Berry phase in Tavis-Cummings model

In this paper we investigate the Berry phase in Tavis-Cummings model in the rotating wave approximation. The dipole-dipole interaction between the atoms is considered. The eigenfunctions of the system are obtained and thus the Berry phase is evaluated explicitly in terms of the introduction of the phase shift. It is shown that the Berry phase can be easily controlled by the atom-cavity coupling strength, the cavity frequency detuning, which can be important in applications in geometric quantum computing.     

Pair-density-wave correlations in the Kondo-Heisenberg model

We show, using density-matrix renormalization-group calculations complemented by field-theoretic arguments, that the spin-gapped phase of the one dimensional Kondo-Heisenberg model exhibits quasi-long-range superconducting correlations only at a nonzero momentum. The local correlations in this phase resemble those of the pair-density-wave state which was recently proposed to describe the phenomenology of the striped ordered high-temperature superconductor La(2-x)Ba(x)CuO?, in which the spin, charge, and superconducting orders are strongly intertwined.     

Non-trivial Berry phase for an asymmetric one-dimensional potential in the free electron limit

We find a non-trivial Berry phase for a finite potential, even in the delocalized-electron limit. We obtain this result for a one-dimensional, periodic sawtooth potential, though our analysis is applicable to other systems. We show that this result is due to both the periodicity of the time-independent wave function and the effects of interband degeneracies. We also find, for the sawtooth potential, that each band is uniquely characterized by its Berry phase’s functional dependence on the potential’s parameters. Thus, each band may be identified by the behavior of its Berry phase.     

Geometric phase and quantum phase transition in the one-dimensional compass model

We study the geometric phase of the ground state of the one-dimensional compass model in a transverse field. The critical properties of the system in terms of the geometric phase are calculated and discussed. The results show that the general character of quantum phase transitions (QPTs) in the model can be revealed by the Berry phase of the ground state. This study extends the relations between geometric phases and QPTs.     

On the calculation of the Berry phase in a solvable model

We study fermions defined on a one-dimensional interval, for which the interaction is given by a four-parameter family of boundary conditions. We compare the full solution to the adiabatic approximation and determine the Berry phase for a number of typical orbits in parameter space. We observe the occurrence of a non-trivial fundamental group and discuss the possibilities of avoided crossings and apparent crossings.     

A one-dimensional model with phase transition

Two repellent particles are bound to occupy two among thek _n +1 adjacent sites 0=x ₀ ⁽ⁿ⁾ <x ₁ ⁽ⁿ⁾ <...<x _kn ⁽ⁿ⁾ =1, sayx _q ⁽ⁿ⁾ ,x _q+1 ⁽ⁿ⁾ . Define the Hamiltonian _q ⁽ⁿ⁾ =–ln(x _q+1 ⁽ⁿ⁾ –x _q ⁽ⁿ⁾ ) and the partition function     

A one-dimensional model with phase transition

A one-dimensional model is studied with nearest neighbor interaction and certain forbidden configurations. In this model it is possible to investigate the phase transition even on the microcanonical level, and it turns out that phases can coexist under certain circumstances.     

Solar-neutrino problem and the Berry phase

Summary The solar-neutrino problem is studied here from the point of view that neutrinos interacting with torsion generated by the solar magnetic field may develop the Berry phase which, through its relationship with the chiral anomaly, changes the space-time structure of weak interaction. Indeed, it is found that the axial vector part is cancelled out and we have only the residual vector part. This reduces the capture rate by a factor 1/4 which helps us to solve the puzzle. The author of this paper has agreed not to receive the proofs for correction.     

Vortex dynamics in superfluids and the Berry phase

There is a close analogy between the dynamics of electrons in a strong magnetic field and the dynamics of quantized vortices in superfluids and superconductors. In both systems an important part is played by a term in the Lagrangian linear in velocity that corresponds to a Berry phase in the quantum theory. This Berry phase can be calculated from the usual trial wave function for a vortex. This has important consequences for quantum tunneling of vortices, and leads unambiguously to the form of the Magnus force in a superconductor.     

Berry phase in magnetic superconductors

In magnetic systems, electronic bands often acquire nontrivial topological structure characterized by gauge flux distribution in momentum k space. It sometimes follows that the phase of the wave functions cannot be defined uniquely over the whole Brillouin zone. In this Letter, we develop a theory of superconductivity in the presence of this gauge flux both in two- and three-dimensional systems. It is found that the superconducting gap has "nodes" as a function of k where the Fermi surface is penetrated by a gauge string.     

Zitterbewegung and gravitational Berry phase

Berry phases mix states of positive and negative energy in the propagation of fermions and bosons in external gravitational and electromagnetic fields and generate Zitterbewegung oscillations. The results are valid in any reference frame and to any order of approximation in the metric deviation.     

Dimerized phase and entanglement in the one-dimensional spin-1 bilinear biquadratic model

Dimerized phase and quantum entanglement are investigated in the one-dimensional spin-1 bilinear biquadratic model. Employing the infinite matrix product state representation, groundstate wavefunctions are numerically obtained by using the infinite time evolving block decimation method in the infinite lattice system. From a bipartite entanglement measure of the groundstates, i.e., von Neumann entropy, the phase transition points can be clearly extracted. Moreover, the even-bond and odd-bond von Neumann entropies show two different values in the spontaneous dimerized phase. It implies that the quantum entanglement can distinguish the two degenerate groundstates. Then, we define a dimer entropy in the spontaneous dimerized phase. Comparing to the dimer order parameter, the dimer entropy can play a role of a local order parameter to characterize the spontaneous dimerized phase.     

Berry phase in a nonisolated system

We investigate the effect of the environment on a Berry phase measurement involving a spin-half. We model the spin + environment using a biased spin-boson Hamiltonian with a time-dependent magnetic field. We find that, contrary to naive expectations, the Berry phase acquired by the spin can be observed, but only on time scales which are neither too short nor very long. However this Berry phase is not the same as for the isolated spin-half. It does not have a simple geometric interpretation in terms of the adiabatic evolution of either bare spin states or the dressed spin resonances. This result is crucial for proposed Berry phase measurements in superconducting nanocircuits.     

Berry phase in a composite system

The Berry phase in a composite system with one driven subsystem has been studied in this Letter. We choose two coupled spin-1 / 2 systems as the composite system; one of the subsystems is driven by a time-dependent magnetic field. We show how the Berry phases depend on the coupling between the two subsystems, and the relation between the Berry phases of the composite system and those of its subsystems.     

非线性系统的非对角Berry相

研究了非线性系统中非对角情况的Berry相位, 给出了非线性非对角Berry相位的计算公式. 结果表明, 在非线性非对角情况下, 总相位包含有动力学相位, 通常意义的Berry相位, 以及非线性引起的附加相位. 此外, 还包含有非对角情况时所特有的新的附加项. 这新的一项表示, 当系统哈密顿慢变时产生的Bogoliubov涨落, 与另一个瞬时本征态之间的交叉效应, 进而对总的Berry相位产生影响. 作为应用, 对二能级玻色爱因斯坦凝聚体系, 具体计算了非线性非对角的Berry相位. 关键词： Berry 相位 非对角 绝热演化 玻色爱因斯坦凝聚