The 1D interacting Bose gas in a hard wall box

We consider the integrable one-dimensional delta-function interacting Bose gas in a hard wall box which is exactly solved via the coordinate Bethe Ansatz. The ground state energy, including the surface energy, is derived from the Lieb-Liniger type integral equations. The leading and correction terms are obtained in the weak coupling and strong coupling regimes from both the discrete Bethe equations and the integral equations. This allows the investigation of both finite-size and boundary effects in the integrable model. We also study the Luttinger liquid behaviour by calculating Luttinger parameters and correlations. The hard wall boundary conditions are seen to have a strong effect on the ground state energy and phase correlations in the weak coupling regime. Enhancement of the local two-body correlations is shown by application of the Hellmann-Feynman theorem.Comment: 23 pages, 7 figures. Improved version. Extra figure added for the weak coupling regime. New expression for the interaction-dependent cloud size and additional reference

Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases

We investigate the elementary excitations of charge and spin degrees for the 1D interacting two-component Bose and Fermi gases by means of the discrete Bethe ansatz equations. Analytic results in the limiting cases of strong and weak interactions are derived, where the Bosons are treated in the repulsive and the fermions in the strongly attractive regime. We confirm and complement results obtained previously from the Bethe ansatz equations in the thermodynamic limit.Comment: 12 pages, 1 figur

Quantum phase diagram of an exactly solved mixed spin ladder

We investigate the quantum phase diagram of the exactly solved mixed spin-(1/2,1) ladder via the thermodynamic Bethe ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases associated with su(2), su(4) and su(6) symmetries. In the presence of a strong magnetic field, there is a third and full saturation magnetization plateaux within the strong antiferromagnetic rung coupling regime. Gapless and gapped phases appear in turn as the magnetic field increases. For weak rung coupling, the fractional magnetization plateau vanishs and exhibits new quantum phase transitions. However, in the ferromagnetic coupling regime, the system does not have a third saturation magnetization plat eau. The critical behaviour in the vicinity of the critical points is also derived systematically using the TBA.Comment: 20 pages, 2 figure

Exact results for the 1D interacting mixed Bose-Fermi gas

The exact solution of the 1D interacting mixed Bose-Fermi gas is used to calculate ground-state properties both for finite systems and in the thermodynamic limit. The quasimomentum distribution, ground-state energy and generalized velocities are obtained as functions of the interaction strength both for polarized and non-polarized fermions. We do not observe any demixing instability of the system for repulsive interactions.Comment: 12 pages, 4 figures, better comparison with hydrodynamic approach, typos corrected, references added, improved figure

One-dimensional interacting anyon gas: Low-energy properties and haldane exclusion statistics

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations

Assessing dolomite surface reactivity at temperatures from 40 to 120 degrees C by hydrothermal atomic force microscopy

This study investigated the reactivity of the (1 0 4) dolomite surface in the system MgCO3–CaCO3–NaCl–H2O via a suite of aqueous solution–dolomite hydrothermal atomic force microscopy interaction experiments at temperatures from 40 to 120 °C, pH ranging from 4 to 8, pressures up to 5 bars, and over a wide range of aqueous fluid saturation state. Dolomite dissolution was observed in the presence of undersaturated aqueous fluids. Dissolution produced crystallographically well defined etch pits, consistent with the stoichiometric release of ordered lattice cations. In low to moderately saturated fluids, dolomite growth began by the growth of one or two layers of carbonate (layer height <3 Å) which morphologically reproduced the initial surface features, resembling the template effect as previously described by Astilleros et al. (2003, 2006) and Freij et al. (2004). Further growth was strongly inhibited and did not show any systematic crystallographically orientated growth morphologies. At aqueous fluid saturation states exceeding 500, nucleation and growth was observed on the dolomite surfaces at moderate rates, but these did not exhibit the characteristic dolomite crystallographic orientation after the growth of several layers. Taken together these observations suggest that the direct precipitation of dolomite from aqueous solution is disfavored at temperatures to at least 120 °C due to the poisoning of the dolomite surface for further growth by the precipitation of one to four Ca–Mg carbonate layers on these surfaces

Evidence for the super Tonks-Girardeau gas

We provide evidence in support of a recent proposal by Astrakharchik at al. for the existence of a super Tonks-Girardeau gas-like state in the attractive interaction regime of quasi-one-dimensional Bose gases. We show that the super Tonks-Giradeau gas-like state corresponds to a highly-excited Bethe state in the integrable interacting Bose gas for which the bosons acquire hard-core behaviour. The gas-like state properties vary smoothly throughout a wide range from strong repulsion to strong attraction. There is an additional stable gas-like phase in this regime in which the bosons form two-body bound states behaving like hard-core bosons.Comment: 10 pages, 1 figure, 2 tables, additional text on the stability of the super T-G gas-like stat

Thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies

The thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies are investigated via the integrable su(3) model in terms of the quantum transfer matrix method and the recently developed high temperature expansion method for exactly solved models. It is shown that large single-ion anisotropy may result in a singlet gapped phase in the spin-1 chain which is significantly different from the standard Haldane phase. A large in-plane anisotropy may destroy the gapped phase. On the other hand, in the vicinity of the critical point a weak in-plane anisotropy leads to a different phase transition than the Pokrovsky-Talapov transition. The magnetic susceptibility, specific heat and magnetization evaluated from the free energy are in excellent agreement with the experimental data for the compounds NiC_2H_8N_2)_2Ni(CN)_4 and Ni(C_{10}H_8N_2)_2Ni(CN)_4.H_2O.Comment: 18 pages, 6 figures, to appear in PR

Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions

We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits in the repulsive and attractive regimes.Comment: 27 pages, 6 figures, key reference added, typos correcte

Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

(abbreviated) This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of real compounds. The ground state properties of the integrable two-leg spin-1/2 and the mixed spin-(1/2,1) ladder models at zero temperature are analyzed by means of the Thermodynamic Bethe Ansatz. Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are investigated in terms of the recently introduced High Temperature Expansion method, which is discussed in detail. It is shown that in the strong coupling limit the integrable spin-1/2 ladder model exhibits three quantum phases: (i) a gapped phase in the regime $H<H_{c1}$, (ii) a fully polarised phase for $H>H_{c2}$, and (iii) a Luttinger liquid magnetic phase in the regime $H_{c1}<H<H_{c2}$. The critical behaviour in the vicinity of the critical points is of the Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for a range of strong coupling ladder compounds. Similar analysis of the mixed spin-(1/2,1) ladder model reveals a rich phase diagram, with a 1/3 and a full saturation magnetisation plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetisation plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetisation curve obtained from the exact result derived from the HTE. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also investigated.Comment: 90 pages, 33 figures, extensive revisio