Emergent geometry from entanglement distribution

Entanglement is one of the most relevant features of the quantum world, constituting the main resource in quantum technologies and characterizing the different phases of quantum matter. Study of the distribution of quantum entanglement in different parts of the quantum many-body states often unveils many interesting features related to the physical system. In this talk, I will discuss one such interesting feature, namely, the area law for the entanglement entropy of low-energy states of local Hamiltonians. In particular, I will present results from our recent works where we attempt to explore the connection between the area-law for entanglement and geometry, which emerges from the distribution of quantum entanglement across all possible bipartitions of a pure quantum many-body state. I will discuss the methodology in detail, along with some numerical as well as exact results. In addition to this, some examples will be shown where the geometry stems from the entanglement distribution may lead to a geometry very different than suggested by the Hamiltonian.

Reference: 

[1] Phys. Rev. B 101, 195134 (2020).

[2] J. Phys. A: Math. Theor. 54 305301 (2021).