Triviality of entanglement entropy in the Galilean vacuum

Hason, Itamar

doi:10.1016/j.physletb.2018.02.064

Cited by 7 publications

(8 citation statements)

References 33 publications

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“…A vanish when η → 0. This is expected from (2.35), as emphasised in [43,68]; hence the limit k F → 0 and the evaluation of S (α) A commute. We find it worth anticipating that the leading term of the large η expansion for the entanglement entropy is S (α) (8.14) and (8.16)), in agreement with the one dimensional case of the general result found in [27], obtained for fixed k F and R → ∞.…”

Section: Indicate That S (α)mentioning

confidence: 63%

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Entanglement entropies of an interval in the free Schrödinger field theory at finite density

Mintchev,

Pontello,

Sartori

et al. 2022

Preprint

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We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schrödinger field theory at finite density and zero temperature, which is a non relativistic model with Lifshitz exponent z = 2. We prove that the entanglement entropies are finite functions of one dimensionless parameter proportional to the area of a rectangular region in the phase space determined by the Fermi momentum and the length of the interval. The numerical results show that the entanglement entropy is a monotonically increasing function. By employing the properties of the prolate spheroidal wave functions of order zero or the asymptotic expansions of the tau function of the sine kernel, we find analytic expressions for the expansions of the entanglement entropies in the asymptotic regimes of small and large area of the rectangular region in the phase space. These expansions lead to prove that the analogue of the relativistic entropic C function is not monotonous. Extending our analyses to a class of free fermionic Lifshitz models labelled by their integer dynamical exponent z, we find that the parity of this exponent determines the properties of the bipartite entanglement for an interval on the line.

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Section: Indicate That S (α)mentioning

confidence: 63%

“…In this manuscript we study the entanglement entropies of an interval A = [−R, R] on the line for the free fermionic spinless Schrödinger field theory at zero temperature and finite density µ. When µ = 0, we have S A = 0, as observed in [43,68].…”

Section: F On the Large η Expansion 1 Introductionmentioning

confidence: 98%

Entanglement entropies of an interval in the free Schrödinger field theory at finite density

Mintchev,

Pontello,

Sartori

et al. 2022

Preprint

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“…Turning to another potential application, we believe the coset structures described herein may be useful for studying entanglement entropies, along the lines of [39]. We note recent work indicates that the entanglement structure of the Galilean vacuum is trivial [80]. The argument makes crucial use of the existence of the U (1) (particle number) symmetry generator N .…”

Section: Discussion and Outlookmentioning

confidence: 81%

Homogeneous nonrelativistic geometries as coset spaces

Hartong

Keeler

Obers

2018

Class. Quantum Grav.

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We generalize the coset procedure of homogeneous spacetimes in (pseudo-)Riemannian geometry to non-Lorentzian geometries. These are manifolds endowed with nowhere vanishing invertible vielbeins that transform under local non-Lorentzian tangent space transformations. In particular we focus on nonrelativistic symmetry algebras that give rise to (torsional) Newton-Cartan geometries, for which we demonstrate how the Newton-Cartan metric complex is determined by degenerate co-and contravariant symmetric bilinear forms on the coset. In specific cases we also show the connection of the resulting nonrelativistic coset spacetimes to pseudo-Riemannian cosets via Inönü-Wigner contraction of relativistic algebras as well as null reduction. Our construction is of use for example when considering limits of the AdS/CFT correspondence in which nonrelativistic spacetimes appear as gravitational backgrounds for nonrelativistic string or gravity theories.In view of their importance in nonrelativistic holography 2 , Lifshitz and Schrödinger spacetimes were already studied via coset constructions in [44] (and applied in e.g. [45-47]). Since nonrelativistic algebras are not semi-simple and have a degenerate Cartan-Killing metric, the standard (Riemannian) coset method of contracting the (inverse) vielbeins with the (inverse) Cartan-Killing metric, obtaining the metric and its inverse, does not apply. Instead of the Cartan-Killing metric, [44] uses the most general non-degenerate group invariant symmetric bilinear form, as [48] did for the Nappi-Witten WZW model on the non-semi simple group E c 2 , which is the centrally extended 2-dimensional Euclidean group. Thus [44] recovers the so-called Lifshitz and Schrödinger spacetimes, first proposed in [49, 50] and [51, 52], from a pseudo-Riemannian coset construction by performing cosets on the Lifshitz and Schrödinger groups respectively.However, aside from the somewhat counterintuitive concept of proposing locally relativistic spacetimes as duals to nonrelativistic field theories [34], difficulties with field profile reconstruction [53][54][55] as well as spacetime reconstruction [56] motivate the consideration of alternatives. As advocated in e.g. [25], such nonrelativistic spacetimes are more naturally viewed as Newton-Cartan spacetimes, described by a clock 1-form, degenerate spatial metric and an extra U (1) connection that contains the Newtonian potential. As we will see in this paper, the key observation is first of all that for certain choices of subgroup H ⊂ G the invariant bilinear form on the coset is necessarily degenerate. Consequently there are two (degenerate) distinct group-invariant bilinear forms on the coset: a covariant bilinear form (Ω ab ) and a corresponding dual bilinear form (Ω ab ). These objects are obviously not inverses of each other as they are both degenerate. With these two objects, we can construct the Newton-Cartan geometric data 3 for several interesting cases.Since some nonrelativistic algebras can be obtained using Inönü-Wigner contractions of relativi...

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“…Therefore it factorizes, |0 = i |0 i and the entanglement entropy on a finite region is trivial. This point was emphasized in [34]; it can also be obtained directly as the m → ∞ limit of the EE for a Dirac fermion. Now let us add some charge, so that the new ground state has N e > 0.…”

Section: Jhep03(2021)079mentioning

confidence: 91%

Aspects of quantum information in finite density field theory

Daguerre

Medina

Solís

et al. 2021

J. High Energ. Phys.

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We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.

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Triviality of entanglement entropy in the Galilean vacuum

Cited by 7 publications

References 33 publications

Entanglement entropies of an interval in the free Schrödinger field theory at finite density

Entanglement entropies of an interval in the free Schrödinger field theory at finite density

Homogeneous nonrelativistic geometries as coset spaces

Aspects of quantum information in finite density field theory

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