Particle partition entanglement of one dimensional spinless fermions

H. Barghathi, E. Casiano-Diaz and A. Del Maestro, J. Stat. Mech. 083108 (2017). (arXiv:1703.10587.)

Abstract:

We investigate the scaling of the Rényi entanglement entropies for a particle bipartition of interacting spinless fermions in one spatial dimension. In the Tomonaga-Luttinger liquid regime, we calculate the second Renyi entanglement entropy and show that the leading order finite-size scaling is equal to a universal logarithm of the system size plus a non-universal constant. Higher-order corrections decay as power-laws in the system size with exponents that depend only on the Luttinger parameter. We confirm the universality of our results by investigating the one dimensional t−V model of interacting spinless fermions via exact-diagonalization techniques. The resulting sensitivity of the particle partition entanglement to boundary conditions and statistics points to its utility in future studies of quantum liquids.

Description

This repository includes all data and plotting scripts to generate the figures in H. Barghathi, E. Casiano-Diaz and A. Del Maestro, J. Stat. Mech. 083108 (2017). All data was generated via exact diagonalization https://github.com/DelMaestroGroup/tV_diagonalize using a code forked from MelkoCollective/BH_diagonalize.

The creation of these materials was supported in part by the National Science Foundation under Award No. DMR-1553991.

PartitionSchematic (Figure 1)

EntanglementEntropies (Figure 2)

FiniteSizeScaling (Figure 3)

InteractionDependence (Figure 4)

EntropyVsParticlePartitionSize (Figure 5)

DegeneracyEffect (Figure 6)