Odd thermodynamic limit for the Loschmidt echo
Abstract
Is it possible to readily distinguish a system made by an Avogadro's number of identical elements and one with a single additional one? Usually, the answer to this question is negative but, in this work, we show that in antiferromagnetic quantum spin rings a simple outofequilibrium experiment can do so, yielding two qualitatively and quantitatively different outcomes depending on whether the system includes an even or an odd number of elements. We consider a local quantumquench setup and calculate a generating function of the work done, namely, the Loschmidt echo, showing that it displays different features depending on the presence or absence of topological frustration, which is triggered by the even/oddness in the number of the chain sites. We employ the prototypical quantum Ising chain to illustrate this phenomenology, which we argue being generic for antiferromagnetic spin chains, as it stems primarily from the different low energy spectra of frustrated and nonfrustrated chains. Our results thus prove that these wellknown spectral differences lead indeed to distinct observable characteristics and open the way to harvest them in quantum thermodynamics protocols.
 Publication:

Physical Review B
 Pub Date:
 May 2022
 DOI:
 10.1103/PhysRevB.105.184424
 arXiv:
 arXiv:2105.06483
 Bibcode:
 2022PhRvB.105r4424T
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 10 pages, 3 figures. Updated to published version