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Mintchev, Mihail; Pontello, Diego; Tonni, Erik

Entanglement entropies of an interval in the free Schrödinger field theory on the half line. (English) Zbl 1531.81032

J. High Energy Phys. 2022, No. 9, Paper No. 90, 54 p. (2022).
Summary: 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.

Cited in 2 Documents

MSC:

81P17 Quantum entropies
81P40 Quantum coherence, entanglement, quantum correlations
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81P42 Entanglement measures, concurrencies, separability criteria

Keywords:

boundary quantum field theory; field theories in lower dimensions; space-time symmetries

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References:

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