Fano resonances and entanglement entropy

Abstract

We study the entanglement in the ground state of a chain of free spinless fermions with a single side-coupled impurity. We find a logarithmic scaling for the entanglement entropy of a segment neighboring the impurity. The prefactor of the logarithm varies continuously and contains an impurity contribution described by a one-parameter function, while the contribution of the unmodified boundary enters additively. The coefficient is found explicitly by pointing out similarities with other models involving interface defects. The proposed formula gives excellent agreement with our numerical data. If the segment has an open boundary, one finds a rapidly oscillating subleading term in the entropy that persists in the limit of large block sizes. The particle number fluctuation inside the subsystem is also reported. It is analogous with the expression for the entropy scaling, however with a simpler functional form for the coefficient.

Exact results for the entanglement across defects in critical chains

“…This holds also for more complicated defects [6]. In a series of recent papers, calculations were also done for continuous fermionic systems, and the same coefficient was found [7][8][9].…”

Time evolution of entanglement negativity across a defect

“…In general, the behaviour of the half-chain entanglement depends crucially on whether a density bias is applied between the fermionic leads separated by the defect. For the unbiased case, one finds a logarithmic growth of entanglement, with the same prefactor that governs the equilibrium entropy scaling in the presence of a defect, which was studied both numerically and analytically for hopping chains [15][16][17][18][19] as well as in the continuum [20,21]. The exact same relation can actually be found in conformal field theory (CFT) calculations [22], connecting entropy dynamics after the quench to the problem of ground-state entanglement across a conformal interface [23,24].…”

On entanglement evolution across defects in critical chains

“…Since e S , which is the effective number of terms in the Schmidt decomposition, then follows a power law, one can view c eff as a variable critical exponent. It was studied in a number of papers for discrete [1][2][3][4][5] and continuous [6][7][8] systems and an exact analytical formula was obtained [3], also for the Rényi entropy [7,10] and for bosons [9,10]. Technically, the variation is caused by a gap in the single-particle eigenvalue spectrum of the reduced density matrix (RDM) and the relevant physical parameter is the transmission amplitude of the defect.…”