2010/10/31 by Gregory Levine, G. C. Levine, Barry Friedman +1
Physics and Astronomy · #Density matrix #Entropy (arrow of time) #Fermion #Hilbert space #Mathematical physics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #Wave function #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.83.125118
10 pages, 6 figures; added discussion section; accepted Phys. Rev. B
arxiv created 2011/02/16 · openalex publication_date 2011/03/28 · arxiv updated 2013/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The entanglement entropy of two gapless noninteracting fermion subsystems is computed approximately in a way that avoids the introduction of replicas and a geometric interpretation of the reduced density matrix. We exploit the similarity between the Schmidt basis wave function and superfluid BCS wave function and compute the entropy using the BCS approximation. Within this analogy, the Cooper pairs are particle-hole pairs straddling the boundary and the effective interaction between them is induced by the projection of the Hilbert space onto the incomplete Schmidt basis. The resulting singular interaction may be thought of as ``lifting'' the degeneracy of the single-particle distribution function. For two coupled fermion systems of linear size L, we solve the BCS gap equation approximately to find the entropy S\ensuremath≈(w2/t2)lnL, where w is the hopping amplitude at the boundary of the subsystem and 2t is the bandwidth. We further interpret this result based upon the relationship between entanglement spectrum, entropy, and number fluctuations.