Entanglement entropies of an interval in the free Schrödinger field theory at finite density
arXiv:2201.04522 · doi:10.1007/JHEP07(2022)120
Abstract
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 . 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 function is not monotonous. Extending our analyses to a class of free fermionic Lifshitz models labelled by their integer dynamical exponent , we find that the parity of this exponent determines the properties of the bipartite entanglement for an interval on the line.
83 pages, 15 figures. Published version
References in corpus (39)
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Towards a derivation of holographic entanglement entropy
- Gravity duals for non-relativistic CFTs
- Holographic c-theorems in arbitrary dimensions
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Entanglement negativity in quantum field theory
- Seeing a c-theorem with holography
- Quantum Noise as an Entanglement Meter
- Topological Order and Conformal Quantum Critical Points
- Nonrelativistic conformal field theories
- Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
- Relative entropy and the Bekenstein bound
- Entanglement hamiltonians in two-dimensional conformal field theory
- On String Theory Duals of Lifshitz-like Fixed Points
- Entanglement scaling in critical two-dimensional fermionic and bosonic systems
- Finite temperature entanglement negativity in conformal field theory
- The entanglement entropy of one-dimensional gases
- Universal entanglement entropy in 2D conformal quantum critical points
- On the partial transpose of fermionic Gaussian states
- Universal corrections to scaling for block entanglement in spin-1/2 XX chains
- Local temperatures and local terms in modular Hamiltonians
- Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
- Holographic entanglement entropy: near horizon geometry and disconnected regions
- Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
- On entanglement hamiltonians of an interval in massless harmonic chains
- Area law and vacuum reordering in harmonic networks
- Entanglement Hamiltonians for non-critical quantum chains
- Modular Hamiltonians for the massless Dirac field in the presence of a boundary
- Modular Hamiltonians for the massless Dirac field in the presence of a defect
- Free fermions on a line: asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics
- Anisotropic Unruh temperatures
- Modular Hamiltonian of a chiral fermion on the torus
- Holographic spontaneous anisotropy
- Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice
- Emptiness formation probability and Painlevé V equation in the XY spin chain
- The Limit of the Entanglement Entropy
- Entanglement Entropy with Lifshitz Fermions
- Aspects of quantum information in finite density field theory
- Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermion