Particle partition entanglement of bosonic Luttinger liquids

Abstract

We consider the Rényi entanglement entropy of bosonic 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 Luttinger liquid theory for the Lieb-Liniger model of $\delta$-function interacting bosons in the one dimensional spatial continuum.

arXiv comment10 pages, 8 figures; updated figure 5, added references, revised text, reformatted

References in corpus (49)

• Quantum entanglement
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Luttinger Liquid Behavior in Carbon Nanotubes
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Quantum Entanglement in Fermionic Lattices
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Bosonizing one-dimensional cold atomic gases
• The entanglement of indistinguishable particles shared between two parties
• Entanglement entropy of two disjoint intervals in conformal field theory
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement entropy in fermionic Laughlin states
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• Universal terms for the entanglement entropy in 2+1 dimensions
• Parity effects in the scaling of block entanglement in gapless spin chains
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Entanglement Entropy in the O(N) model
• Interference between independent fluctuating condensates
• Extracting entanglement from identical particles
• General Relation between Entanglement and Fluctuations in One Dimension
• Full quantum distribution of contrast in interference experiments between interacting one dimensional Bose liquids
• Unusual Corrections to Scaling in Entanglement Entropy
• Bipartite entanglement entropy in fractional quantum Hall states
• Quantum Entanglement of Identical Particles
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Exact quantum Monte Carlo study of one dimensional trapped fermions with attractive contact interactions
• Correlation functions and momentum distribution of one-dimensional Bose systems
• Helium-4 Luttinger liquids in nanopores
• Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains
• Entanglement scaling in two-dimensional gapless systems
• A path integral Monte Carlo method for Rényi entanglement entropies
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• Dynamical theory of superfluidity in one dimension
• Entanglement between particle partitions in itinerant many-particle states
• Particle entanglement in continuum many-body systems via quantum Monte Carlo
• Particle partitioning entanglement in itinerant many-particle systems
• Rényi entanglement entropies in quantum dimer models : from criticality to topological order
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• The propagator for the step potential and delta function potential using the path decomposition expansion

Cited by in corpus (11)

• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Spatial entanglement entropy in the ground state of the Lieb-Liniger model
• Local density of states and particle entanglement in topological quantum fluids
• Particle partition entanglement of one dimensional spinless fermions
• Extracting the Luttinger parameter from a single wave function
• Balls and Walls: A Compact Unary Coding for Bosonic States
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• One-particle entanglement for one dimensional spinless fermions after an interaction quantum quench
• Properties of fermionic systems with the Path-integral ground state method
• A Scaling Function for the Particle Entanglement Entropy of Fermions
• Equivalence of Spatial and Particle Entanglement Growth After a Quantum Quench