Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo
arxiv(2024)
摘要
We develop a protocol, dubbed entanglement microscopy, to obtain the full
reduced density matrix associated with subregions in quantum Monte Carlo
simulations for bosonic and fermionic manybody systems. Our microscopy allows
to perform quantum state tomography, and thus gives access to true entanglement
measures, such as the logarithmic negativity (LN). 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 in a large
parameter window near the Ising QCP in 2d, in contrast to 1d. We also
analytically obtain the large-temperature power law scaling of the fermionic LN
for general interacting systems. Our approach allows one to perform quantum
state tomography locally in a way that is analogous to atomic-scale imaging
with a scanning tunneling microscope. Controlled entanglement microscopy opens
a new window into quantum matter, with countless systems waiting to be
explored.
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