spin‐half particle in a magnetic field. Finally, some potential applications of this approach and possible generalizations that can be of interest in the field of condensed matter physics are mentioned.

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Topological Complexity in AdS₃/CFT₂

Abt

Erdmenger

Hinrichsen

et al. 2018

Fortschritte der Physik

106

123

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We consider subregion complexity within the AdS3/CFT2 correspondence. We rewrite the volume proposal, according to which the complexity of a reduced density matrix is given by the spacetime volume contained inside the associated Ryu‐Takayanagi (RT) surface, in terms of an integral over the curvature. Using the Gauss‐Bonnet theorem we evaluate this quantity for general entangling regions and temperature. In particular, we find that the discontinuity that occurs under a change in the RT surface is given by a fixed topological contribution, independent of the temperature or details of the entangling region. We offer a definition and interpretation of subregion complexity in the context of tensor networks, and show numerically that it reproduces the qualitative features of the holographic computation in the case of a random tensor network using its relation to the Ising model. Finally, we give a prescription for computing subregion complexity directly in CFT using the kinematic space formalism, and use it to reproduce some of our explicit gravity results obtained at zero temperature. We thus obtain a concrete matching of results for subregion complexity between the gravity and tensor network approaches, as well as a CFT prescription.

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Distance between Quantum States and Gauge-Gravity Duality

Cited by 183 publications

References 25 publications

Quantum information metric on ℝ × S d − 1

Quantum information metric on ℝ × S d − 1

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Topological Complexity in AdS₃/CFT₂

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Distance between Quantum States and Gauge-Gravity Duality

Cited by 183 publications

References 25 publications

Quantum information metric on ℝ × S d − 1

Quantum information metric on ℝ × S d − 1

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Topological Complexity in AdS3/CFT2

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Product

Resources

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Topological Complexity in AdS₃/CFT₂