Diagnosing phase transitions through time scale entanglement

Abstract

Spatial entanglement of wave functions has matured into an enthralling and very active research area. Here, we unearth a completely different kind of entanglement, the entanglement between different time scales. This is feasible through quantics tensor train diagnostics (QTTD), wherein the bond dimension for an -particle correlation function allows diagnosing the temporal entanglement. As examples, we study time-scale entanglement of the Hubbard dimer, the four-site Hubbard ring with and without next-nearest neighbor hopping and the single-impurity Anderson model. Besides introducing the QTTD method, our major finding is that the time-scale entanglement is generically maximal at phase transitions and crossovers. This is independent of the correlation function studied. Thus, QTTD is a universal tool for detecting quantum phase transitions, ground state crossings in finite systems, and thermal crossovers.