Spectrum and transition rates of the XX chain analyzed via Bethe ansatz (original) (raw)

Spinon excitations in the XX chain: spectra, transition rates, observability

Journal of Physics A: Mathematical and General, 2006

The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1/2 XX model on a lattice with an even or odd number N of lattice sites and periodic boundary conditions. Exact product formulas for the transition rates derived via Bethe ansatz are used to calculate asymptotic expressions of the 2-spinon and 4-spinon parts (for large even N ) as well as of the 1-spinon and 3-spinon parts (for large odd N ) of the dynamic spin structure factors. The observability of these spectral contributions is assessed for finite N and for N → ∞.

Transition rates via Bethe ansatz for the spin-½ Heisenberg chain

Europhysics Letters (EPL), 2002

We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s = 1 2 Heisenberg model to calculate and numerically evaluate transition rates pertaining to dynamic spin structure factors. For real solutions z1, . . . , zr of the Bethe ansatz equations, the size of the determinants is of order r ×r. We present applications to the zero-temperature spin fluctuations parallel and perpendicular to an external magnetic field.

Transition rates via Bethe ansatz for the spin-� Heisenberg chain

Europhysics Letters, 2002

We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s = ½ Heisenberg model to calculate and numerically evaluate transition rates pertaining to dynamic spin structure factors. For real solutions z1,..., zr of the Bethe ansatz equations, the size of the determinants is of order r×r. We present applications to the zero-temperature spin fluctuations parallel and perpendicular to an external magnetic field.

Thermodynamic Bethe ansatz for the spin-1/2 staggered XXZ-model

Nuclear Physics B, 2003

We develop the technique of Thermodynamic Bethe Ansatz to investigate the ground state and the spectrum in the thermodynamic limit of the staggered XXZ models proposed recently as an example of integrable ladder model. This model appeared due to staggered inhomogeneity of the anisotropy parameter ∆ and the staggered shift of the spectral parameter. We give the structure of ground states and lowest lying excitations in two different phases which occur at zero temperature.

Transition rates via Bethe ansatz for the spin-1/2 planar XXZ antiferromagnet

Journal of Physics A: Mathematical and General, 2003

A novel determinantal representation for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s = 1 2 XXZ model is used to calculate transition rates for dynamic spin structure factors in the planar regime. In a first application, high-precision numerical data are presented for lineshapes and band edge singularities of the in-plane (xx) two-spinon dynamic spin structure factor.

Interaction and thermodynamics of spinons in the XX chain

Journal of Physics A: Mathematical and Theoretical, 2008

The mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) For finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N → ∞ the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling, and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane-Shastry model.

Origin of the singular Bethe ansatz solutions for the Heisenberg XXZ spin chain

Physica A: Statistical Mechanics and its Applications, 2000

We investigate symmetry properties of the Bethe ansatz wave functions for the Heisenberg XXZ spin chain. The XXZ Hamiltonian commutes simultaneously with the shift operator T and the lattice inversion operator V in the space of Ω = ±1 with Ω the eigenvalue of T . We show that the Bethe ansatz solutions with normalizable wave functions cannot be the eigenstates of T and V with quantum number (Ω, Υ) = (±1, ∓1) where Υ is the eigenvalue of V . Therefore the Bethe ansatz wave functions should be singular for nondegenerate eigenstates of the Hamiltonian with quantum number (Ω, Υ) = (±1, ∓1). It is also shown that such states exist in any nontrivial down-spin number sector and that the number of them diverges exponentially with the chain length.

XXX Spin Chain: from Bethe Solution to Open Problems

2007

We present some open problems in the field of exactly solvable models. Two of the problems are related to the correlation functions of the XXX spin chain and the XXZ spin chain, one to the entropy of subsystems and one to the six vertex model with domain wall boundary conditions.

Bethe Ansatz for XXX chain with negative spin

International Journal of Modern Physics A

XXX spin chain with spin s = −1 appears as an effective theory of Quantum Chromodynamics. It is equivalent to lattice nonlinear Schroediger's equation: interacting chain of harmonic oscillators [bosonic]. In thermodynamic limit each energy level is a scattering state of several elementary excitations [lipatons]. Lipaton is a fermion: it can be represented as a topological excitation [soliton] of original [bosonic] degrees of freedom, described by the group Z 2 . We also provide the CFT description (including local quenches) and Yang-Yang thermodynamics of the model. * haoke72@163.com