TY  - JOUR
A1  - Fumani, F. Khastehdel
A1  - Nemati, Somayyeh
A1  - Mahdavifar, Saeed
T1  - Quantum critical lines in the ground state phase diagram of spin-1/2 frustrated transverse-field ising chains
JF  - Annalen der Physik
N2  - 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.
KW  - axial next nearest neighbour Ising chains
KW  - quantum correlations
KW  - quantum
KW  - phase transitions
Y1  - 2020
U6  - https://doi.org/10.1002/andp.202000384
SN  - 0003-3804
SN  - 1521-3889
VL  - 533
IS  - 2
PB  - Wiley-VCH
CY  - Weinheim
ER  - 
TY  - JOUR
A1  - Arrighi, Pablo
A1  - Nesme, Vincent
A1  - Werner, Reinhard F.
T1  - One-Dimensional quantum cellular automata
JF  - International journal of unconventional computing : non-classical computation and cellular automata
N2  - 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.
KW  - cellular automata
KW  - quantum
KW  - neighborhood
KW  - block representation
Y1  - 2011
SN  - 1548-7199
VL  - 7
IS  - 4
SP  - 223
EP  - 244
PB  - Old City Publishing Science
CY  - Philadelphia
ER  -