Entanglement entropy fluctuation and distribution for open systems

Abstract

The entanglement entropy generated by quantum transport, similar to any physical observable quantity, is a stochastic variable that has its distribution and can fluctuate. The fundamental question is how to define the entanglement entropy operator which allows one to discuss entanglement entropy fluctuation. By introducing the entanglement entropy operator, we develop a theoretical framework to calculate the entanglement entropy fluctuation as well as its higher order cumulants generated by electronic transport in open systems. The distribution of entanglement entropy generated by opening or closing a quantum point contact (QPC) is solved exactly. When the transmission coefficient of QPC is one-half, the entanglement entropy is maximized and fluctuationless. We also establish a general relation between the generated entanglement entropy fluctuation and charge fluctuation. We apply our theory to electronic transport through a quantum dot and study the generated entanglement entropy in the transient regime. Universal behavior is found for the cumulants of entanglement entropy at short times.

Full-counting statistics of energy transport of molecular junctions in the polaronic regime

“…It is known that quantum transport is determined in nature by stochastic process which can be characterized by the corresponding distribution function [21]. The study of full-counting statistics (FCS) pioneered by Levitov and Lesovik [22][23][24] could provide us with a full view of the probability distribution of electron and energy transport [18][19][20][25][26][27][28][29][30][31][32][33][34][35][36]. The key in FCS is to obtain the generating function (GF) which is actually the Fourier transform of the probability distribution of the related physical quantity.…”

“…The key in FCS is to obtain the generating function (GF) which is actually the Fourier transform of the probability distribution of the related physical quantity. Using the NEGF technique [37][38][39][40] and the path integral method under the two-time quantum measurement scheme [27,[41][42][43], GF was formulated as a Fredholm determinant in the time domain for both phonon [29][30][31] and electron [27,[32][33][34][35] transport. This formalism enables one to study the transport properties in the transient regime providing more information on the short time dynamics [32].…”

Hopping-Induced Ground-State Magnetism in 6H Perovskite Iridates

“…The process is sensitive to the changes in energy, momentum and polarization of inelastically scattered x-ray photons representing elementary excitations in a material. With the development of high-resolution spectrometers [21], it is now possible to resolve low-energy excitations to such SOC-states in a RIXS experiment [3,22]. The low-energy spin-orbit excitonic process Energy loss (eV) for an atomic scenario is depicted in the inset of Fig.…”

“…The energy losses ∆ω = ω i − ω 1 , ω 2 , then correspond to the energy costs for the different arrangements of the electrons within the SOC t 2g orbitals. Even though RIXS has already been employed to study spin-orbit excitations in DP Ir 5+ systems, marginal inter-site hopping has had an undetectable effect on the RIXS spectra which could be interpreted by a bare atomic model [3,5,16,22]. In contrast, we here show using RIXS that enhancement in inter-site hopping due to close placement of Ir 5+ ions drives the 6H-iridates (Ba 3 M Ir 2 O 9 (M = Mg, Zn, Ca, and Sr)) into a regime where the effective SOC strength is weakened and the ground state deviates from non-magnetic singlets (Fig.…”

Short-time dynamics of molecular junctions after projective measurement

“…Generating function (GF), from which one can get high-order cumulants by taking derivatives with respect to the counting field, is the key in studying FCS and has various applications. Entanglement entropy is difficult to be measured experimentally, it was proposed that a series of the charge cumulants which are measurable can be used to approach it [29][30][31][32][33] . The dynamical Lee-Yang zeros of GF of an observable in open quantum systems can be accessed using high-order cumulants [34][35][36][37] .…”