Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model

MacCormack, Ian; Liu, Aike; Ryu, Shinsei

doi:10.1088/1751-8121/ab3944

Cited by 38 publications

(33 citation statements)

References 58 publications

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“…Indeed the functional form of the stress tensor (5.19), as seen from the gravity perspective and Banados geometries matches the interpretation of a stress tensor computed in a CFT on a specific foliation of the bulk (i.e. the curvilinear cutoff advocated in [47]). Moreover, the appearance of the local temperature and explicit position dependence (5.20) further supports this fact in our example.…”

Section: Jhep01(2021)027supporting

confidence: 56%

“…2 Despite its many nontrivial features, one can compute many quantities in the SSD model (and other inhomogeneous CFTs) rather easily, owing to the transformation properties of CFTs. One can use the transformation properties of holographic CFTs, for example, to compute the finite temperature entanglement entropy of an arbitrary interval [x 1 , x 2 ] in an SSD deformed CFT on an interval L [47]:…”

Section: Jhep01(2021)027mentioning

confidence: 99%

“…Let us now elaborate on entanglement entropy, which can be derived universally for a class of 2d inhomogeneous CFTs [47]. As we discussed before, the inhomogeneous deformations of CFTs that we consider are defined by the background metric…”

Section: Entanglement Energy and Kinematic Spacementioning

confidence: 99%

“…In the dual gravitational picture, the inhomogeneous CFTs can be thought to live on appropriately curved foliations of the bulk AdS 3 space [47]. Entanglement entropy in the curved space CFTs can then be computed with the Ryu-Takayanagi procedure [2] using position-dependent cutoffs determined by the foliation.…”

Section: Jhep01(2021)027mentioning

confidence: 99%

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Geometry and complexity of path integrals in inhomogeneous CFTs

Caputa

MacCormack

2021

J. High Energ. Phys.

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In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting up and solving the general optimization problem, we study specific examples, including the Möbius, SSD and Rainbow deformed CFTs, and analyze path integral geometries and complexity for universal classes of states in these models. We find that metrics for optimal path integrals coincide with particular slices of AdS3 geometries, on which Einstein’s equations are equivalent to the condition for minimal path integral complexity. We also find that while leading divergences of path integral complexity remain unchanged, constant contributions are modified in a universal, position dependent manner. Moreover, we analyze entanglement entropies in inhomogeneous CFTs and show that they satisfy Hill’s equations, which can be used to extract the energy density consistent with the first law of entanglement. Our findings not only support comparisons between slices of bulk spacetimes and circuits of path integrations, but also demonstrate that path integral geometries and complexity serve as a powerful tool for understanding the interesting physics of inhomogeneous systems.

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Section: Jhep01(2021)027supporting

confidence: 56%

Section: Jhep01(2021)027mentioning

confidence: 99%

Section: Entanglement Energy and Kinematic Spacementioning

confidence: 99%

Section: Jhep01(2021)027mentioning

confidence: 99%

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Geometry and complexity of path integrals in inhomogeneous CFTs

Caputa

MacCormack

2021

J. High Energ. Phys.

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“…In order to make analytical progress, we compensate for the lack of time and space translation symmetry by allowing ourselves access to the infinitely generated conformal symmetry group. Concretely, we study a driven conformal field theory (CFT), where the time-evolution operator alternates between a uniform (1 + 1)-dimensional CFT and one of its nonhomogeneous versions known as sine-square deformation (SSD) [17][18][19][20][21][22], first introduced in the context of lattice systems as an efficient way to suppress boundary effects [23][24][25][26][27][28]. This setup has been previously studied with a periodic Floquet drive, where it displays a rich phase diagram with both heating and nonheating phases [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Fine structure of heating in a quasiperiodically driven critical quantum system

Lapierre

Choo

Tiwari

et al. 2020

Phys. Rev. Research

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We study the heating dynamics of a generic one-dimensional critical system when driven quasiperiodically. Specifically, we consider a Fibonacci drive sequence comprising the Hamiltonian of uniform conformal field theory (CFT) describing such critical systems and its sine-square deformed counterpart. The asymptotic dynamics is dictated by the Lyapunov exponent which has a fractal structure embedding Cantor lines where the exponent is exactly zero. Away from these Cantor lines, the system typically heats up fast to infinite energy in a nonergodic manner where the quasiparticle excitations congregate at a small number of select spatial locations resulting in a buildup of energy at these points. Periodic dynamics with no heating for physically relevant timescales is seen in the high-frequency regime. As we traverse the fractal region and approach the Cantor lines, the heating slows enormously and the quasiparticles completely delocalize at stroboscopic times. Our setup allows us to tune between fast and ultraslow heating regimes in integrable systems.

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Rényi divergences from Euclidean quenches

Chowdhury

Datta

David

2020

J. High Energ. Phys.

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We study the generalisation of relative entropy, the Rényi divergence D α (ρ||ρ β ) in 2d CFTs between an excited state density matrix ρ, created by deforming the Hamiltonian, and the thermal density matrix ρ β . Using the path integral representation of this quantity as a Euclidean quench, we obtain the leading contribution to the Rényi divergence for deformations by scalar primaries and by conserved holomorphic currents in conformal perturbation theory. Furthermore, we calculate the leading contribution to the Rényi divergence when the conserved current perturbations have inhomogeneous spatial profiles which are versions of the sine-square deformation (SSD). The dependence on the Rényi parameter (α) of the leading contribution have a universal form for these inhomogeneous deformations and it is identical to that seen in the Rényi divergence of the simple harmonic oscillator perturbed by a linear potential. Our study of these Rényi divergences shows that the family of second laws of thermodynamics, which are equivalent to the monotonicity of Rényi divergences, do indeed provide stronger constraints for allowed transitions compared to the traditional second law.

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Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model

Cited by 38 publications

References 58 publications

Geometry and complexity of path integrals in inhomogeneous CFTs

Geometry and complexity of path integrals in inhomogeneous CFTs

Fine structure of heating in a quasiperiodically driven critical quantum system

Rényi divergences from Euclidean quenches

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