Unconventional geometric quantum phase gates with two SQUIDs in a cavity

We present a potential scheme to implement two-qubit quantum phase gates through an unconventional geometric phase shift with two four-level SQUIDs in a cavity. The SQUID qubits undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, acquiring a geometric phase depending conditionally upon the SQUIDs’ states. Under certain conditions, the SQUID qubits are disentangled with the cavity mode and the SQUIDs’ states remain in their ground states during the gate operation, thus the gate is insensitive to both the SQUIDs’ “spontaneous emission” and the cavity decay.     

Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy

We study the ground-state and thermal entanglement in the mixed-spin (S,s)=(1,1/2) Heisenberg chain with single-ion anisotropy D using exact diagonalization of small clusters. In this system, a quantum phase transition is revealed to occur at the value D=0, which is the bifurcation point for the global ground state; that is, when the single-ion anisotropy energy is positive, the ground state is unique, whereas when it is negative, the ground state becomes doubly degenerate and the system has the ferrimagnetic long-range order. Using the negativity as a measure of entanglement, we find that a pronounced dip in this quantity, taking place just at the bifurcation point, serves to signal the quantum phase transition. Moreover, we show that the single-ion anisotropy helps to improve the characteristic temperatures above which the quantum behavior disappears.     

Quantum entanglement and quantum phase transitions in frustrated Majumdar-Ghosh model

By using the density matrix renormalization group technique, the quantum phase transitions in the frustrated Majumdar-Ghosh model are investigated. The behaviors of the conventional order parameter and the quantum entanglement entropy are analyzed in detail. The order parameter is found to peak at J₂∼0.58, but not at the Majumdar-Ghosh point (J₂=0.5). Although, the quantum entanglements calculated with different subsystems display dissimilarly, the extremes of their first derivatives approach to the same critical point. By finite size scaling, this quantum critical point J^C₂ converges to around 0.301 in the thermodynamic limit, which is consistent with those predicted previously by some authors (Tonegawa and Harada, 1987 [6]; Kuboki and Fukuyama, 1987 [7]; Chitra et al., 1995 [9]). Across the J^C₂, the system undergoes a quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase.     

Quantum phase transition of entanglement in Heisenberg spin model with quantized field

In this paper, we investigate the entanglement of a two-spin system with Heisenberg exchange interaction in a quantized field. The pairwise entanglement between bipartite subsystems is obtained. It is shown that the entanglement exhibits a quantum phase transition due to the variation of exchang coupling. Phase diagrams are obtained explicitly. The analogy of the quantum phase transition compared to the case under a classical field are addressed.     

Quantum phase transition in the anisotropic one-dimensional XY model with long-range interactions

In this paper we study the one-dimensional XY model with single ion anisotropy and long-range interaction that decay as a power law. The model has a quantum phase transition, at zero temperature, at a critical value D_c of the anisotropy parameter D. For values of D below D_c we use a self-consistent harmonic approximation. We have found that the critical temperature increases with D for small values of this parameter. For values of D above D_c we use the bond operator technique and calculate the gap as a function of D, at zero temperature.     

Off-diagonal long-range order in the ground state of the two-dimensional antiferromagnetic Heisenberg model

A two-dimensional Jordan-Wigner transformation, together with a fermion-boson mapping, has been used to transform the two-dimensional antiferromagnetic Heisenberg model (2D AFMHM) into an interacting boson system with a fixed number of particles. We found that the excitation energy depends linearly on the momentum for small energy, and it is 1.80J for (π,π). Our results suggest that the ground state of the 2D AFMHM is a quantum liquid, and the order is off-diagonal long-range order associated with the Bose-Einstein condensation.     

Monte Carlo investigation of phase transitions in the frustrated Heisenberg model on a triangular lattice

The critical properties and phase transitions of the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated using the Monte Carlo method with a replica algorithm. The critical temperature has been determined and the character of the phase transitions has been analyzed using the method of fourth-order Binder cumulants. A second-order phase transition has been found in the three-dimensional frustrated Heisenberg model on a triangular lattice. The static magnetic and chiral critical exponents of the heat capacity α, the susceptibility γ and γ _k , the magnetization β and β _k , the correlation length ν and ν _k , as well as the Fisher exponents η and η _k , have been calculated in terms of the finite-size scaling theory. It has been demonstrated that the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice forms a new universality class of the critical behavior.     

Global quantum discord and quantum phase transition in XY model

We study the relationship between the behavior of global quantum correlations and quantum phase transitions in XY model. We find that the two kinds of phase transitions in the studied model can be characterized by the features of global quantum discord (GQD) and the corresponding quantum correlations. We demonstrate that the maximum of the sum of all the nearest neighbor bipartite GQDs is effective and accurate for signaling the Ising quantum phase transition, in contrast, the sudden change of GQD is very suitable for characterizing another phase transition in the XY model. This may shed lights on the study of properties of quantum correlations in different quantum phases.     

Entanglement, fidelity, and quantum phase transition in antiferromagnetic-ferromagnetic alternating Heisenberg chain

The fidelity and entanglement entropy in an antiferromagnetic-ferromagnetic alternating Heisenberg chain are investigated by using the method of density-matrix renormalization-group. The effects of anisotropy on fidelity and entanglement entropy are investigated. The relations between fidelity, entanglement entropy and quantum phase transition are analyzed. It is found that the quantum phase transition point can be well characterized by both the ground-state entropy and fidelity for large system.     

Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first-order quantum phase transition

We introduce a frustrated spin 1/2 Hamiltonian which is an extension of the two dimensional J1-J2 Heisenberg model. The ground states of this model are exactly obtained at a first-order quantum phase transition between two valence bond crystals. At this point, the low energy excitations are deconfined spinons and spin-charge separation occurs under doping in the limit of low concentration of holes. In addition, this point is characterized by the proliferation of topological defects.     

Non-equilibrium phase transition of the fully frustrated square lattice Coulomb gas model

The non-equilibrium phase transitions of the fullyfrustrated (f = 1/2) square lattice Coulomb gas (CG) modeldriven by external electrical fields are studied in the frameworkof the short-time dynamic scaling approach. The criticaltemperature T_c, the static and dynamic critical exponents2β/ν, ν, and z are obtained for several smalldriving fields. The results show that T_c decreases with theincrease of electric field, and 2β/ν and z arestrongly dependent on the external electric field. Interestingly,contrary to the equilibrium case, in the presence of smallelectric field, the calculated exponent ν is close to that inpure 2D Ising model, which provides numerical evidence thatexternal electric field may change the universality class of thef = 1/2 CG system.     

Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

Ising transition in the two-dimensional quantum J1-J2 Heisenberg model

We study the thermodynamics of the spin-S two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings in its collinear phase (J(2)/J(1)>0.5), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio J(2)/J(1) is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin and temperature dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li2VOSiO4 and related compounds.     

Magnetic fluctuations at a field-induced quantum phase transition

We report an inelastic neutron-scattering study at the field-induced magnetic quantum phase transition of CeCu5.8Au0.2. The data can be described better by the spin-density-wave scenario than by a local quantum critical point, while the latter scenario was shown to be applicable to the zero-field concentration-tuned quantum phase transition in CeCu6-xAux for x=0.1. This constitutes direct microscopic evidence for a difference in the quantum fluctuation spectra at a magnetic quantum critical point driven by different tuning parameters.