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120
Holographic duality with a view toward many-body physics
, 2009
"... These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided ..."
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Cited by 150 (2 self)
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These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.
Entanglement entropy and conformal field theory
, 2009
"... We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint ..."
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Cited by 92 (11 self)
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We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of non-equilibrium situations, are also considered.
Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches
, 2011
"... We study the evolution and scaling of the entanglement entropy after two types of quenches for a 2+1 field theory, using a conjectured holographic technique for its computation. We study a thermal quench, dual to the addition of a shell of uncharged matter to four dimensional Anti–de Sitter (AdS4) s ..."
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Cited by 45 (1 self)
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We study the evolution and scaling of the entanglement entropy after two types of quenches for a 2+1 field theory, using a conjectured holographic technique for its computation. We study a thermal quench, dual to the addition of a shell of uncharged matter to four dimensional Anti–de Sitter (AdS4) spacetime, and study the subsequent formation of a Schwarzschild black hole. We also study an electromagnetic quench, dual to the addition of a shell of charged sources to AdS4, following the subsequent formation of an extremal dyonic black hole. In these backgrounds we consider the entanglement entropy of two types of geometries, the infinite strip and the round disc, and find distinct behavior for each. Some of our findings naturally supply results analogous to observations made in the literature for lower dimensions, but we also uncover several new phenomena, such as (in some cases) a discontinuity in the time derivative of the entanglement entropy as it nears saturation, and for the electromagnetic quench, a logarithmic growth in the entanglement entropy with time for both the disc and strip, before settling to saturation. We briefly discuss the possible origin of the new phenomena in terms of the features of the conjectured dual field theory.
Spectral weight in holographic scaling geometries
, 2012
"... We compute the low energy spectral density of transverse currents in theories with holographic duals that exhibit an emergent scaling symmetry characterized by dynam-ical critical exponent z and hyperscaling violation exponent θ. For any finite z and θ, the low energy spectral density is exponential ..."
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Cited by 39 (6 self)
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We compute the low energy spectral density of transverse currents in theories with holographic duals that exhibit an emergent scaling symmetry characterized by dynam-ical critical exponent z and hyperscaling violation exponent θ. For any finite z and θ, the low energy spectral density is exponentially small at nonzero momentum. This indicates that any nonzero momentum low energy excitations of putative hidden Fermi surfaces are not visible in the classical bulk limit. We furthermore show that if the limit z → ∞ is taken with the ratio η = −θ/z> 0 held fixed, then the resulting theory is locally quantum critical with an entropy density that vanishes at low temperatures as s ∼ T η. In these cases the low energy spectral weight at nonzero momentum is not exponentially suppressed, possibly indicating a more fermionic nature of these theories.
Quantum corrections to holographic entanglement entropy, JHEP 1311
, 2013
"... We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop cor-rection to this formula. The minimal surface divides t ..."
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Cited by 33 (2 self)
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We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop cor-rection to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.ar X iv
Holographic entanglement beyond classical gravity,” arXiv:1306.4682 [hep-th
"... The Rényi entropies and entanglement entropy of 1+1 CFTs with gravity duals can be computed by explicit construction of the bulk spacetimes dual to branched covers of the boundary geometry. At the classical level in the bulk this has recently been shown to reproduce the conjectured Ryu-Takayanagi f ..."
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Cited by 26 (3 self)
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The Rényi entropies and entanglement entropy of 1+1 CFTs with gravity duals can be computed by explicit construction of the bulk spacetimes dual to branched covers of the boundary geometry. At the classical level in the bulk this has recently been shown to reproduce the conjectured Ryu-Takayanagi formula for the holographic entanglement entropy. We study the one-loop bulk corrections to this formula. The functional determinants in the bulk geometries are given by a sum over certain words of generators of the Schottky group of the branched cover. For the case of two disjoint intervals on a line we obtain analytic answers for the one-loop entanglement entropy in an expansion in small cross-ratio. These reproduce and go beyond anticipated universal terms that are not visible classically in the bulk. We also consider the case of a single interval on a circle at finite temperature. At high temperatures we show that the one-loop contributions introduce expected finite size corrections to the entanglement entropy that are not present classically. At low temperatures, the one-loop corrections capture the mixed nature of the density matrix, also not visible classically below the Hawking-Page temperature.ar
