Scaling of Entanglement Entropy in Point Contact Free Fermion Systems

Abstract

The scaling of entanglement entropy is computationally studied in several $1\le d\le 2$ dimensional free fermion systems that are connected by one or more point contacts (PC). For both the $k$-leg Bethe lattice $(d=1)$ and $d=2$ rectangular lattices with a subsystem of $L^d$ sites, the entanglement entropy associated with a {\sl single} PC is found to be generically $S\sim L$. We argue that the $O(L)$ entropy is an expression of the subdominant $O(L)$ entropy of the bulk entropy-area law. For $d=2$ (square) lattices connected by $m$ PCs, the area law is found to be $S\sim a{L}^{d-1}+bm\log L$ and is thus consistent with the anomalous area law for free fermions ($S\sim L\log L$) as $m\to L$. For the Bethe lattice, the relevance of this result to Density Matrix Renormalization Group (DMRG) schemes for interacting fermions is discussed.

arXiv comment7 pages, 12 figures

References in corpus (26)

• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Bosonization and Strongly Correlated Systems
• Calculation of reduced density matrices from correlation functions
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Violation of the entropic area law for Fermions
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Entanglement Entropy and the Fermi Surface
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Fine-grained entanglement loss along renormalization group flows
• Ground state projection of quantum spin systems in the valence bond basis
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Efficient simulation of infinite tree tensor network states on the Bethe lattice
• The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
• Valence Bond Entanglement Entropy
• Entanglement entropy in a boundary impurity model
• Conformal Field Theory on the Fermi Surface
• Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance
• Zero dimensional area law in a gapless fermion system
• Density matrix renormalization group algorithm for Bethe lattices of spin 1/2 or 1 sites with Heisenberg antiferromagnetic exchange
• Entanglement Entropy of Coupled Conformal Field Theories and Fermi Liquids

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• Entanglement Entropy on the Cayley Tree
• Scaling of Entanglement Entropy for the Heisenberg Model on Clusters Joined by Point Contacts