We study the magnetic behaviors of a spin-1/2 quantum compass chain (QCC) in a transverse magnetic field, by means of the analytical spinless fermion approach and numerical Lanczos method. In the absence of the magnetic field, the phase diagram is divided into four gapped regions. To determine what happens by applying a transverse magnetic field, using the spinless fermion approach, critical fields are obtained as a function of exchanges. Our analytical results show, the field-induced effects depend on in which one of the four regions the system is. In two regions of the phase diagram, the Ising-type phase transition happens in a finite field. In another region, we have identified two quantum phase transitions in the ground state magnetic phase diagram. These quantum phase transitions belong to the universality class of the commensurate-incommensurate phase transition. We also present a detailed numerical analysis of the low energy spectrum and the ground state magnetic phase diagram. In particular, we show that the intermediate state (hc 1 < h < hc 2 ) is gapful, describing the spin-flop phase.

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We study fidelity and fidelity susceptibility by addition of entanglement of entropy in the onedimensional quantum compass model in a transverse magnetic field. All four recognized gapped regions in the ground-state phase diagram (GSPD) are in the range of our calculation. We show that the difference between the position of the sharp drop of fidelity h * from real critical field hc is inversely related to the number of particles (N ) with a relation such as h * = hc + Σj cjN −1/ν for a finite chain. In this relation ν is the correlation length critical exponent. The scaling behavior of the extremum of fidelity susceptibility shows that the amount of ν depends on the selected area of GSPD. Furthermore, we calculated a recently proposed quantum information theoretic measure, Von-Neumann entropy, and show that this measure provides appropriate signatures of the quantum phase transitions (QPT)s occurring at the critical fields. We calculated Von-Neumann entropy between one-, two-and three-particle blocks with the rest of the system. We show that in an alternating model such as quantum compass model, the value of entanglement between a twoparticle block with the rest of the system is more dependent on the power of exchange couplings connecting the block with the rest of the system than the power of exchange coupling between two particles in the own block. In other words, a pair with a strong coupling does not see the rest of the system. Also, in some areas of GSPD, amount of entanglement of a two-particle block in an odd link is the same as that of an even link in a factorized point independent on where the block is.

Motivated by the ability of triangular spin ladders to implement quantum information processing, we propose a type of such systems whose Hamiltonian includes the XX Heisenberg interaction on the rungs and Dzyaloshinskii–Moriya (DM) coupling over the legs. In this work, we discuss how tuning the magnetic interactions between elements of a nanomagnetic cell which contains four qubits influences on the dynamical behavior of entanglement shared between any pairs of the system. In this work, we make use of concurrence for monitoring entanglement. It is realized that the generation of quantum W states is an important feature of the present model when the system evolves unitarily with time. In general, coincidence with the emergence of W states, the concurrences of all pairs are equal to 2/N, where N is the number of system’s qubits. We also obtain the precise relationship between the incidence of such states and the value of DM interaction as well as the time of entanglement transfer. Finally, by studying the two-point quantum correlations and expectation values of different spin variables, we find that xx and yy correlations bring the entanglement to a maximum value for W states, whereas for these states, zz correlation between any pairs completely quenches. Our results reveal that although does not commute with the system’s Hamiltonian, its expectation value remains constant during time evolution which is a generic property of quantum W states.

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