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.     

Numerical study of the one-dimensional quantum compass model

The ground state magnetic phase diagram of the one-dimensional quantum compass model (QCM) is studied using the numerical Lanczos method. A detailed numerical analysis of the low energy excitation spectrum is presented. The energy gap and the spin-spin correlation functions are calculated for finite chains. Two kind of the magnetic long-range orders, the Néel and a type of the stripe-antiferromagnet, in the ground state phase diagram are identified. Based on the numerical analysis, the first and second order quantum phase transitions in the ground state phase diagram are identified.     

Dilution effects in two-dimensional quantum orbital systems

Interacting orbital degrees of freedom in a Mott insulator are essentially directional and frustrated. In this Letter, the effect of dilution in a quantum-orbital system with this kind of interaction is studied by analyzing a minimal orbital model which we call the two-dimensional quantum compass model. We find that the decrease of the ordering temperature due to dilution is stronger than that in spin models, but it is also much weaker than that of the classical model. The difference between the classical and the quantum-orbital systems arises from the enhancement of the effective dimensionality due to quantum fluctuations.     

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.     

Two models of quantum random walk

We present an overview of two models of quantum random walk. In the first model, the discrete quantum random walk, we present the explicit solution for the recurring amplitude of the quantum random walk on a one-dimensional lattice. We also introduce a new method of solving the problem of random walk in the most general case and use it to derive the hitting amplitude for quantum random walk on the hypercube. The second is a special model based on a local interaction between neighboring spin-1/2 particles on a one-dimensional lattice. We present explicit results for the relevant quantities and obtain an upper bound on the speed of convergence to limiting probability distribution.     

Dimerization,trimerization and quantum pumping

We study one-dimensional topological models with dimerization and trimerization and show that these models can be generated using interaction or optical superlattice. The topological properties of these models are demonstrated by the appearance of edge states and the mechanism of dimerization and trimerization is analyzed. Then we show that a quantum pumping process can be constructed based on each one-dimensional topological model. The quantum pumping process is explicitly demonstrated by the instantaneous energy spectrum and local current. The result shows that the pumping is assisted by the gapless states connecting the bands and one charge is pumped during a cycle, which also defines a nonzero Chern number. Our study systematically shows the connection of one-dimensional topological models and quantum pumping, and is useful for the experimental studies on topological phases in optical lattices and photonic quasicrystals.     

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.     

Sustained quantum coherence and entanglement in the avian compass

In artificial systems, quantum superposition and entanglement typically decay rapidly unless cryogenic temperatures are used. Could life have evolved to exploit such delicate phenomena? Certain migratory birds have the ability to sense very subtle variations in Earth's magnetic field. Here we apply quantum information theory and the widely accepted "radical pair" model to analyze recent experimental observations of the avian compass. We find that superposition and entanglement are sustained in this living system for at least tens of microseconds, exceeding the durations achieved in the best comparable man-made molecular systems. This conclusion is starkly at variance with the view that life is too "warm and wet" for such quantum phenomena to endure.     

Exact solution to a class of generalized Kitaev spin-1/2 models in arbitrary dimensions

We construct a class of exactly solvable generalized Kitaev spin-1/2 models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An exactly solvable quantum spin-1/2 model can be mapped to a gas of free Majorana fermions coupled to static Z2 gauge fields. We classify these exactly solvable models according to their parent models. Any model belonging to this class can be generated by one of the parent models. For illustration, a two dimensional(2D) tetragon-octagon model and a three dimensional(3D) xy bond model are studied.     

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.     

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.     

Localization of quantum walks on finite graphs

We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.     

Elementary excitations in nanochannel arrays of quantum wires

We present an analytical model for the Coulomb interaction effects in quantum wires forming a nanochannel array. We study the elementary excitations (plasmons and electron-hole excitations) of electron arrays forming three-dimensional structures. The plasmon spectrum of boson arrays is also calculated. Our model applies to bulk material with one-dimensional conduction channels as realized in organic or polymer crystals and in nanochannel array glasses.     

Relativistic quantum particle in a time-dependent homogeneous field

A model of the relativistic quantum particle under the action of a time-dependent force is considered. This exactly solvable model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space is one-dimensional Lobachevsky space. We have explicitly constructed the wave functions and propagators for this model in both x- and p-representations. We have also found a solution of a definite class of partial differential and finite-difference equations, which can be interpreted as the operator identities.     

Quantum-phase transition in a XY model

In this paper we study quantum-phase transition in the one-dimensional XY model with an XY easy-plane single ion anisotropy. We use the path-integral formalism, but consider the effect of quantum fluctuations, which renormalize the parameters of the system, using the self-consistent harmonic approximation. We show that the quantum fluctuations increase the effective coupling constant of the model.     

Quantum discord and classical correlation signatures of mobility edges in one-dimensional aperiodic single-electron systems

We investigate numerically the quantum discord and the classical correlation in a one-dimensional slowly varying potential model and a one-dimensional Soukoulis–Economou ones, respectively. There are well-defined mobility edges in the slowly varying potential model, while there are discrepancies on mobility edges in the Soukoulis–Economou ones. In the slowly varying potential model, we find that extended and localized states can be distinguished by both the quantum discord and the classical correlation. There are sharp transitions in the quantum discord and the classical correlation at mobility edges. Based on these, we study “mobility edges” in the Soukoulis–Economou model using the quantum discord and the classical correlation, which gives another perspectives for these “mobility edges”. All these provide us good quantities, i.e., the quantum discord and the classical correlation, to reflect mobility edges in these one-dimensional aperiodic single-electron systems. Moreover, our studies propose a consistent interpretation of the discrepancies between previous numerical results about the Soukoulis–Economou model.     

Quantum oscillations in confined and degenerate Fermi gases. I. Half-vicinity model

We propose an analytical model for the prediction and accurate calculation of size and density dependent quantum oscillations in thermodynamic and transport properties of confined and degenerate Fermi gases. Our model considers only half-vicinity states of Fermi level. We show that the half-vicinity model quite accurately estimates quantum oscillations depending on confinement and degeneracy. Periods of quantum oscillations are even analytically expressed for one-dimensional case. Furthermore, similarities between functional behaviors of total occupancy variance and conventional density of states functions at Fermi level are discussed.     

A One-Dimensional Model of Hydrogen Molecular Ion

We present a study on a one-dimensional hydrogen molecular ion under the Born-Oppenheimer approximation. A canonical transformation produces the classical system directlyto be a pendulum. The quantum Schrodinger equation is solved analytically and theelectronic energy curves show that the bound states of this 1D model differ from the 2D and 3DH₂⁺. The vibration spectroscopy is also obtained by employing the Morse's eigen wavefunctionsas basis vectors to diagonalize the Hamiltonian for R. The semiclassical quantization yieldselectronic energies in agreement with the quantum ones reasonably.     

Scaling of reduced fidelity susceptibility in the one-dimensional transverse-field XY model

We show that the reduced fidelity susceptibility in the family of one-dimensional XY model obeys scaling behavior in the vicinity of quantum critical points both analytically and numerically. The logarithmic divergence behavior suggests that the reduced fidelity susceptibility can act as an indicator of quantum phase transition.     

Frustrated spin model as a hard-sphere liquid

We show that one-dimensional topological objects (kinks) are natural degrees of freedom for an antiferromagnetic Ising model on a triangular lattice. Its ground states and the coexistence of spin ordering with an extensive zero-temperature entropy can easily be understood in terms of kinks forming a hard-sphere liquid. Using this picture we explain effects of quantum spin dynamics on that frustrated model, which we also study numerically.