@article{FumaniNematiMahdavifar2020,
  author    = {Fumani, F. Khastehdel and Nemati, Somayyeh and Mahdavifar, Saeed},
  title     = {Quantum critical lines in the ground state phase diagram of spin-1/2 frustrated transverse-field ising chains},
  series = {Annalen der Physik},
  volume    = {533},
  journal   = {Annalen der Physik},
  number    = {2},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0003-3804},
  doi       = {10.1002/andp.202000384},
  pages     = {8},
  year      = {2020},
  abstract  = {This paper focuses on the ground state phase diagram of a 1D spin-1/2 quantum Ising model with competing first and second nearest neighbour interactions known as the axial next nearest neighbour Ising model in the presence of a transverse magnetic field. Here, using quantum correlations, both numerically and analytically, some evidence is provided to clarify the identification of the ground state phase diagram. Local quantum correlations play a crucial role in detecting the critical lines either revealed or hidden by symmetry-breaking. A non-symmetry-breaking disorder transition line can be identified by the first derivative of both entanglement of formation and quantum discord between nearest neighbour spins. In addition, the quantum correlations between the second neighbour spins can also be used to reveal Kosterlitz-Thouless phase transition when their interaction strength grows and becomes closer to the first nearest neighbour one. The results obtained using the Jordan-Wigner transformation confirm the accuracy of the numerical case.},
  language  = {en}
}
@article{ArrighiNesmeWerner2011,
  author    = {Arrighi, Pablo and Nesme, Vincent and Werner, Reinhard F.},
  title     = {One-Dimensional quantum cellular automata},
  series = {International journal of unconventional computing : non-classical computation and cellular automata},
  volume    = {7},
  journal   = {International journal of unconventional computing : non-classical computation and cellular automata},
  number    = {4},
  publisher = {Old City Publishing Science},
  address   = {Philadelphia},
  issn      = {1548-7199},
  pages     = {223 -- 244},
  year      = {2011},
  abstract  = {We define and study quantum cellular automata (QCA). We show that they are reversible and that the neighborhood of the inverse is the opposite of the neighborhood. We also show that QCA always admit, modulo shifts, a two-layered block representation. Note that the same two-layered block representation result applies also over infinite configurations, as was previously shown for one-dimensional systems in the more elaborate formalism of operators algebras [18]. Here the proof is simpler and self-contained, moreover we discuss a counterexample QCA in higher dimensions.},
  language  = {en}
}