Longitudinal magnetization dynamics in the quantum Ising ring: A Pfaffian method based on correspondence between momentum space and real space
Abstract
As perhaps the most studied paradigm for a quantum phase transition, the periodic quantum Ising chain is exactly solvable via the JordanWigner transformation followed by a Fourier transform that diagonalizes the model in the momentum space of spinless fermions. Although the above procedures are wellknown, there remain some subtle points to be clarified regarding the correspondence between the realspace and momentumspace representations of the finitesize quantum Ising ring, especially those related to fermion parities. In this work, we establish the relationship between the two fully aligned ferromagnetic states in real space and the two degenerate momentumspace ground states of the classical Ising ring, with the former being a special case of the factorized ground states of the more general X Y Z model on the frustrationfree hypersurface. Based on this observation, we then provide a Pfaffian formula for calculating realtime dynamics of the paritybreaking longitudinal magnetization with the system initially prepared in one of the two ferromagnetic states and under translationally invariant drivings. The formalism is shown to be applicable to large systems with the help of online programs for the numerical computation of the Pfaffian, thus providing an efficient method to numerically study, for example, the emergence of discrete time crystals in related systems.
 Publication:

Physical Review E
 Pub Date:
 April 2020
 DOI:
 10.1103/PhysRevE.101.042108
 arXiv:
 arXiv:2001.00511
 Bibcode:
 2020PhRvE.101d2108W
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 14 pages, 4 figures, to appear in Physical Review E