The exact solution of the A (2) n integrable lattice models is presented. The free energy and excitation energies of the vertex models are found as functions of the spectral and anisotropy parameters as well as the finite-size corrections yielding the central charges and conformal dimensions. These lattice models yield a new massive QFT where the mass spectrum and the S-matrix are obtained through the light-cone approach. The ground state and excitation energies of a new anisotropic spin-one integrable chain associated to the A (2) 2 model are computed.The exact solution of the A (2) n integrable lattice models is presented. The free energy and excitation energies of the vertex models are found as functions of the spectral and anisotropy parameters as well as the finite-size corrections yielding the central charges and conformal dimensions. These lattice models yield a new massive QFT where the mass spectrum and the S-matrix are obtained through the light-cone approach. The ground state and excitation energies of a new anisotropic spin-one integrable chain associated to the A (2) 2 model are computed.

Journal of Physics A Mathematical and GeneralSep 7, 19902 citations

Fermionic spectra in integrable models

Rinat Kedem

Jan 1, 20140 citations

Numerical Renormalization Group for Continuum One-Dimensional Systems

Robert Konik, Yury Adamov

We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Wilson's numerical renormalization group with Zamolodchikov's truncated conformal spectrum approach. The key to the method is that such theories provide a set of completely understood eigenstates for which matrix elements can be exactly computed. In this procedure the RG flow of physical observables can be studied both numerically and analytically. To demonstrate the approach, we study the spectrum of a pair of coupled quantum Ising chains and correlation functions in a single quantum Ising chain in the presence of a magnetic field.We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Wilson's numerical renormalization group with Zamolodchikov's truncated conformal spectrum approach. The key to the method is that such theories provide a set of completely understood eigenstates for which matrix elements can be exactly computed. In this procedure the RG flow of physical observables can be studied both numerically and analytically. To demonstrate the approach, we study the spectrum of a pair of coupled quantum Ising chains and correlation functions in a single quantum Ising chain in the presence of a magnetic field.

arXiv:cond-mat/0701605Physical Review LettersApr 6, 200784 citations

Exact solutions of 1-D Hubbard model with open boundary conditions and the conformal dimensions under boundary magnetic fields

Tetsuo Deguchi, Rui‐Hong Yue

The Bethe ansatz equations of the 1-D Hubbard model under open boundary conditions are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model with open boundaries. Through the finite-size correction, we obtain the energy spectrum of the open chain and discuss the effects of boundary magnetic fields applied only at the edges of the chain. Several physical implications of the finite-size spectrum are discussed from the viewpoint of the boundary conformal field theories (BCFT); the conformal dimension of the spin excitation is quite sensitive to the boundary magnetic fields, and this sensitivity can be explained in terms of the $π/2$ -phase shift of the BCFT. For several limiting cases such as for the half-filling case, the conformal dimensions are explicitly calculated.The Bethe ansatz equations of the 1-D Hubbard model under open boundary conditions are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model with open boundaries. Through the finite-size correction, we obtain the energy spectrum of the open chain and discuss the effects of boundary magnetic fields applied only at the edges of the chain. Several physical implications of the finite-size spectrum are discussed from the viewpoint of the boundary conformal field theories (BCFT); the conformal dimension of the spin excitation is quite sensitive to the boundary magnetic fields, and this sensitivity can be explained in terms of the $π/2$-phase shift of the BCFT. For several limiting cases such as for the half-filling case, the conformal dimensions are explicitly calculated.

arXiv:cond-mat/9704138Apr 16, 19977 citations

Variational model for one-dimensional quantum magnets

Yu. B. Kudasov, R. V. Kozabaranov

arXiv:1801.10602Physics Letters AFeb 27, 20184 citations

π/2

-phase shift of the BCFT. For several limiting cases such as for the half-filling case, the conformal dimensions are explicitly calculated.