Quantum Phase Transitions In Spin-1 Research Articles

Entropic uncertainty relation and quantum phase transition in spin-1/2 Heisenberg chain

Based on the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), we study the quantum phase transition (QPT) of a spin-1/2 frustrated Heisenberg chain and show that QMA entropy can be a useful tool to detect QPT. For the six-site case, we choose the reduced two-site as the detecting system and obtain the analytical result of QMA entropy and its bound. We find that the QMA entropy of the ground state is discontinuous at the first-order QPT point. Meanwhile for the excited state, the catastrophe point of QMA entropy approaches the infinite-order QPT point, which is confirmed by the numerical results in the 8-, 10- and 12-site cases. Moreover, we study the behavior of QMA entropy undergoing the dephasing process. Interestingly, two-site QMA entropy can still indicate the QPT point when the state degenerates into a mixed state. In this sense, QMA entropy is more effective than quantum correlation in reflecting the quantum criticality.

Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the $SU(2)$ symmetry and $Z_{2}$ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.

Magnetism and quantum phase transitions in spin-1/2 attractive fermions with polarization

An extensive investigation is given for magnetic properties and phase transitions in one-dimensional (1D) Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means of the dressed energy formalism. An iteration method is presented to derive higher order corrections for the ground-state energy, critical fields and magnetic properties. Numerical solutions of the dressed energy equations confirm that the analytic expressions for these physical quantities and resulting phase diagrams are highly accurate in the weak and strong coupling regimes, capturing the precise nature of magnetic effects and quantum phase transitions in 1D interacting fermions with population imbalance. Moreover, it is shown that the universality class of linear field-dependent behaviour of the magnetization holds throughout the whole attractive regime.

Reduced fidelity and quantum phase transitions in spin-1/2 frustrated Heisenberg chains

We use reduced fidelity to characterize quantum phase transitions in the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain with frustration. For the ground state and the low-lying excited states, explicit results of the reduced fidelities between the nearest-neighbor and next-nearest-neighbor spins are given in both the even-size and odd-size cases. We find the reduced fidelity is an effective tool in detecting the quantum phase transitions associated with level crossings for the finite-size systems. Interestingly, the reduced fidelity between next-nearest-neighbor spins is evidently more sensitive at the quantum phase transition points than the nearest-neighbor case. Moreover, the reduced fidelity of the low-lying excited states is a good indicator both for the first-order and infinite-order quantum phase transitions of the system.