Doped coupled frustrated spin-1/2 chains with four-spin exchange

The role of various magnetic interchain couplings is investigated by numerical methods in doped frustrated quantum spin chains. A nonmagnetic dopant introduced in a gapped spin chain releases a free spin-1/2 soliton. The formation of a local magnetic moment is analyzed in terms of soliton confinement. A four-spin coupling which might originate from cyclic exchange is shown to produce such a confinement. Dopants on different chains experience an effective space-extended nonfrustrating pairwise spin interaction.     

The general solution of two-dimensional matrix Toda chain equations with fixed ends

It is shown that the two-dimensional matrix Toda chain determines the group of discrete symmetries of the two-dimensional matrix nonlinear Schrödinger equation (the matrix generalization of the Davey-Stewartson system). The general solution of this chain with definite boundary conditions is obtained in explicit form.     

Energy separation of single-particle and continuum states in an S = 1/2 weakly coupled chains antiferromagnet

Inelastic neutron scattering is used to study transverse-polarized magnetic excitations in the quasi-one-dimensional S = 1/2 antiferromagnet BaCu2Si2O7, where the saturation value for the Neel order parameter is m(0) = 0.12&mgr;(B) per spin. At low energies the spectrum is totally dominated by resolution-limited spin-wave-like excitations. An excitation continuum sets in above a well-defined threshold frequency. Experimental results are discussed in the context of current theories for weakly interacting quantum half-integer-spin chains.     

An explicit one-soliton solution of the (2+1)-dimensional generalized sine-gordon equations

The (n+1)-dimensional differential geometric generalization of the sine-Gordon equation (SGE) given by Tenenblat and Terng is solved explicitly in the casen=2 to obtain a one-soliton solution. The solution yields the soliton solution of the (1+1)-dimensional SGE in the limit as one of the three independent variables approaches infinity. However, more than one variable plays the role of time in these limits.     

Investigation of the magnetic properties of chains with alternating ferro-and antiferromagnetic exchange interactions in the Heisenberg model with spin S=1/2

The quantum Monte Carlo method is used to calculate the susceptibility and pairwise spin-spin correlation functions of chains with alternating ferro (K)-and antiferromagnetic (J)-exchange interactions within the Heisenberg model with spin S=1/2. From the susceptibility, the energy gap between the ground state and excited triplet states is determined or arbitrary ratios K/J. The value of the gap coincides with the Haldane gap for spin S=1 when K/J>1.25. Fiz. Tverd. Tela (St. Petersburg) 41, 1650–1651 (September 1999)     

The complete N =2, d = 10 supergravity

The alternative N = 2, d = 10 supergravity, which is not derivable by dimensional reduction from the N = 1, d = 11 theory, is constructed at the full non-linear level. The transformation laws of the component fields and the equations of motion are derived and shown to be consistent. The derivation makes use of superspace techniques and exploits the fact that the scalars belong to the coset space SU(1,1)/U(1).     

Quantum Monte Carlo Investigation of the magnetic properties of weakly interacting antiferromagnetic chains with an alternating exchange interaction with spin S = 1/2

An approximation dependence of the spontaneous magnetic moment at a site, σ/σ(0) ? 1 = and the antiferromagnet-singlet state phase boundary, J ₂/J ₁ = 0.52(3)δ, are determined by the quantum Monte Carlo method in the self-consistent sublattice molecular field approximation for weakly inter-acting (J ₂) antiferromagnetic chains with spin S = 1/2 and alternating exchange interaction (J ₁ ± δ). The Néél temperature and a number of critical temperatures which could be related with the filling energy of two singlets (ΔS ^z = 0) and one triplet (ΔS ^z = 1) spin bands, each of which is split by the sublattice field (h ^{x, y} ≠ h ^z into two subbands, are determined on the basis of the computed correlation radii of the two-and four-spin correlation function, the squared total spin 〈 (S ^z)²〉 with respect to the longitudinal components, the dimerization parameter, and the correlation functions between the nearest neighbors with respect to longitudinal and transverse spin components. On the basis of the Monte Carlo calculations, the critical temperatures and possible energy gaps at the band center are determined for the antiferromagnets CuWO₄ and Bi₂CuO₄ and for the singlet compounds (VO)₂P₂O₇ and CuGeO₃, agreeing satisfactorily with existing results, and new effects are also predicted.     

1-Soliton solution of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and time-dependent coefficients

In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.     

Ground state of a spin 1/2 charged particle in an even-dimensional magnetic field

We investigate the ground state structure of the Schrödinger operator (Pauli Hamiltonian)H with a magnetic fieldb for a spin 1/2 charged particle in ^{2d 2d d} . We consider the case whereb is given by the complex exterior derivative of a functionW on ^d of the form W. We find that dim kerH is related to the asymptotic behavior ofW at infinity. More precisely, if there exists a constantC such that there exists the nonzero limit lim_|z|e ^w(z) /|z|^–C , then dim kerH is equal to the number of all monomialsf ind variables such that the degree off is smaller than |C| -d. In the case whereC , under a weaker assumption this conclusion holds. Moreover, we clarify the structure of kerH.     

Finite-size calculations of FQHE states at filling ν=1/2

Summary We present the results of numerical calculations, performed in the spherical geometry, of FQHE states ofN≤12 electrons in the lowest Landau level at filling ν=1/2. The extrapolated value for the energy per particle is −0.469±0.005, in the usual unitse ²/a ₀. Densities and pair correlation functions of the ground states are computed. The pair correlations are ?Wigner-crystal-like?, with maxima corresponding to regular polyhedra. ForN=4, 8 and 10 we find that the system presents a broken rotational invariance which generalizes the broken particle-hole symmetry already known in different gauges. Quasi-particles, quasi-holes and the ?exciton? spectrum are computed, and some microscopic wave functions are examined. The quasi-particles and the quasi-holes are not localized; this suggests a possible ?deformability? of the system.

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Riassunto Si presentano risultati di alcuni calcoli numerici, eseguiti usando la geometria sferica, di stati FQHE diN≤12 elettroni nel livello di Landau piú basso a ?riempimento? ν=1/2. Il valore estrapolato dell'energia per particella risulta pari a −0.469±0.005, nelle usuali unitàe ²/a ₀. Si calcolano la funzione densità e la funzione di correlazione di coppia corrispondenti allo stato fondamentale. Le funzioni di correlazione di coppia sono ?tipo cristallo di Wigner? con massimi corrispondenti ai poliedri regolari. PerN=4, 8 e 10 noi troviamo che il sistema presenta una simmetria rotazionale rotta che generalizza la rottura della simmetria particella-buca che era già nota in altre scelte di gauge. Si calcolano le quasi-particelle, le quasi-buche e lo spettro degli ?eccitoni?, e si esaminano alcune funzioni d'onda microscopiche. Le quasi-particelle e le quasi-buche non sono localizzate; questo suggerisce una possibile ?deformabilità? del sistema.

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Резюме Мы предлагаем результаты численных вычислений, вьшолненных в сферической геометрии, FQHE состояний дляN≤12 электронов на низшем уровне Ландау при заполнении ν=1/2. Экстрополированная величина энергии на одну частицу составляет −0.469±0.005, в обыкновенных единицахe ²/a ₀. Вычисляются функции плотности и функции парных корреляций для основных состояний. Функции парных корреляций оказываюгся ?подобны кристаллу Вигнера? с максимумами, соответствующими обычным многогранникам. ДляN=4,8 и 10 мы получаем, что рассматриваемая система представляет нарушенную симметрию ?частица-дырка?, уже известную в других калибровках. Вычисляются квази-частицы, квази-дырки и спектр ?экситонов?. Исследуются некоторые микроскопические волновые функции. Квази-частицы и квази-дырки не локализованы, что предполагает возможность ?деформируемости? системы.

     

Quantum phase transitions in matrix product states of one-dimensional spin-1/2 chains

For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases ｜Ψa 〉=｜1··· 1 representing all particles spin up and ｜Ψb 〉=｜0··· 0 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state ｜Ψpt =√2/2（｜1··· 1 ＋｜0··· 0）. At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit 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 potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.     

String order and degenerate entanglement spectrum of S = 1 / 2 and S = 1 Heisenberg bond-alternating chains

Generalized string orders and entanglement spectrum of S = 1/2 and S = 1 Heisenberg bond-alternating chains have been investigated by the infinite time-evolving block decimation (iTEBD) method. Generalized string order parameters with appropriate θ are capable of distinguishing all the topological phases. Central charges c ? 1 and critical exponents β ?1/12 indicate all the topological QPTs belong to the Gaussian universality class. Interestingly, odd- and even-fold degeneracies of the entanglement spectrum are observed. Even-fold (doubly) degenerate entanglement spectra and the typical two-fold degenerate lowest-lying level are found to exist in both the spin-1/2 dimer and the S = 1 Haldane phases. However, odd-fold degenerate entanglement spectra with three-fold degenerate lowest-lying level are observed in both the S = 1 dimer and the S = 2 Haldane phase. The degeneracy of the lowest-lying entanglement spectrum level, which can be understood by entanglement spectra in the dimer limit (J ₁ = 0), is adopted to estimate the lowest boundary of the bipartite entanglement. The entanglement spectrum and the generalized string orders are valuable for uncovering the underlying features of these symmetry-protect topological (SPT) states. Similar entanglement spectrum shows that the S = 1 (S = 2) Haldane phase is essentially the same as the S = 1/2 (S = 1) dimer phase.     

N=1/2 Wess-Zumino model is renormalizable

The Wess-Zumino model on N=1/2 nonanticommutative superspace, which contains the dimension-6 term F3, is shown to be renormalizable to all orders in perturbation theory, upon adding F and F2 terms to the original Lagrangian. The renormalizability is possible, even with this higher-dimension operator, because the Lagrangian is not Hermitian. Such deformed field theories arise naturally in string theory with a graviphoton background.     

Rotational description of the negative-parity states in transitional N = 89 nuclei

It is demonstrated that level energies and pick-up spectroscopic factors for the low-spin negative-parity states in transitional N = 89 nuclei can be successfully described in the particle-rotor model with Nilsson single-particle orbitals, provided that both Coriolis and recoil effects are properly taken into account.     

The T = 1, isospin triplet states in A = 30 nuclei

The level structure of ³⁰S was studied using the ${}^{28}\text{Si}\text{(τ,}\text{n}\text{p}\text{)}\text{reaction at}\text{E}{}_{\mathrm{\tau }}\text{= 9.5}\text{MeV}\text{,}\text{and}\text{J}{}^{\mathrm{\pi }}$ values were determined for some proton-emitting states by the neutron-proton angular correlation measurements. The Coulomb displacement energy of the isospin triplet state of A = 30 nuclei was analyzed using first-order perturbation theory. Large deviations from perturbation theory were found for the ground state, the 2⁺₁ state, the 3^?₁ state and the second excited 0⁺ state. These results might be explained by the effect of the pairing correlation of the two valence protons in ³⁰S under the assumption of charge symmetry for the nucleon-nucleon interaction.     

Resistivity of 2D electrons with ν=1/2 in a zero magnetic field

The dependence of the resistivity of 2D electrons with Landau level filling factor ν=1/2 in a zero magnetic field is studied experimentally as a function of the carrier density. It is found that the ratio of the resistivity for B=0 and ν=1/2 is a linear function of the carrier density, as predicted by a theory based on the scattering of composite fermions by spatial fluctuations of the effective static magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 154–158 (10 August 1997)