Functional integral theories of low-dimensional quantum Heisenberg models

Abstract

We investigate the low-temperature properties of the quantum Heisenberg models, both ferromagnetic and antiferromagnetic, in one and two dimensions. We study two diferent large-N formulations, using Schwinger bosons and S = 2 fermions, and solve for their low-order thermodynamic properties. Comparison with exact solutions in one dimension demonstrates the applicability of this expansion to the physical models at N =2. For the square lattice, we find at the mean-field level a low-temperature correlation length which behaves as (cc exp(A /T}, where A asymptotically approaches 2~S for large spin S, but As i/z-1. 16 and As &-5.46. We mention the relevance of our results to recent experiments in La2Cu04.

Fermionic theory for quantum antiferromagnets with spinS>12

“…In 1D, the gauge fluctuations can be removed by a time-dependent Read-Newns gauge transformation and thus have no effect to the low-energy properties. 6 The situation is very different in two or higher dimensions where the stability of the meanfield state depends on dimensionality and the ͑gauge͒ structure of the gauge field fluctuations. For instance, Z 2 spin liquid is believed to be stable at 2D ͑Ref.…”

“…3 However, it was suggested that for some antiferromagnetic materials, strong quantum fluctuations due to small spin magnitude and low dimensionality combined with geometric frustration may lead to quantum coherent, spin disordered ground states. 4,5 In such cases, a quantum fluid approach 6 is probably a better starting point to describe the low-energy physics instead of usual spin-wave or semiclassical approach.…”

“…In the "bosonic" approach 6,7 spins are represented by spin up and down Schwinger bosons with the constraint that total boson number at each site is 2S. A spin-disordered state is obtained in a mean-field theory as long as Bose condensation does not occur.…”

“…Up to now, the fermionic approach is mainly restricted to S = 1 2 spin systems. 6,8 Because of the Pauli exclusion principle, we cannot put more than two spin up or down fermions on a site to form S Ͼ 1 2 objects as in bosonic approach. One way out is to introduce more species of fermions.…”

“…6,11,12 In these approaches, N species of particles are introduced to construct the SU͑N͒-spin operator and Hamiltonians. 12 The major difference between our approach and the SU͑N͒ approaches is that ͑2S +1͒ species of fermions are introduced to form a SU͑2͒ spin ͓or irreducible representation of SU͑2͒ group͔ in our approach.…”