Universal properties from quantum many-body dynamics

Abstract

The Loschmidt echo—the amplitude for a quantum state to return to itself—provides a route to the universal properties of a critical many-body system. Continued from real to imaginary time, it becomes the partition function of a conformal field theory on a strip, and its universal data—the central charge and the operator content—are encoded in the spectrum of a transfer matrix, obtained by contracting the space–time tensor network along the space direction. We apply this framework to a transverse-field Ising model extended by a nextnearest-neighbour coupling: a non-integrable chain that remains critical and in the Ising universality class over a wide range of that coupling. After a quench to the critical point, the temporal entanglement that governs the cost of the transverse contraction grows only logarithmically with the evolution time, so the method remains efficient at times where conventional evolution algorithms are limited by the entanglement barrier. We develop a translation-invariant matrix product operator, accurate to second order in the time step, that represents the time evolution of the model, and use two power methods to compute the leading eigenvectors and eigenvalues of the resulting non-Hermitian transfer matrix. Within the accessible time windows, our results are consistent with the central charge and operator content predicted by the Ising universality class.