General spectral function expressions of a 1D correlated model

We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of pseudofermion operators such that the spectral functions can be written as a convolution of pseudofermion dynamical correlation functions. Our results are valid for all finite energy and momentum values and are used elsewhere in the study of the unusual finite-energy properties of quasi-one-dimensional compounds and the new quantum systems of ultra-cold fermionic atoms on an optical lattice.Comment: 25 pages, no figure

Order by disorder in a four flavor Mott-insulator on the fcc lattice

The classical ground states of the SU(4) Heisenberg model on the face centered cubic lattice constitute a highly degenerate manifold. We explicitly construct all the classical ground states of the model. To describe quantum fluctuations above these classical states, we apply linear flavor-wave theory. At zero temperature, the bosonic flavor waves select the simplest of these SU(4) symmetry breaking states, the four-sublattice ordered state defined by the cubic unit cell of the fcc lattice. Due to geometrical constraints, flavor waves interact along specific planes only, thus rendering the system effectively two dimensional and forbidding ordering at finite temperatures. We argue that longer range interactions generated by quantum fluctuations can shift the transition to finite temperatures

Degeneracy and ordering of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice

We investigate the zero-temperature behavior of the classical Heisenberg model on the triangular lattice in which the competition between exchange interactions of different orders favors a relative angle between neighboring spins in the interval (0,2pi/3). In this situation, the ground states are noncoplanar and have an infinite discrete degeneracy. In the generic case, the set of the ground states is in one to one correspondence (up to a global rotation) with the non-crossing loop coverings of the three equivalent honeycomb sublattices into which the bonds of the triangular lattice can be partitioned. This allows one to identify the order parameter space as an infinite Cayley tree with coordination number 3. Building on the duality between a similar loop model and the ferromagnetic O(3) model on the honeycomb lattice, we argue that a typical ground state should have long-range order in terms of spin orientation. This conclusion is further supported by the comparison with the four-state antiferromagnetic Potts model [describing the case when the angle between neighboring spins is equal to arccos(-1/3)], which at zero temperature is critical and in terms of the solid-on-solid representation is located exactly at the point of roughening transition. At other values of the angle between neighboring spins an additional constraint appears, whose presence drives the system into an ordered phase (unless this angle is equal to pi/2, when another constraint is removed and the model becomes trivially exactly solvable).Comment: 10 pages, 5 figure

Dynamical Functions of a 1D Correlated Quantum Liquid

We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion

Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices

Combining a semi-classical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest-neighbor interactions is shown to be the consequence of a subtle quantum order-by-disorder mechanism. By contrast, thermal fluctuations favor two-sublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mott-insulating states of three-flavor fermionic atoms in optical lattices are discussed.Comment: 4 pages, 3 figures, minor changes, references adde

Finite-Energy Spectral-Weight Distributions of a 1D Correlated Metal

We derive general closed-form analytical expressions for the finite-energy one- and two-electron spectral-weight distributions of an one-dimensional correlated metal with on-site electronic repulsion. Our results also provide general expressions for the one- and two-atom spectral functions of a correlated quantum system of cold fermionic atoms in a one-dimensional optical lattice with on-site atomic repulsion. In the limit of zero spin density our spectral-function expressions provide the correct zero-spin density results. Our results reveal the dominant non-perturbative microscopic many-particle mechanisms behind the exotic spectral properties observed in quasi-one-dimensional metals and correlated systems of cold fermionic atoms in one-dimensional optical lattices.Comment: 30 pages, no figure