Explicit Hamiltonians inducing volume law for entanglement entropy in fermionic lattices
Year: 2015
Authors: Gori G., Paganelli S., Sharma A., Sodano P., Trombettoni A.
Autors Affiliation: CNR, IOM DEMOCRITOS Simulat Ctr, I-34136 Trieste, Italy; Univ Aquila, Dipartimento Sci Fis & Chim, I-67010 Coppito, Italy; Univ Fed Rio Grande do Norte, Int Inst Phys, BR-59078400 Natal, RN, Brazil; Tel Aviv Univ, Sch Chem, Sackler Fac Exact Sci, IL-69978 Tel Aviv, Israel; Univ Fed Rio Grande do Norte, Dept Fis Teor & Expt, BR-59072970 Natal, RN, Brazil; Ist Nazl Fis Nucl, Sez Perugia, I-06123 Perugia, Italy; SISSA, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, I-34136 Trieste, Italy.
Abstract: We show how the area law for entanglement entropy may be violated by free fermions on a lattice, and we look for conditions leading to the emergence of a volume law. We give an explicit construction of the states with maximal entanglement entropy based on the fact that, once a bipartition of the lattice in two complementary sets A and (A) over bar is given, the states with maximal entanglement entropy (volume law) may be factored into Bell pairs (BPs) formed by two states with support on A and (A) over bar. We then exhibit, for translational invariant fermionic systems on a lattice, a Hamiltonian whose ground state is such that it yields an exact volume law. As expected, the corresponding Fermi surface has a fractal topology. We also provide some examples of fermionic models for which the ground state may have an entanglement entropy S-A between the area and the volume law, building an explicit example of a one-dimensional free fermion model where S-A (L) proportional to L-beta, with beta being intermediate between beta = 0 (area law) and beta = 1 (BP state inducing volume law). For this model, the dispersion relation has a zigzag structure leading to a fractal Fermi surface whose counting box dimension equals, for large lattices, beta. Our analysis clearly relates the violation of the area law for the entanglement entropy of the ground state to the emergence of a nontrivial topology of the Fermi surface.
Journal/Review: PHYSICAL REVIEW B
Volume: 91 (24) Pages from: 245138-1 to: 245138-13
More Information: We would like to thank A. Bayat, F. Buccheri, J. Magan, and E. Tonni for useful discussions. During the completion of this work, we became aware of results on volumetric law in fermionic lattices with inhomogeneous nearest-neighbor hoppings by G. Ramirez, J. Rodriguez-Laguna, and G. Sierra [82]: it is a pleasure to thank them for discussions and useful correspondence. P.S. thanks the Ministry of Science, Technology and Innovation of Brazil for financial support and CNPq for granting a Bolsa de Produtividade em Pesquisa. P.S. and S.P. acknowledge partial support from MCTI and UFRN/MEC (Brazil). S.P. is supported by a Rita Levi-Montalcini fellowship of MIUR. A. S. acknowledges support from CNPq, and from The Center for Nanoscience and Nanotechnology at Tel Aviv University and the PBC Indo-Israeli Fellowship. A.T. acknowledges support from the Italian PRIN Fenomeni quantistici collettivi: dai sistemi fortemente correlati ai simulatori quantistici (PRIN 2010_2010LLKJBX) and hospitality from the International Institute of Physics (Natal), where part of this work was carried out. G. G. and A.T. acknowledge support by the European Commission FET proactive initiative MatterWave (Grant No. FP7-ICT-601180).KeyWords: Reduced Density-matrices; Quantum; Systems; StatesDOI: 10.1103/PhysRevB.91.245138Citations: 45data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2025-09-14References taken from IsiWeb of Knowledge: (subscribers only)
