2015/05/31 by Angelo Russomanno, Shraddha Sharma, Amit Dutta +2
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Critical point (mathematics) #Dirac delta function #Essential singularity #Floquet theory #Function (biology) #Ising model #Quantum chaos and dynamical systems #Quantum many-body systems #Singularity #Square lattice #Transverse plane #Work (physics) #cond-mat.quant-gas #quant-ph
paper · pdf · doi:10.1088/1742-5468/2015/08/p08030
published as Jour. Stat. Mech. (2015) P08030 · 24 pages, 5 figures, published in Jour. Stat. Mech. Corrected error in the demonstration of appendix C
openalex publication_date 2015/08/26 · arxiv created 2015/11/19 · arxiv updated 2015/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the work statistics of a periodically-driven integrable closed quantum system, addressing in particular the role played by the presence of a quantum critical point. Taking the example of a one-dimensional transverse Ising model in the presence of a spatially homogeneous but periodically time-varying transverse field of frequency , we arrive at the characteristic cumulant generating function G ( u ), which is then used to calculate the work distribution function P ( W ). By applying the Floquet theory we show that, in the infinite time limit, P ( W ) converges, starting from the initial ground state, towards an asymptotic steady state value whose small- W behaviour depends only on the properties of the small-wave-vector modes and on a few important ingredients: the time-averaged value of the transverse field, h 0 , the initial transverse field, , and the equilibrium quantum critical point , which we find to generate a sequence of non-equilibrium critical points , with l integer. When , we find a ‘universal’ edge singularity in P ( W ) at a threshold value of which is entirely determined by . The form of that singularity—Dirac delta derivative or square root—depends on h 0 being or not at a non-equilibrium critical point h * l . On the contrary, when , G ( u ) decays as a power-law for large u , leading to different types of edge singularity at . Generalizing our calculations to the case in which we initialize the system in a finite temperature density matrix, the irreversible entropy generated by the periodic driving is also shown to reach a steady state value in the infinite time limit.