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.

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.

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.

A scheme for conditional quantum phase gate via bimodal cavity and a∧-type three-level atom

We propose a scheme to implement a two-qubit conditional quantum phase gate for the intracavity field via a single three-level ∧-type atom driven by two modes in a high-Q cavity. The quantum inforraation is encoded on the Fock states of the bimodal cavity. The gate＇s averaged fidelity is expected to reach 99.8%.

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.

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.

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.

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.

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.

Implementation of quantum phase gate between two atoms via Rydberg antiblockade and adiabatic passage

Combining adiabatic passage and Rydberg antiblockade, we propose a scheme to implement a two-qubit phase gate between two Rydberg atoms. Detuning parameters between frequencies of atomic transitions and those of the corresponding driving lasers are carefully chosen to offset the blockade effect of two Rydberg atoms, so that an effective Hamiltonian,representing a single-photon detuning L-type three-level system and concluding the quantum state of two Rydberg atoms excited simultaneously, is obtained. The adiabatic-passage technique, based on the effective Hamiltonian, is adopted to implement a two-atom phase gate by using two time-dependent Rabi frequencies. Numerical simulations indicate that a high-fidelity two-qubit p-phase gate is constructed and its operation time does not have to be controlled accurately. Besides,owing to the long coherence time of the Rydberg state, the phase gate is robust against atomic spontaneous emission.

Fidelity spectrum:A tool to probe the property of a quantum phase

Fidelity measures the similarity between two states and is widely adapted by the condensed matter community as a probe of quantum phase transitions in many-body systems. Despite its success in witnessing quantum critical points, information about the fine structure of a quantum phase one can get from this approach is still limited. Here, we proposed a scheme called fidelity spectrum, By studying the fidelity spectrum, one can obtain information about the characteristics of a phase. In particular, we investigated the spectra in the one-dimensional transverse-field Ising model and the two- dimensional Kitaev model on a honeycomb lattice. It was found that the sPectra have qualitative differences in the critical and non-critical regions of the two models. From the distributions of them, the dominating k modes in a particular phase could also be captured.

Hybrid of Quantum Phases for Induced Dipole Moments

The quantum phase effects for induced electric and magnetic dipole moments are investigated. It is shown that the phase shift received by the induced electric dipole has the same form as the one induced by magnetic dipole moment, therefore the total phase is a hybrid of these two types of phase. This feature indicates that to have a decisive measurement on either one of these two phases, it is necessary to measure the velocity dependence of the observed phase.

A scheme of quantum phase gate for trapped ion

We propose a scheme to implement two-qubit controlled quantum phase gate（CQPG） via a single trapped two-level ion located in the standing wave field of a quantum cavlty, in which the trap works beyond the Lamb--Dicke limit. When the light field is resonant with the atomic transition ｜g） →← ｜e） of the ion located at the antinode of the standing wave, we can perform CQPG between the internal and external states of the trapped ion; while the frequency of the light field is chosen to be resonant with the first red sideband of the collective vibrational mode of the ion located at the node of the standing wave, we can perform CQPG between the cavity mode and the collective vibrational mode of the trapped ion. Neither the Lamb--Dicke approximation nor the assistant classical laser is needed. Also we can generate a GHZ state if assisted with a classical laser.

Quantum phase transition and Coulomb blockade effect in triangular quantum dots with interdot capacitive and tunnel couplings

The quantum phase transition and the electronic transport in a triangular quantum dot system are investigated using the numerical renormalization group method.We concentrate on the interplay between the interdot capacitive coupling V and the interdot tunnel coupling t.For small t,three dots form a local spin doublet.As t increases,due to the competition between V and t,there exist two first-order transitions with phase sequence spin-doublet-magnetic frustration phase-orbital spin singlet.When t is absent,the evolutions of the total charge on the dots and the linear conductance are of the typical Coulomb-blockade features with increasing gate voltage.While for sufficient t,the antiferromagnetic spin correlation between dots is enhanced,and the conductance is strongly suppressed for the bonding state is almost doubly occupied.

Quantum phases of Bose gases on a lattice with pair-tunneling

We investigate the strongly interacting lattice Bose gases on a lattice with two-body interaction of nearest neighbors characterized by pair tunneling. The excitation spectrum and the depletion of the condensate of lattice Bose gases are investigated using the Bogoliubov transformation method and the results show that there is a pair condensate as well as a single particle condensate. The various possible quantum phases, such as the Mott-insulator phase （MI）, the superfluid phase （SF） of an individual atom, the charge density wave phase （CDW）, the supersolid phase （SS）, the pair-superfluid （PSF） phase, and the pair-supersolid phase （PSS） are discussed in different parametric regions within our extended Bose-Hubbard model using perturbation theory.

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.

One-step implementation of an N-qubit quantum phase gate through a double Raman passage

We propose a scheme for controllably implementing an N-qubit phase gate by one step within a ground-state subspace of N three-state atoms trapped in a cavity through a double Raman passage. We can extend our scheme to the realisation of an arbitrary N-qubit phase gate by appropriately adjusting coupling strengths and detunings between atoms and external driving fields. The advantage of this one-step scheme is its robustness against decoherence.

Robust scheme for implemention of quantum phase gates for two atoms

We propose a scheme for implementing conditional quantum phase gates for two four-state atoms trapped in a cavity. The two ground states of the atoms are coupled through two Raman processes induced by the cavity mode and two classical fields. Under certain conditions nonresonant Raman processes lead to two-atom coupling and can be used to produce conditional phase gates. The scheme is insensitive to cavity decay, thermal photons, and atomic spontaneous emission. The scheme does not require individual addressing of the atoms.

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.

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.