This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe Ansatz arising from the anyonic commutation relations. The thermodynamic Bethe Ansatz equations defining the temperature dependent properties of the model are also derived, from which some groundstate properties are obtained. PACS numbers: 02.30.Ik, 05.30.PrA number of 1D models in quantum many-body physics have been solved by the Bethe Ansatz following Bethe's pioneering work on the exact solution of the 1D Heisenberg magnetic spin chain in 1931 [1,2]. During the past 75 years the Bethe Ansatz has been developed and applied to physical problems such as the 1D δ-function interacting Bose [3,4] and Fermi[5] gases, the 1D Hubbard model [6] and 2D vertex models [7,8] (many of these key papers are collected in Ref. [9]). The solution of such models contributed to the development of the celebrated Yang-Baxter equation, which gives the consistency conditions for many-body scattering problems and plays a crucial role in quantum integrable systems [10,11,12,13,14,15] and in modern mathematical physics [16,17]. The related establishment of the quantum inverse scattering method [11,18,19] provided widespread applications of the Yang-Baxter equation in low-dimensional quantum systems, such as the Kondo problem [20], the Anderson model [21] and long range interaction systems [22, 23]. A further pioneering application of the Bethe Ansatz was to the 1D δ-function interacting Bose gas [3] which is related to the quantum nonlinear Schrödinger equation. This model provides an important realistic physical description of an interacting 1D Bose gas. It is also arguably one of the most simplest and pedagogic models solved in terms of the BetheAnsatz. In general the applicability of the Bethe Ansatz depends on the reducibility of the multi-particle scattering matrix to the product of many two-particle scattering matrices. The starting point for the Bethe Ansatz approach in quantum many-body physics is to reduce the eigenvalue problem of the field theoretic hamiltonian into a quantum mechanical many-body problem. The wavefunction of the many-body hamiltonian inherits the statistical signature of the interacting particles, which leads to striking and subtle quantum many-body effects.For example, significantly different quantum effects between the 1D δ-function interacting Bose and Fermi gases are seen clearly from the Bethe Ansatz solutions [3,5].On the other hand, anyons [24,25] may also exist in both two and one dimension, obeying fractional statistics. For a 2D electron gas in the fractional quantum Hall (FQH) regime, the quasi-particles are charged anyons [26]. A more general description of quantum statistics is provided by Haldane exclusion statistics [27], which is a formulation of fractional statistics based on a generalized Pauli exclusion principle, now called generalized exclusion statistics [28,29]. In 1D, a wavefunction with anyonic symmetry may ...

Local electron-ion pseudopotentials fitted to dominant density parameters of the solid state (valence, equilibrium average electron density and interstitial electron density) have been constructed and tested for sixteen simple metals. Calculated solid-state properties present little evidence of the need for pseudopotential non-locality, but this need is increasingly evident as the pseudopotentials are transferred further from their solid-state origins. Transferability is high for Na, useful for ten other simple metals (K, Rb, Cs, Mg, Al, Ga, In, Tl, Sn, and Pb), and poor for Li, Be, Ca, Sr and Ba. In the bulk solid, we define a predictor of transferability and check the convergence of second-order pseudopotential perturbation theory for bcc Na. For sixatom octahedral clusters, we find that the pseudopotential correctly predicts self-compressions or self-expansions of bond length with respect to the bulk for Li, Na, Mg, and Al, in comparison with all-electron results; dimers of these elements are also considered. For the free atom, we examine the bulk cohesive energy (which straddles the atomic and solid-state limits), the atomic excitation energies and the atomic density. For the cohesive energy, we also present the results of the simpler stabilized jellium and universal-binding-energy-curve models. The needed nonlocality or angular-momentum dependence of the pseudopotential has the conventional character, and is most strongly evident in the excitation energies.

An extensive investigation is given for magnetic properties and phase transitions in one-dimensional Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means of the dressed energy formalism. An iteration method is presented to derive higher order corrections for the ground state energy, critical fields and magnetic properties. Numerical solutions of the dressed energy equations confirm that the analytic expressions for these physical quantities and resulting phase diagrams are highly accurate in the weak and strong coupling regimes, capturing the precise nature of magnetic effects and quantum phase transitions in one-dimensional interacting fermions with population imbalance. Moreover, it is shown that the universality class of linear field-dependent behaviour of the magnetization holds throughout the whole attractive regime.

A comprehensive study of the lattice dynamics, elastic moduli, and liquid metal resistivities for 16 simple metals in the bcc and fcc crystal structures is made using a density-based local pseudopotential. The phonon frequencies exhibit excellent agreement with both experiment and nonlocal pseudopotential theory. The bulk modulus is evaluated by the long wave and homogeneous deformation methods, which agree after a correction is applied to the former. Calculated bulk and Voigt shear moduli are insensitive to crystal structure, and long-wavelength soft modes are found in certain cases. Resistivity calculations confirm that electrons scatter off the whole Kohn-Sham potential, including its exchange-correlation part as well as its Hartree part. All of these results are found in second-order pseudopotential perturbation theory. However, the effect of a nonperturbative treatment on the calculated lattice constant is not negligible, showing that higher-order contributions have been subsumed into the pseudopotential by construction. For bcc sodium, the band structures of local and nonlocal pseudopotentials are found to be almost identical. ͓S0163-1829͑97͒01321-0͔