Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo

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.

10+10 pages, 4+12 figures

References in corpus (15)

• Entanglement negativity in quantum field theory
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Genuine Multipartite Entanglement in the Cluster-Ising Model
• Entanglement negativity between separated regions in quantum critical systems
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Diagnosing $SO(5)$ Symmetry and First-Order Transition in the $J-Q_3$ Model via Entanglement Entropy
• Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
• Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• The teaching from entanglement: 2D SU(2) antiferromagnet to valence bond solid deconfined quantum critical points are not conformal
• Finite Temperature Entanglement Negativity of Fermionic Symmetry Protected Topological Phases and Quantum Critical Points in One Dimension
• The Fate of Entanglement
• Separable Ball around any Full-Rank Multipartite Product State

Cited by in corpus (6)

• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Robustness of Magic in the quantum Ising chain via Quantum Monte Carlo tomography
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Long-range multipartite entanglement near measurement-induced transitions
• Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach
• Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d