Entanglement in Many-Body Systems

TL;DR

Entanglement in Many-Body Systems surveys how quantum correlations manifest in interacting spin, fermionic, and bosonic lattices across zero and finite temperatures. It surveys measures and witnesses, then details model systems (spin chains, Hubbard-type models, spin-boson and harmonic lattices) and their pairwise and multipartite entanglement properties, including entanglement entropy and localizable entanglement. A central theme is the connection between entanglement and quantum phase transitions, area laws, and topological order, extended to dynamics, quenches, and RG flow. The work underscores both the theoretical frameworks (convex roofs, monogamy, Gaussian entanglement, MPS/DMRG) and experimental prospects for detecting entanglement via thermodynamic witnesses, susceptibilities, or macroscopic responses. Overall, it highlights how entanglement serves as a unifying lens to understand phases, criticality, and information processing in many-body quantum systems, with strong implications for future quantum technologies and fundamental physics.

Abstract

The recent interest in aspects common to quantum information and condensed matter has prompted a prosperous activity at the border of these disciplines that were far distant until few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermionic and bosonic model systems. Both bipartite and multipartite entanglement will be considered. At equilibrium we emphasize on how entanglement is connected to the phase diagram of the underlying model. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians.

Figures (29)

• Figure 1: A cartoon of the nearest neighbour valence bond state, exact ground state of the spin-$1$ model in Eq.(\ref{['haldane-phase']}) for $\beta=1/3$ (AKLT-model). The ground state is constructed regarding every $S=1$ in the lattice sites as made of a pair of $S=1/2$, and projecting out the singlet state. The singlets are then formed taking pairs of $S=1/2$ in nearest neighbor sites.
• Figure 2: The derivative of the nearest neighbor concurrence as a function of the reduced coupling strength. The curves correspond to different lattice sizes. On increasing the system size, the minimum gets more pronounced and the position of the minimum tends as (see the left side inset) towards the critical point where for an infinite system a logarithmic divergence is present. The right hand side inset shows the behavior of the concurrence for the infinite system. The maximum is not related to the critical properties of the Ising model. [From OstNat]
• Figure 3: Nearest neighbor concurrence of the $XXZ$ model. [From GuLinLi03]
• Figure 4: The rescaled concurrence of the antiferromagnetic LMG model. The first order transition occurs at $h=0$. [From Vidal-Mosseri03]
• Figure 5: The rescaled concurrence between two atoms in the Dicke mode. The concurrence is rescaled in both for finite $N$ and in the thermodynamic limit. The inset shows the finite size scaling. [From lambert04]