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

TL;DR

This paper investigates how a power-law trapping potential influences the scaling of bipartite entanglement in one-dimensional lattice systems at quantum criticality, revealing logarithmic divergence with trap size.

Contribution

It provides a detailed analysis of entanglement scaling under trapping potentials in 1D systems, combining conformal field theory with numerical studies of XY and Bose-Hubbard models.

Findings

Entanglement entropies diverge logarithmically with trap size.

Trapping potential breaks conformal invariance, altering critical behavior.

Scaling laws depend on trap parameters and system specifics.

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.