Finite temperature fidelity susceptibility for one-dimensional quantum systems

We calculate the fidelity susceptibility chi_f for the Luttinger model and show that there is a universal contribution linear in temperature T (or inverse length 1/L). Furthermore, we develop an algorithm - based on a lattice path integral approach - to calculate the fidelity F(T) in the thermodynamic limit for one-dimensional quantum systems. We check the Luttinger model predictions by calculating chi_f(T) analytically for free spinless fermions and numerically for the XXZ chain. Finally, we study chi_f at the two phase transitions in this model.Comment: typo in Eq. (9) corrected, published versio

Operational Entanglement of Symmetry-Protected Topological Edge States

We use an entanglement measure that respects the superselection of particle number to study the non-local properties of symmetry-protected topological edge states. Considering half-filled M-leg Su-Schrieffer-Heeger (SSH) ladders as an example, we show that the topological properties and the operational entanglement extractable from the boundaries are intimately connected. Topological phases with at least two filled edge states have the potential to realize genuine, non-bipartite, many-body entanglement which can be transferred to a quantum register. The entanglement is extractable when the filled edge states are sufficiently localized on the lattice sites controlled by the users. We show, furthermore, that the onset of entanglement between the edges can be inferred from local particle number spectroscopy alone and present an experimental protocol to study the breaking of Bell's inequality.Comment: Final version, minor change

Spin diffusion and the anisotropic spin-1/2 Heisenberg chain

Measurements of the spin-lattice relaxation rate 1/T_1 by nuclear magnetic resonance for the one-dimensional Heisenberg antiferromagnet Sr_2CuO_3 have provided evidence for a diffusion-like contribution at finite temperature and small wave-vector. By analyzing real-time data for the auto- and nearest-neighbor spin-spin correlation functions obtained by the density-matrix renormalization group I show that such a contribution indeed exists for temperatures T>J, where J is the coupling constant, but that it becomes exponentially suppressed for T << J. I present evidence that the frequency-dependence of 1/T_1 in the Heisenberg case is smoothly connected to that in the free fermion case where the exponential suppression of the diffusion-like contribution is easily understood.Comment: 9 pages, 7 figure