Detecting quantum phase transitions via out-of-time-ordered correlators without time reversal

We propose a dynamical method to connect quantum phase transitions (QPTs) and quantum coherence via out-of-time-ordered correlators (OTOCs), which measure the spread of quantum information in a many-body system. Using iconic examples of QPTs, we show that an abrupt change in coherence and entanglement of the ground state across a QPT is observable in the spectrum of multiple quantum coherences, a special type of OTOC first developed in NMR spectroscopy. We develop a robust protocol to obtain the relevant OTOCs using quasi-adiabatic ramps, alleviating the need for time reversal of coherent dynamics [1]. Our protocol is applicable for a broad range of current experiments in trapped ions and optical tweezer arrays.

[1] R. J. Lewis-Swan, S. R. Muleady, A. M. Rey, Phys. Rev. Lett. 125, 240605 (2020).