ELFT HÍRADÓ

[Szeminárium koordinátor <sem-admin AT szfki.hu>]

SZFI SeminarJuhász RóbertWigner RCP SZFIExact bounds on the energy gap of 
transverse-field Ising chains by mapping to random walksTuesday, 12 September 
2023, 10:00, KFKI Campus, Bldg. 1, 2nd floor, Conference RoomBased on a 
relationship with continuous-time random walks discovered by Iglói, Turban, 
and Rieger [Phys. Rev. E 59, 1465 (1999)], we derive exact lower and upper 
bounds on the lowest energy gap of open transverse-field Ising chains, which 
are explicit in the parameters and are generally valid for arbitrary sets of 
possibly random couplings and fields. In the homogeneous chain and in the 
random chain with uncorrelated parameters, both the lower and upper bounds 
are found to show the same finite-size scaling in the ferromagnetic phase and 
at the critical point, demonstrating the ability of these bounds to infer the 
correct finite-size scaling of the critical gap. Applying the bounds to 
random transverse-field Ising chains with coupling-field correlations, a 
model which is relevant for adiabatic quantum computing, the finite-size 
scaling of the gap is shown to be related to that of sums of independent 
random variables. We determine the critical dynamical exponent of the model 
and reveal the existence of logarithmic corrections at special points. 
Reference: R. Juhász, Phys. Rev. B 106, 064204 (2022). Minden érdeklődőt 
szívesen látunk! - Everyone is welcome to attend.Attila Nagysem-admin AT szfki.hu