A note on "Exact Solution of Bipartite Fluctuations in One-Dimensional Fermions"

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current $Q_t$ during time $t$ through the origin when, in the initial condition, the sites are occupied with density $\rho_a$ on the negative axis and with density $\rho_b$ on the positive axis. All the cumulants of $Q_t$ grow like $\sqrt{t}$. In the range where $Q_t \sim \sqrt{t}$, the decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is non-Gaussian. Ou...

The one-dimensional Ising model with nearest neighbour interactions and the zero-temperature dynamics recently considered by Lefevre and Dean -J. Phys. A: Math. Gen. {\bf 34}, L213 (2001)- is investigated. By introducing a particle-hole description, in which the holes are associated to the domain walls of the Ising model, an analytical solution is obtained. The result for the asymptotic energy agrees with that found in the mean field approximation.

In this paper we obtain formulas for the distribution of the left-most up-spin in the Heisenberg-Ising spin-1/2 chain with anisotropy parameter $\Delta$, also known as the XXZ spin-1/2 chain, on the one-dimensional lattice $\mathbb{Z}$ with domain wall initial conditions. We use the Bethe Ansatz to solve the Schr$\"o$dinger equation and a recent antisymmetrization identity of Cantini, Colomo, and Pronko (arXiv:1906.07636) to simplify the marginal distribution of the left-most...

We consider the entanglement entropy for a line segment in the system of noninteracting one-dimensional fermions at zero temperature. In the limit of a large segment length L, the leading asymptotic behavior of this entropy is known to be logarithmic in L. We study finite-size corrections to this asymptotic behavior. Based on an earlier conjecture of the asymptotic expansion for full counting statistics in the same system, we derive a full asymptotic expansion for the von Neu...

We investigate the total asymmetric exclusion process by analyzing the dynamics of the shock. Within this approach we are able to calculate the fluctuations of the number of particles and density profiles not only in the stationary state but also in the transient regime. We find that the analytical predictions and the simulation results are in excellent agreement.

In this paper we return to a model with domain wall fermions in a waveguide. This model contains a Yukawa coupling $y$ which is needed for gauge invariance. A previous paper left the analysis for large values of this coupling incomplete. We fill the gap by developing a systematic expansion suitable for large $y$, and using this, we gain an analytic understanding of the phase diagram and fermion spectrum. We find that in a sense all the species doublers come back for large $y$...

We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig conjecture. The coefficients of this expansion are conjectured to obey certain periodicity relations, which renders the expansion explicitly periodic in the "counting param...

We propose using a mobile magnetic domain wall as a host of zero-energy Majorana fermions in a spin-orbit coupled nanowire sandwiched by two ferromagnetic strips and deposited on an $s$-wave superconductor. The ability to control domain walls by thermal means allows to braid Majorana fermions nonintrusively, which obey non-Abelian statistics. The analytical solutions of Majorana fermions inside domain walls are obtained in the strong spin-orbit regime.

In this work, we provide a method which allows to compute exactly the multipoint and multi-time correlation functions of a one-dimensional stochastic model of dimer adsorption-evaporation with random (uncorrelated) initial states. In particular explicit expressions of the two-point noninstantaneous/instantaneous correlation functions are obtained. The long-time behavior of these expressions is discussed in details and in various physical regimes.

Studying various thermodynamic quantities for the free domain wall fermions for both finite and infinite fifth dimensional extent N_5, we find that the lattice corrections are minimum for $N_T\geq10$ for both energy density and susceptibility, for its irrelevant parameter M in the range 1.45-1.50. The correction terms are, however, quite large for small lattice sizes of $N_T\leq8$. We propose modifications of the domain wall operator, as well as the overlap operator, to reduc...