Genuine tripartite entanglement and quantum phase transition

A new simplified formula is presented to characterize genuine tripartite entanglement of （2 2 n）-dimensional quantum pure states. The formula turns out equivalent to that given in （Quant. Inf. Comp. 7（7） 584 （2007））, hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local （2 2）-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang （Phys. Rev. A 71 030302（R） （2005）） are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.

First-order quantum phase transition and entanglement in the Jaynes-Cummings model with a squeezed light

We study the quantum phase transition and entanglement in the Jaynes-Cummings model with squeezed light,utilize a special transformation method to obtain the analytical ground state of the model within the near-resonance regime,and numerically verify the validity of the analytical ground state.It is found that the ground state exhibits a first-order quantum phase transition at the critical point linearly induced by squeezed light,and the ground state entanglement reaches its maximum when the qubit-field coupling strength is large enough at the critical point.

Entanglement Entropy Signature of Quantum Phase Transitions in a Multiple Spin Interactions Model

Through the Jordan Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green＇s function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition （QPT）. In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order OPT at the tricritical point and an additional new phase called ＂spin waves＂, which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.

Entanglement in the Quantum Phase Transition of the Half-Integer Spin One-Dimensional Heisenberg Model

We use the Bethe’s ansatz method to study the entanglement of spinons in the quantum phase transition of half integer spin one-dimensional magnetic chains known as quantum wires. We calculate the entanglement in the limit of the number of particles . We obtain an abrupt change in the entanglement next the quantum phase transition point of the anisotropy parameter ?from the gapped phase ?to gapless phase .

Entanglement and quantum phase transition in the Heisenberg-Ising model

We use the quantum renormalization-group（QRG） method to study the entanglement and quantum phase transition（QPT） in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.（N.Y.） 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.

Critical entanglement and geometric phase of a two-qubit model with Dzyaloshinski-Moriya anisotropic interaction

We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski Moriya （DM） anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition （QPT）. It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.

Implementing remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems

We propose a scheme for the implementation of remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems. The proposed scheme uses the two ground states of the A-type ions as memory instead of the vibrational mode. And the system is robust against the spontaneous radiation and the dephasing.

Detecting the quantum phase transition from the perspective of quantum information in the Aubry–André model

We investigate the effectiveness of entropic uncertainty, entanglement and steering in discerning quantum phase transitions(QPTs). Specifically, we observe significant fluctuations in entropic uncertainty as the driving parameter traverses the phase transition point. It is observed that the entropic uncertainty, entanglement and quantum steering, based on the electron distribution probability, can serve as indicators for detecting QPTs. Notably, we reveal an intriguing anticorrelation relationship between entropic uncertainty and entanglement in the Aubry–André model. Moreover, we explore the feasibility of detecting a QPT when the period parameter is a rational number. These observations open up new and efficient avenues for probing QPTs.

Quantum phase transition and entanglement in Heisenberg XX spin chain with impurity

In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch.

Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains:Effect of the Dzyaloshinski-Moriya interaction

We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya （DM） interaction, and investigate the effect of the DM interaction on the quantum phase transition （QPT） of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.

The Influence of Entanglements of Net Chains on Phase Transition Temperature of Sensitive Hydrogels in Chemo-Mechanical Coupled Fields

Phase transition of hydrogel,which is polymerized by polymer network,can be regarded as the transition of polymer network stability.The stability of the polymer network might be changed when the external environment changed.This change will lead to the transformation of sensitive hydrogels stability,thus phase transition of hydrogel take place.Here,we present a new free density energy function,which considers the non-gaussianity of the polymer network,chains entanglement and functionality of junctions through adding Gent hyplastic model and Edwards-Vilgis slip-link model to Flory-Huggins theory.A program to calculate the phase transition temperature was written based on new free energy function.Taking PNIPAM hydrogel as an example,the effects of network entanglement on the phase transition temperature of hydrogel were studied by analyzing the microstructure parameters of the hydrogel networks.Analytical results suggest a significant relationship between phase transition temperature and entanglement network.

Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions

We study the dynamical quantum phase transitions(DQPTs)in the XY chains with the Dzyaloshinskii-Moriya interaction and the XZY-YZX type of three-site interaction after a sudden quench.Both the models can be mapped to the spinless free fermion models by the Jordan-Wigner and Bogoliubov transformations with the form■where the quasiparticle excitation spectraεkmay be smaller than 0 for some k and are asymmetrical■It is found that the factors of Loschmidt echo equal 1 for some k corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfyingε_(k)·ε_(-k)<0,when the quench is from the gapless phase.By considering the quench from different ground states,we obtain the conditions for the occurrence of DQPTs for the general XY chains with gapless phase,and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase.This is different from the DQPTs in the case of quench from the gapped phase to gapped phase,in which the DQPTs will always appear.Moreover,we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase.The conclusion can also be extended to the general quantum spin chains.

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z_2 Topological Insulator

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator（TI） and topological crystalline insulator（TCI） in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.

Floquet dynamical quantum phase transitions in transverse XY spin chains under periodic kickings

Floquet dynamical quantum phase transitions(DQPTs),which are nonanalytic phenomena recuring periodically in time-periodic driven quantum many-body systems,have been widely studied in recent years.In this article,the Floquet DQPTs in transverse XY spin chains under the modulation ofδ-function periodic kickings are investigated.We analytically solve the system,and by considering the eigenstate as well as the ground state as the initial state of the Floquet dynamics,we study the corresponding multiple Floquet DQPTs emerged in the micromotion with different kicking moments.The rate function of return amplitude,the Pancharatnam geometric phase and the dynamical topological order parameter are calculated,which consistently verify the emergence of Floquet DQPTs in the system.

Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition （ESQPT） in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.

Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems

We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence（SC） and square of quantum discord（SQD）. The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.

Discord under the influence of a quantum phase transition

This paper studies the discord of a bipartite two-level system coupling to an XY spin-chain environment in a transverse field and investigates the relationship between the discord property and the environment＇s quantum phase transition. The results Show that the quantum discord is also able to characterize the quantum phase transitions. We also discuss the difference between discord and entanglement, and show that quantum discord may reveal more general information than quantum entanglement for characterizing the environment＇s quantum phase transition.

Effect of interaction and temperature on quantum phase transition in anisotropic square-octagon lattice

We investigate the effect of interaction, temperature, and anisotropic parameter on the quantum phase transitions in an anisotropic square-octagon lattice with fermions under the framework of the single band Hubbard model through using the combination of cellular dynamical mean field theory and a continuous time Monte Carlo algorithm. The competition between interaction and temperature shows that with the increase of the anisotropic parameter, the critical on-site repulsive interaction for the metal-insulator transition increases for fixed temperature. The interaction-anisotropic parameter phase diagram reveals that with the decrease of temperature, the critical anisotropic parameter for the Mott transition will increase for fixed interaction cases.

Atom-pair tunneling and quantum phase transition in asymmetry double-well trap in strong-interaction regime

The quantum effect of nonlinear co-tunnelling process, which is dependent on atom-pair tunneling and asymmetry of an double-well trap, is studied by using an asymmetrical extended Bose–Hubbard model. Due to the existence of atompair tunneling that describes quantum phenomena of ultracold atom-gas clouds in an asymmetrical double-well trap, the asymmetrical extended Bose–Hubbard model is better than the previous Bose–Hubbard model model by comparing with the experimental data cited from the literature. The dependence of dynamics and quantum phase transition on atom-pair tunneling and asymmetry are investigated. Importantly, it shows that the asymmetry of the extended Bose–Hubbard model,corresponding to the bias between double wells, leads to a number of resonance tunneling processes, which tunneling is renamed conditional resonance tunneling, and corrects the atom-number parity effect by controlling the bias between double wells.

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic ＂Landau＂ potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.