Ground state structures of a lattice model: honeycomb and tetrahedral lattices

The ground state structures of a lattice model with nearest-neighbor and next-nearest-neighbor interactions were examined by the method of “partitioning” the hamiltonian. This model is Widom's lattice model of microemulsions. Previous analysis had examined only cubic lattices, however the analysis is more general as this paper illustrates.     

Half-filled Kondo lattice on the honeycomb lattice

The unique linear density of state around the Dirac points for the honeycomb lattice brings much novel features in strongly correlated models. Here we study the ground-state phase diagram of the Kondo lattice model on the honeycomb lattice at half-filling by using an extended mean-field theory. By treating magnetic interaction and Kondo screening on an equal footing, it is found that besides a trivial discontinuous first-order quantum phase transition between well-defined Kondo insulator and antiferromagnetic insulating state, there can exist a wide coexistence region with both Kondo screening and antiferromagnetic orders in the intermediate coupling regime. In addition, the stability of Kondo insulator requires a minimum strength of the Kondo coupling. These features are attributed to the linear density of state, which are absent in the square lattice. Furthermore, fluctuation effect beyond the mean-field decoupling is analyzed and the corresponding antiferromagnetic spin-density-wave transition falls into the O(3) universal class. Comparatively, we also discuss the Kondo necklace and the Kane-Mele-Kondo (KMK) lattice models on the same lattice. Interestingly, it is found that the topological insulating state is unstable to the usual antiferromagnetic ordered states at half-filling for the KMK model. The present work may be helpful for further study on the interplay between conduction electrons and the densely localized spins on the honeycomb lattice.     

On universal quantum cloning and state estimation

Both perfect cloning and perfect state estimation of an unknown pure quantum state are impossible, due to principles of quantum mechanics. Nevertheless, they can be performed imperfectly. A link between these two scenarios allows us to derive an upper bound for the fidelity in one of them, given an upper bound is known in the other. Furthermore, it is shown that also a lower bound on cloning is related to an upper bound on state estimation. Received: 15 June 1999 / Revised version: 23 September 1999 / Published online: 10 November 1999     

Antiferromagnetism and Kondo screening on a honeycomb lattice

Magnetic adatoms in the honeycomb lattice have received tremendous attention due to the interplay between Ruderman–Kittel–Kasuya–Yosida interaction and Kondo coupling leading to very rich physics. Here we study the competition between the antiferromagnetism and Kondo screening of local moments by the conduction electrons on the honeycomb lattice using the determinant quantum Monte Carlo method. While changing the interband hybridization V, we systematically investigate the antiferromagnetic-order state and the Kondo singlet state transition, which is characterized by the behavior of the local moment, antiferromagnetic structure factor, and the short range spin-spin correlation. The evolution of the single particle spectrum are also calculated as a function of hybridization V, we find that the system presents a small gap in the antiferromagnetic-order region and a large gap in the Kondo singlet region in the Fermi level. We also find that the localized and itinerant electrons coupling leads to the midgap states in the conduction band in the Fermi level at very small V. Moreover, the formation of antiferromagnetic order and Kondo singlet are studied as on-site interaction U or temperature T increasing, we have derived the phase diagrams at on-site interaction U(or temperature T) and hybridization V plane.     

Blume-Emery-Griffiths model on the honeycomb lattice

Exact results are obtained for a spin-1 system on the honeycomb lattice with the Blume-Emery-Griffiths Hamiltonian –/kT =J _i,j S _i S _j +Ki,jS _i ² _j ² – _i S _i ² +HS _i subject to the constraintK=–ln coshJ. ForJ>0, the system behaves like a spin-1/2 Ising ferromagnet with the free energy analytic everywhere except at the first-order phase boundaryH=0, tanhJ<(2+e )/ . Derivatives of the free energy across this boundary are discontinuous and we obtain the exact expression for the spontaneous magnetization. ForJ<0, the system can be transcribed into an antiferromagnetic spin-1/2 Ising model in a real magnetic field, and from this equivalence portions of the exact phase boundary are determined.     

Exact solution of a three-component system on the honeycomb lattice

A model three-component system is considered in which the bonds of a honeycomb lattice are covered by rodlike molecules of typesAA, BB, andAB. The ends of molecules near a common lattice site interact with energies _AA, _BB, and _AB. The model is equivalent to an Ising model on the 3–12 lattice. Exact results are obtained for the two-phase coexistence curves in the isothermal composition plane.     

Topological states in the Hofstadter model on a honeycomb lattice

We provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t,t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux ϕ. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^{\varphi }$, a quantum phase transition in the 2D-topological insulator state is realized at $t_c$. The phase state is characterized by zero energy Majorana states localized at the boundaries. Taking into account the on-site Coulomb repulsion U (where $U<<1$), the criterion for the stability of a topological insulator state is calculated at $t<<1$, $t\sim U$. Thus, in the case of $U>4\mathrm{\Delta }$, the topological insulator state, which is determined by chiral gapless edge modes in the gap Δ, is destroyed.     

BCS-BEC crossover on the two-dimensional honeycomb lattice

The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.     

Euclidean quantum gravity on a lattice

We construct a number of related euclidean lattice formulations of quantum gravity. The first version incorporates a path integral over discrete manifolds built out of four-cubes embedded in a higher dimensional flat hypercubic lattice. We show this expression is equal to a corresponding path integral in a local lattice field theory. The field theoretic path integral diverges and lacks a satisfactory vacuum state. This divergence can be interpreted as a consequence of a divergent phase space available for topological fluctuations in the four-manifolds of the original path integral. A modified version of the path integral over manifolds converges. We construct a Schrödinger equation and hamiltonian for the modified theory. The hamiltonian is self-adjoint, but as a result of the large phase space available for topological fluctuations, the hamiltonian's spectrum is probably not bounded from below. We show briefly how the flat enveloping space—time can be removed from most of the theories we present and how matter fields can be included.     

Critical behaviour of the hard-core lattice gas on the honeycomb lattice

The hard triangle lattice-gas model (lattice-gas on the honeycomb lattice with first neighbour exclusion) is studied by the phenomenological renormalization method. The critical activity is found to be z = 7.85 and the critical exponents suggest that this model belongs to the 2-D Ising universality class.     

Note on a universal quantum Turing machine

In this Letter, we construct a novel model of universal quantum Turing machine (QTM) by means of a property of Riemann zeta function, which is free from the specific time for an input data and efficiently simulates each step of a given QTM.     

A quantum computer with fixed interaction is universal

It is proved that a quantum computer with fixed and permanent interaction of diagonal type between qubits proposed in the work quant-ph/0201132 is universal. Such a computer is controlled only by one-qubit quick transformations, and this makes it feasible.     

Power-law spin correlations in a perturbed spin model on a honeycomb lattice

We consider the spin-1/2 model on the honeycomb lattice in the presence of a weak magnetic field hα < 1. Such a perturbation destroys the exact integrability of the model in terms of gapless fermions and static Z2 fluxes. We show that it results in the appearance of a long-range tail in the irreducible dynamic spin correlation function: ∝ h(z)(2)f(t,r), where f(t,r) ∝ [max(t,r)]-4 is proportional to the density polarization function of fermions.     

线性光学实现量子普适确切态识别

给出一种量子普适确切态识别的线性光学实现方案.此方案只用到双光子的干涉和符合测量,在实验上是简单可行的.同时提出一种改进方案,通过一定量的辅助光子,使得上述方案成功概率得以提高.这一方案将可应用于量子密钥分配等安全信息交流中. 关键词： 确切态识别 线性光学     

Topological insulators in ternary compounds with a honeycomb lattice

We investigate a new class of ternary materials such as LiAuSe and KHgSb with a honeycomb structure in Au-Se and Hg-Sb layers. We demonstrate the band inversion in these materials similar to HgTe, which is a strong precondition for existence of the topological surface states. In contrast with graphene, these materials exhibit strong spin-orbit coupling and a small direct band gap at the Γ point. Since these materials are centrosymmetric, it is straightforward to determine the parity of their wave functions, and hence their topological character. Surprisingly, the compound with strong spin-orbit coupling (KHgSb) is trivial, whereas LiAuSe is found to be a topological insulator.