Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo

TL;DR

This paper introduces entanglement microscopy, a method to analyze multipartite entanglement in many-body quantum systems, revealing critical behavior and entanglement properties near quantum phase transitions in spin and fermionic models.

Contribution

The paper develops a novel protocol for tomography and entanglement measures using quantum Monte Carlo, applied to complex many-body systems near critical points, including multipartite entanglement analysis.

Findings

Ising QCP shows short-range entanglement with finite entanglement sudden death.

Gross-Neveu QCP exhibits power-law decaying fermionic logarithmic negativity consistent with CFT.

No detectable three-party entanglement near the Ising QCP in 2D with current witnesses.

Abstract

We employ a protocol, dubbed entanglement microscopy, to reveal the multipartite entanglement encoded in the full reduced density matrix of microscopic subregion both in spin and fermionic many-body systems. We exemplify our method by studying the phase diagram near quantum critical points (QCP) in 2 spatial dimensions: the transverse field Ising model and a Gross-Neveu-Yukawa transition of Dirac fermions. Our main results are: i) the Ising QCP exhibits short-range entanglement with a finite sudden death of the LN both in space and temperature; ii) the Gross-Neveu QCP has a power-law decaying fermionic LN consistent with conformal field theory (CFT) exponents; iii) going beyond bipartite entanglement, we find no detectable 3-party entanglement with our two witnesses in a large parameter window near the Ising QCP in 2d, in contrast to 1d. We further establish the singular scaling of general multipartite entanglement measures at criticality, and present an explicit analysis in the tripartite case. We also analytically obtain the large-temperature power-law scaling of the fermionic LN for general interacting systems. Entanglement microscopy opens a rich window into quantum matter, with countless systems waiting to be explored.