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Scaling of Entanglement Entropy in Point Contact Free Fermion Systems
- Source :
- Phys. Rev. A 89, 052305 (2014)
- Publication Year :
- 2014
-
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 $S \sim aL^{d-1} + b m \log{L}$ and is thus consistent with the anomalous area law for free fermions ($S \sim L \log{L}$) as $m \rightarrow L$. For the Bethe lattice, the relevance of this result to Density Matrix Renormalization Group (DMRG) schemes for interacting fermions is discussed.<br />Comment: 7 pages, 12 figures
- Subjects :
- Condensed Matter - Strongly Correlated Electrons
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. A 89, 052305 (2014)
- Publication Type :
- Report
- Accession number :
- edsarx.1402.5437
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevA.89.052305