Classical periodic orbits reveal quantum many-body scars

A new algorithm finds non-thermalizing quantum states by looking for the periodic orbits of a classical dynamical system.

Quantum many-body scars are states that refuse to thermalize: a system prepared in one of them keeps coming back to where it started instead of spreading its energy over all of its degrees of freedom. In Finding Periodic Orbits in Projected Quantum Many-Body Dynamics, published in PRX Quantum, Elena Petrova, Marko Ljubotina, Gökhan Yalnız and Maksym Serbyn locate these states by turning the quantum problem into a classical one. The variational principle projects the full quantum dynamics onto a small set of classical equations of motion, and the periodic orbits of those equations mark where the scars sit. Enlarging the set of states used in the projection sharpens the result the way a stronger magnification sharpens a microscope image, so the algorithm can be pushed until it recovers as much of the quantum system as one needs. The same construction also finds long-lived states in periodically driven systems, which are expected to heat up and sometimes fail to. The work grew out of a collaboration with Gökhan Yalnız from Björn Hof’s group at ISTA, where periodic orbits are a standard tool for understanding turbulence; ISTA has written a news article about it.