The von Neumann entropy asymptotics in multidimensional fermionic systems
arXiv:0706.1805 · doi:10.1063/1.2800167
Abstract
We study the von Neumann entropy asymptotics of pure translation-invariant quasi-free states of d-dimensional fermionic systems. It is shown that the entropic area law is violated by all these states: apart from the trivial cases, the entropy of a cubic subsystem with edge length L cannot grow slower than L^{d-1}ln L. As for the upper bound of the entropy asymptotics, the zero-entropy-density property of these pure states is the only limit: it is proven that arbitrary fast sub-L^d entropy growth is achievable.
10 pages
References in corpus (12)
- Criticality, the area law, and the computational power of PEPS
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Entanglement scaling in critical two-dimensional fermionic and bosonic systems
- Entanglement in fermionic systems
- Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
- Statistics dependence of the entanglement entropy
- Entanglement entropy at infinite randomness fixed points in higher dimensions
- Entanglement in the XX spin chain with an energy current
- Entanglement, Haag-duality and type properties of infinite quantum spin chains
- Fluctuations in subsystems of the zero temperature XX chain: Emergence of an effective temperature
- Non-zero entropy density in the XY chain out of equilibrium
- Entanglement-Entropy for Groundstates, Low-lying and Highly Excited Eigenstates of General (Lattice) Hamiltonians
Cited by in corpus (26)
- Area laws for the entanglement entropy - a review
- Holographic Entanglement Entropy: An Overview
- Quantum entanglement in condensed matter systems
- Reduced density matrices and entanglement entropy in free lattice models
- Bipartite Fluctuations as a Probe of Many-Body Entanglement
- Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
- Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
- Entanglement entropies in free fermion gases for arbitrary dimension
- Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
- Entanglement negativity in two-dimensional free lattice models
- Area law violation for the mutual information in a nonequilibrium steady state
- Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
- Entanglement and particle correlations of Fermi gases in harmonic traps
- A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy
- Entanglement entropy of integer Quantum Hall states in polygonal domains
- Entanglement entropy in quantum spin chains with broken reflection symmetry
- Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law
- Entanglement does not generally decrease under renormalization
- Oscillating terms in the Renyi entropy of Fermi liquids
- Many body physics from a quantum information perspective
- Entanglement entropy of compressible holographic matter: loop corrections from bulk fermions
- Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
- Universal Finite-Size Corrections of the Entanglement Entropy of Quantum Ladders and the Entropic Area Law
- Entanglement entropy of random partitioning
- Entanglement of electrons and the lattice in a Luttinger system
- Universal entanglement signatures of quantum liquids as a guide to fermionic criticality