Particle partition entanglement of one dimensional spinless fermions

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 Rényi 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 supports its utility as a probe of quantum liquids.

arXiv comment19 pages, 6 figures

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• Local density of states and particle entanglement in topological quantum fluids
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• Balls and Walls: A Compact Unary Coding for Bosonic States
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
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• A Scaling Function for the Particle Entanglement Entropy of Fermions
• Matrix product states and first quantization
• Equivalence of Spatial and Particle Entanglement Growth After a Quantum Quench