Lifshitz holography

Taylor, Marika

doi:10.1088/0264-9381/33/3/033001

Cited by 167 publications

(205 citation statements)

References 245 publications

(545 reference statements)

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“…It will be intersting to consider possible differences with Lifshitz holography [75] as the anomalies found in this work differ from those of Lifshitz backgrounds. We also know that the low energy effective action for Quantum Hall systems involves the Schrödinger field coupled to, in general, a background gravitational field in d + 1 dimensions; where d = 2n.…”

Section: Discussionmentioning

confidence: 96%

Gravitational anomalies on the Newton-Cartan background

Fernandes

Mitra

2017

Phys. Rev. D

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We derive the trace and diffeomorphism anomalies of the Schrödinger field minimally coupled to the Newton-Cartan background using Fujikawa's path integral approach. This approach in particular enables us to calculate the one-loop contributions due to all the fields of the NewtonCartan structure. We determine the coefficients and demonstrate that gravitational anomalies for this theory always arise in odd dimensions. Due to the gauge field contribution of the background we find that in 2 + 1 dimensions the trace anomaly contains terms which have a form similar to that of the 1 + 1 and 3 + 1 dimensional relativistic trace anomalies. This result reveals that the Newton-Cartan background which satisfies the Frobenius condition possesses a Type A trace anomaly in contrast with the result of Lishitz spacetimes. As an application we demonstrate that the coefficient of the term similar to the 1 + 1 dimensional relativistic trace anomaly satisfies a c-theorem condition.

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Section: Discussionmentioning

confidence: 96%

Gravitational anomalies on the Newton-Cartan background

Fernandes

Mitra

2017

Phys. Rev. D

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“…It would be very interesting to perform a similar analysis in different Lifshitz models (see, e.g., Ref. [32]) to see if this is a common feature to all.…”

Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 97%

Holographic Equilibration of Nonrelativistic Plasmas

et al. 2016

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We study far-from-equilibrium physics of strongly interacting plasmas at criticality and zero charge density for a wide range of dynamical scaling exponents z in d dimensions using holographic methods. In particular, we consider homogeneous isotropization of asymptotically Lifshitz black branes with full backreaction. We find stable evolution and equilibration times that exhibit small dependence of z and are of the order of the inverse temperature. Performing a quasinormal mode analysis, we find a corresponding narrow range of relaxation times, fully characterized by the fraction z=ðd − 1Þ. For z ≥ d − 1, equilibration is overdamped, whereas for z < d − 1, we find oscillatory behavior. Finally, and most interestingly, we observe that also the nonlinear evolution, although differing significantly from a quasinormal mode fit, is to a high degree of precision characterized by the fraction z=ðd − 1Þ. Introduction.-Quantum criticality has been a focus of interest both in theoretical and experimental physics over the past few decades. It is believed to be a key ingredient in the solution to the various yet unsolved problems such as the high T c superconductivity [1]. In particular, the dynamics of a system near a continuous quantum phase transition is governed by a universal, scale invariant theory characterized by the dimensionality d, the dynamical scaling exponent z, and the various other critical exponents that are independent of the microscopic Hamiltonian of the system. In these systems, the characteristic energy scale Δ, such as the gap separating the first excited state from the ground state, vanishes as the correlation length ξ diverges as Δ ∼ ξ −z . For instance, z ¼ 1 occurs at the touching points of the band structure of monolayer graphene, z ¼ 2 can describe the case of bilayer graphene, and z ¼ 2, 3 occur in heavy fermion systems; see, e.g., Refs. [2][3][4][5][6].The existence of a quantum critical point at vanishing temperature determines the behavior of observables also at finite temperature, and even beyond the thermal equilibrium, in the so-called quantum critical region of the parameter space. In fact, a basic way to characterize this quantum critical region is to consider the response of the system to a small disturbance, determined by the equilibration time τ eq [7]. The quantum critical region corresponds to short relaxation times τ eq ∼ 1=T [8], whereas local equilibrium is reached much more slowly as τ eq ≫ 1=T outside the quantum critical region [1].In this Letter, we want to go one step further and ask the question, what happens when such a quantum critical system is taken completely out of equilibrium, when the perturbation is not small, but of the same order as the Hamiltonian? We answer this question partially in the particular situation when the collective excitations of the system are characterized by global, hydrodynamic

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“…[24][25][26][27]. 2 We would like to thank Tadashi Takayanagi for bringing our attention to these references during the final steps of this work.…”

Section: Jhep07(2017)120mentioning

confidence: 99%

Entanglement in Lifshitz-type quantum field theories

Mozaffar

Mollabashi

2017

J. High Energ. Phys.

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Abstract:We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz free scalar theory. We present simple intuitive arguments based on "non-local" effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the z → ∞ limit. We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior. In (2 + 1)-dimensions we also study some shape dependent aspects of entanglement. We argue that in the massless limit corner contributions are no more additive for large enough dynamical exponent due to non-local effects of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.

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Lifshitz holography

Cited by 167 publications

References 245 publications

Gravitational anomalies on the Newton-Cartan background

Gravitational anomalies on the Newton-Cartan background

Holographic Equilibration of Nonrelativistic Plasmas

Entanglement in Lifshitz-type quantum field theories

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