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425
Gravity duals for nonrelativistic CFTs
 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE
"... We attempt to generalize the AdS/CFT correspondence to nonrelativistic conformal field theories which are invariant under a Galilean conformal group. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and more generally, a family of universality classes of quantu ..."
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Cited by 120 (2 self)
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We attempt to generalize the AdS/CFT correspondence to nonrelativistic conformal field theories which are invariant under a Galilean conformal group. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust. We develop the holographic dictionary and compute some twopoint correlators. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions. April
Towards strange metallic holography
"... We initiate a holographic model building approach to ‘strange metallic ’ phenomenology. Our model couples a neutral Lifshitzinvariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by Dbranes. In the physical ..."
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Cited by 116 (18 self)
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We initiate a holographic model building approach to ‘strange metallic ’ phenomenology. Our model couples a neutral Lifshitzinvariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by Dbranes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent z appropriately we can match the nonFermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group flow in Lifshitz theories, such as the appearance of relevant chargecharge interactions when z ≥ 2. We outline a program to extend this model building approach to other anomalous observables of
Membranes at Quantum Criticality
, 2009
"... We propose a quantum theory of membranes designed such that the groundstate wavefunction of the membrane with compact spatial topology Σh reproduces the partition function of the bosonic string on worldsheet Σh. The construction involves worldvolume matter at quantum criticality, described in the ..."
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Cited by 107 (0 self)
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We propose a quantum theory of membranes designed such that the groundstate wavefunction of the membrane with compact spatial topology Σh reproduces the partition function of the bosonic string on worldsheet Σh. The construction involves worldvolume matter at quantum criticality, described in the simplest case by Lifshitz scalars with dynamical critical exponent z = 2. This matter system must be coupled to a novel theory of worldvolume gravity, also exhibiting quantum criticality with z = 2. We first construct such a nonrelativistic “gravity at a Lifshitz point ” with z = 2 in D + 1 spacetime dimensions, and then specialize to the critical case of D = 2 suitable for the membrane worldvolume. We also show that in the secondquantized framework, the string partition function is reproduced if the spacetime ground state takes the form of a BoseEinstein condensate of membranes in
Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
, 2009
"... We extend the definition of “spectral dimension ” (usually defined for fractal and lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that in quantum gravity dominated by a Lifshitz point with dynamical critical exponent z in D+1 spacetime dimensions, the spectr ..."
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Cited by 81 (0 self)
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We extend the definition of “spectral dimension ” (usually defined for fractal and lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that in quantum gravity dominated by a Lifshitz point with dynamical critical exponent z in D+1 spacetime dimensions, the spectral dimension of spacetime is equal to ds = 1 + D z. In the case of gravity in 3 + 1 dimensions presented in arXiv:0901.3775, which is dominated by z = 3 in the UV and flows to z = 1 in the IR, the spectral dimension of spacetime flows from ds = 4 at large scales, to ds = 2 at short distances. Remarkably, this is the qualitative behavior of ds found numerically by Ambjørn, Jurkiewicz and Loll in their causal dynamical
Gravity duals of Lifshitzlike fixed points
"... We find candidate macroscopic gravity duals for scaleinvariant but nonLorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute twopoint correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormal ..."
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Cited by 78 (0 self)
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We find candidate macroscopic gravity duals for scaleinvariant but nonLorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute twopoint correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t → λzt, x → λx; we focus on the case with z = 2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.
Evolution of Entanglement Entropy in OneDimensional Systems
, 2005
"... We study the unitary time evolution of the entropy of entanglement of a onedimensional system between the degrees of freedom in an interval of length ℓ and its complement, starting from a pure state which is not an eigenstate of the hamiltonian. We use path integral methods of quantum field theory ..."
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Cited by 65 (3 self)
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We study the unitary time evolution of the entropy of entanglement of a onedimensional system between the degrees of freedom in an interval of length ℓ and its complement, starting from a pure state which is not an eigenstate of the hamiltonian. We use path integral methods of quantum field theory as well as explicit computations for the transverse Ising spin chain. In both cases, there is a maximum speed v of propagation of signals. In general the entanglement entropy increases linearly with time t up to t = ℓ/2v, after which it saturates at a value proportional to ℓ, the coefficient depending on the initial state. This behavior may be understood as a consequence of causality. Address for correspondence 1 I.
Quantum Criticality and YangMills Gauge Theory
, 2008
"... We present a family of nonrelativistic YangMills gauge theories in D +1 dimensions whose freefield limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z = 2. The ground state wavefunction is intimately related to the partition function of relativistic ..."
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Cited by 58 (0 self)
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We present a family of nonrelativistic YangMills gauge theories in D +1 dimensions whose freefield limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z = 2. The ground state wavefunction is intimately related to the partition function of relativistic YangMills in D dimensions. The gauge couplings exhibit logarithmic scaling and asymptotic freedom in the upper critical spacetime dimension, equal to 4 + 1. The theories can be deformed in the infrared by a relevant operator that restores Poincaré invariance as an accidental symmetry. In the largeN limit, our nonrelativistic gauge
Quantum Gravity at a Lifshitz Point
, 2009
"... We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z = 3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is ..."
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Cited by 53 (0 self)
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We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z = 3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is powercounting renormalizable in 3 + 1 dimensions. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory flows naturally to the relativistic value z = 1, and could therefore serve as a possible candidate for a UV completion of Einstein’s general relativity or an infrared modification thereof. The effective speed of light, the Newton constant and the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic
Entanglement in manybody systems
 quantph/0703044, 2007. in the quantum Ising model 43
"... The recent interest in aspects common to quantum information and condensed matter has prompted a flory of activity at the border of these disciplines that were far distant untill few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, ..."
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Cited by 44 (1 self)
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The recent interest in aspects common to quantum information and condensed matter has prompted a flory of activity at the border of these disciplines that were far distant untill few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in manybody systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermion and boson model systems. Both bipartite and multipartite entanglement will be considered. In equilibrium we show how entanglement is tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of manybody Hamiltonians. Contents