Entanglement entropy with Lifshitz fermions

Hartmann, Dion M. F.; Kavanagh, Kevin

doi:10.21468/scipostphys.11.2.031

Cited by 8 publications

(9 citation statements)

References 41 publications

(73 reference statements)

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“…The fermionic spinfull model in d = 1 in the presence of the quartic interaction has been studied through renormalization group methods [40][41][42]. Free fermionic spinless models in d = 1 with positive integer values of z have been also considered [43]. Let us remark that, in our analysis of the entanglement entropies for this free model, we do not approximate the dispersion relation with a linear dispersion relation at the Fermi points (Tomonaga's approximation) [44,45].…”

Section: Introductionmentioning

confidence: 99%

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

Mintchev

Pontello

Sartori

et al. 2022

J. High Energ. Phys.

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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 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: Introductionmentioning

confidence: 99%

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

Mintchev

Pontello

Sartori

et al. 2022

J. High Energ. Phys.

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show abstract

“…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: 61%

“…The fermionic spinfull model in d = 1 in the presence of the quartic interaction has been studied through renormalisation group methods [40][41][42]. Free fermionic spinless models in d = 1 with positive integer values of z have been also considered [43]. Let us remark that, in our analysis of the entanglement entropies for this free model, we do not approximate the dispersion relation with a linear dispersion relation at the Fermi points (Tomonaga's approximation) [44,45].…”

Section: F On the Large η Expansion 1 Introductionmentioning

confidence: 99%

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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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“…When this model is defined on the line, the entanglement entropies of an interval [−R, R] ⊂ R have been studied in [41], finding that they are finite functions of the dimensionless parameter η ≡ R k F 0, where k F is the Fermi momentum, and that the entanglement entropy S A is a monotonically increasing function of η . The µ = 0 case has been considered earlier in [42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Entanglement entropies of an interval in the free Schrödinger field theory on the half line

Mintchev,

Pontello,

Tonni

2022

Preprint

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We study the entanglement entropies of an interval adjacent to the boundary of the half line for the free fermionic spinless Schrödinger field theory at finite density and zero temperature, with either Neumann or Dirichlet boundary conditions. They are finite functions of the dimensionless parameter given by the product of the Fermi momentum and the length of the interval. The entanglement entropy displays an oscillatory behaviour, differently from the case of the interval on the whole line. This behaviour is related to the Friedel oscillations of the mean particle density on the half line at the entangling point. We find analytic expressions for the expansions of the entanglement entropies in the regimes of small and large values of the dimensionless parameter. They display a remarkable agreement with the curves obtained numerically. The analysis is extended to a family of free fermionic Lifshitz models labelled by their integer Lifshitz exponent, whose parity determines the properties of the entanglement entropies. The cumulants of the local charge operator and the Schatten norms of the underlying kernels are also explored.

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Entanglement entropy with Lifshitz fermions

Cited by 8 publications

References 41 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

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 on the half line

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