Scaling of bipartite entanglement in one-dimensional lattice systems with a trapping potential

Abstract

We study the effects of a power-law trapping potential on the scaling behaviour of the entanglement at the quantum critical point of one-dimensional (1D) lattice particle systems. We compute bipartite von Neumann and Renyi entropies in the presence of the trap, and analyze their scaling behaviour with increasing the trap size. As a theoretical laboratory, we consider the quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We then investigate confined particle systems described by the 1D Bose-Hubbard model in the superfluid phase (around the center of the trap). In both cases conformal field theory predicts logarithmically divergent bipartite entanglement entropies for the homogeneous systems without trap. The presence of the trapping potential breaks conformal invariance, affecting the critical behaviour of the homogeneous system. Our results show that the bipartite entanglement entropies diverge logarithmically with increasing the trap size, and present notable scaling behaviours in the trap-size scaling limit.

25 pages, 38 figs, corrected some misprints

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Entanglement spectrum in one-dimensional systems
• Formation of spatial shell structures in the superfluid to Mott insulator transition
• Parity effects in the scaling of block entanglement in gapless spin chains
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Exact relationship between the entanglement entropies of XY and quantum Ising chains
• Entanglement in spin chains with gradients
• Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice

Cited by in corpus (26)

• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• The entanglement entropy of one-dimensional gases
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Exact relations between particle fluctuations and entanglement in Fermi gases
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Finite-size scaling at quantum transitions
• Random matrices and entanglement entropy of trapped Fermi gases
• Entanglement spectrum of random-singlet quantum critical points
• Entanglement entropy of two disjoint intervals in c=1 theories
• Entanglement Entropy of Quantum Wire Junctions
• The entanglement entropy of 1D systems in continuous and homogenous space
• Entanglement and particle correlations of Fermi gases in harmonic traps
• Equilibrium and off-equilibrium trap-size scaling in 1D ultracold bosonic gases
• Corrections to scaling for block entanglement in massive spin-chains
• Surface and bulk entanglement in free-fermion chains
• Scaling properties of work fluctuations after quenches at quantum transitions
• Critical parameters from trap-size scaling in trapped particle systems
• Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap
• Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles
• Quasi-long-range order in trapped systems
• Entanglement in composite free-fermion systems
• Information measures for a local quantum phase transition: Lattice bosons in a one-dimensional harmonic trap
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions
• Critical dynamics in trapped particle systems
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss