Threshold singularities in the one-dimensional Hubbard model

Abstract

We consider excitations with the quantum numbers of a hole in the one-dimensional Hubbard model below half-filling. We calculate the finite-size corrections to the energy. The results are then used to determine threshold singularities in the single-particle Green's function for commensurate fillings. We present the analogous results for the Yang-Gaudin model ͑electron gas with ␦-function interactions͒.

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

“…Notice that the ω − 2c2s (q) line is not the same as the spinon mass shell, in contrast with the lower edge for the metallic phase. 17,20 Finally, we note that in the limit U → 0 the line ω − 2c2s (q) becomes the lower edge of the electron-hole continuum, ω − 2c2s (q) → 2 sin q, whereas the lower edge of the two-holon continuum becomes the upper edge of the electron-hole continuum, ω − 2c (q) → 4 sin(q/2). As U → 0, we expect that all the spectral weight of S(q, ω) becomes confined between ω − 2c2s (q) and ω − 2c (q) in order to recover the free electron result.…”

“…Although we are not able to derive the bare coupling constants starting from the Hubbard model for general U , we shall assume that κ R,L are positive for U > 0 because otherwise we would not recover the known results for the Heisenberg model. Moreover, it is known that the finite size spectrum for excited states of the Hubbard model that contain high energy holes in the spin band fits the "shifted" conformal field theory form, 17 suggesting that the marginal operator should be irrelevant for any finite U . With the asymptotic decoupling of the impurity spinon, the symmetry of the effective model (51) becomes…”

“…Notice that the exponents predicted by the SU (2) invariant impurity models are all half-integers, in contrast with the continuously varying exponents of the metallic phase. 10,17 IV. NUMERICAL RESULTS…”

“…This approach, combined with the BA solution, has also been applied to calculate edge exponents for the spectral function of the Hubbard model away from half filling. 17 In this work we are interested in finite energy dynamical correlation functions for the Hubbard model at halffilling. Clearly, the edge exponents of the Mott insulating phase should differ from those of the metallic phase studied in Refs.…”

“…[4][5][6][7][8] In addition, ultracold atoms trapped in optical lattices have emerged as a new means to study coherent dynamics of 1D models, including integrable ones which are not realizable in condensed matter systems. 9 At the same time, significant progress has been achieved in developing analytical [10][11][12][13][14][15][16][17][18][19][20][21][22] and numerical [23][24][25] techniques to study dynamical correlation functions in the high energy regime where conventional Luttinger liquid theory 26,27 does not apply. Analytically, it is possible to compute exponents of power-law singularities that develop near thresholds of the spectrum of dynamical correlation functions at arbitrarily high energies.…”