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Excited states in Bethe ansatz solvable models and the dressing of spin and charge

Eoin Quinn, Sergey A. Frolov

Published Jan 1, 2013• 8 citations
OpenAlex

Abstract

A general formalism for the study of excitations above equilibrium in Bethe ansatz\nsolvable models is presented. Nonzero temperature expressions for dressed energy,\nmomentum, spin and charge are obtained. The zero temperature excitations of the\nHubbard-Shastry models are examined in detail, and special attention is paid to the\ndressing of spin and charge of excited quasi-particles. These are in general momentum\ndependent and are only spin-charge separated when the ground state is half- lled and\nhas zero magnetisation

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A general formalism for the study of excitations above equilibrium in Bethe ansatz\nsolvable models is presented. Nonzero temperature expressions for dressed energy,\nmomentum, spin and charge are obtained. The zero temperature excitations of the\nHubbard-Shastry models are examined in detail, and special attention is paid to the\ndressing of spin and charge of excited quasi-particles. These are in general momentum\ndependent and are only spin-charge separated when the ground state is half- lled and\nhas zero magnetisation
A general formalism for the study of excitations above equilibrium in Bethe ansatz solvable models is presented. Nonzero temperature expressions for dressed energy, momentum, spin and charge are obtained, and it is found that the dressed spin and charge are in general momentum dependent. For an electronic model one may only have spin-charge separation at zero temperature where the ground state is half-filled and has zero magnetisation. Finally, the excitations of the Hubbard-Shastry models are examined in detail.
Abstract In this note, we discuss the low and high temperature contribution of thermodynamic Bethe ansatz (TBA) dressed excitations in the thermodynamics and energy-magnetization relaxation within the generalized hydrodynamics approach in the linear response regime. In particular, we show how the temperature dependent dispersions of the excitations reproduce well known behavior of the specific heat, magnetic susceptibility, spin and energy Drude weights. In this context, we derive a further formulation of the Drude weights from the finite wavevector relaxation. Furthermore, we contrast the TBA description of thermodynamics and dynamics in terms of a multitude of string excitations to that in terms of a single quasi-particle in low energy effective theories.
Building on the fundamentals introduced in part I, we employ the Bethe ansatz to study some ground-state properties (energy, magnetization, susceptibility) of the one-dimensional s=1/2 Heisenberg antiferromagnet in zero and nonzero magnetic field. The 2-spinon triplet and singlet excitations from the zero-field ground state are discussed in detail, and their energies are calculated for finite and infinite chains. Procedures for the numerical calculation of real and complex solutions of the Bethe ansatz equations are discussed and applied. The paper is designed as a tutorial for beginning graduate students. It includes 10 problems for further study.
Abstract We present a general derivation of the spectrum of excitations for gapless states of zero entropy density in Bethe ansatz solvable models. Our formalism is valid for an arbitrary choice of bare energy function which is relevant to situations where the Hamiltonian for time evolution differs from the Hamiltonian in a (generalized) Gibbs ensemble, i.e. out of equilibrium. The energy of particle and hole excitations, as measured with the time-evolution Hamiltonian, is shown to include additional contributions stemming from the shifts of the Fermi points that may now have finite energy. The finite-size effects are also derived and the connection with conformal field theory discussed. The critical exponents can still be obtained from the finite-size spectrum, however the velocity occurring here differs from the one in the constant Casimir term. The derivation highlights the importance of the phase shifts at the Fermi points for the critical exponents of asymptotes of correlations. We generalize certain results known for the ground state and discuss the relation to the dressed charge (matrix). Finally, we discuss the finite-size corrections in the presence of an additional particle or hole, which are important for dynamical correlation functions.
The non-equilibrium steady states of integrable models are believed to be described by the Generalized Gibbs Ensemble (GGE), which involves all local and quasi-local conserved charges of the model. In this work we investigate integrable lattice models solvable by the nested Bethe Ansatz, with group symmetry SU(N) S U ( N ) , N\ge 3 N ≥ 3 . In these models the Bethe Ansatz involves various types of Bethe rapidities corresponding to the “nesting” procedure, describing the internal degrees of freedom for the excitations. We show that a complete set of charges for the GGE can be obtained from the known fusion hierarchy of transfer matrices. The resulting charges are quasi-local in a certain regime in rapidity space, and they completely fix the rapidity distributions of each string type from each nesting level.