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Bulletin of the American Physical Society

Universality of Particle and Spatial Entanglement After an Interaction Quench in a Tomonaga-Luttinger Liquid

Adrian Del Maestro, Bernd Rosenow

Published Mar 6, 2019• 0 citations
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We consider the R\'enyi entanglement entropy of bosonic Tomonaga-Luttinger liquids under a particle bipartition and demonstrate that the leading order finite-size scaling is logarithmic in the system size with a prefactor equal to the inverse Luttinger parameter. While higher-order corrections involve a microscopic length scale, the leading-order scaling depends only on this sole dimensionless parameter which characterizes the low-energy quantum hydrodynamics. This result contrasts the leading entanglement entropy scaling under a spatial bipartition, for which the coefficient is universal and independent of the Luttinger parameter. Using quantum Monte Carlo calculations, we explicitly confirm the scaling predictions of Tomonaga-Luttinger liquid theory for the Lieb-Liniger model of $\ensuremath{\delta}$-function interacting bosons in the one-dimensional spatial continuum.
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.
We study the dynamics resulting from an abrupt change of the two-particle interaction in two models of closed one-dimensional Fermi systems: (a) the field theoretical Tomonaga-Luttinger model and (b) a microscopic lattice model. Using a nonperturbative approach which is controlled for small two-particle interactions, we are able to reach large times allowing us to access the properties of the steady state of the lattice model. Comparing those to the exact solution of the full dynamics in the Tomonaga-Luttinger model, we provide evidence for universal Luttinger liquid behavior.