Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition

Abstract

We investigate the fluctuations of the spin current for the onedimensional XX spin chain starting from the domain wall initial condition. The generating function of the current is shown to be written as a determinant with the Bessel kernel. An exact analytical expression for the large deviation function is obtained by applying the Coulomb gas method. Our results are also compared with DMRG calculations. * hmoriya@stat.phys.titech.ac.jp

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

“…Further, as shown in Ref. [33], the determinant with the discreet Bessel kernel can be transformed to the Fredholm determinant with the continuous Bessel kernel with the result…”

“…(43)), performing transformation to the "energy" space ϕ → E = − cos ϕ and accounting for the finite temperature in the same way as in Sec. 3, we represent the return amplitude in the thermodynamic limit as the Fredholm determinant (32) with the kernel (33). The leading asymptotics (34) can be obtained performing manipulations similar to those in Sec.…”

“…(138) In Ref. [33] it was proved that the discrete Bessel kernel is also equivalent to the continuous one det…”

“…In this case FCS was considered in Ref. [32,33], where the authors managed to connect it to the random-matrix theory and also express as a Fredholm determinant of the Bessel type kernel. We verify that the proper change of basis provides a direct transformation between their and our kernels.…”

Fluctuations in Ballistic Transport from Euler Hydrodynamics

“…For quantum transport of free fermions, the SCGF of U (1) charges is given by the celebrated Levitov-Lesovik formula [13,14], which has applications in mesoscopic physics. Free-particle advanced techniques have been used [15,16,17,18,19,20], see also [21], and exact results exist in certain integrable impurity models [22] and in general 1+1dimensional conformal field theory (CFT) [23,24], see the review [25]. These systems admit ballistic transport, and nonequilibrium currents are generated by the partitioning protocol [26,27,28] (see also [25] and references therein), where an imbalance exists in the initial condition.…”