Field theory of ferrimagnetic Hubbard chains

We present an extensive study of the AB(2) polymeric Hubbard chains with ex perimental motivation in inorganic and organic compounds. In the half-fille d strong-coupling limit, these systems can be mapped onto a quantum antifer romagnetic spin-1/2 AB(2) Heisenberg model that presents a zero-temperature quantum phase transition to a ferrimagnetic ground state. We derive the sp in-wave modes with the same correct ferromagnetic dispersion relation calcu lated through two different techniques. We also build an Euclidean integral formulation in the coherent state representation which naturally gives ris e to Wess-Zumino terms of topological origin. The low-energy infrared behav ior of the AB(2) chains is properly described through a renormalization gro up analysis by the semiclassical fixed point of a one-dimensional quantum n onrelativistic nonlinear sigma model with critical dynamical exponent z = 2 . Their low-temperature behavior is shown to be the same of a quantum ferro magnetic spin-1/2 Heisenberg chain, as evidenced by the temperature depende nce of the correlation length, susceptibility, and specific heat. On the ot her hand, a quantum critical fixed point is also found, with the same zero- temperature critical behavior of a classical Heisenberg system in D = d + z = 3 dimensions. Its low-temperature critical properties are related to the latter through the crossover exponent phi = z nu(3), where nu(3) is the co rrelation length exponent of the D = 3 classical Heisenberg model. Sufficie ntly strong quantum critical fluctuations destroy the ordered ground state of the quantum z = 2 nonlinear sigma model (but not that of the quantum AB( 2) Heisenberg spin systems, in agreement with a theorem by Lieb), giving ri se to a quantum disordered phase at zero temperature. These results are sup ported by a connection between the quantum AB(2) Heisenberg and generalized quantum rotor models. [S0163-1839(99)14671-6].