Single-site Mean-field Theory Research Articles

Competing ground states of strongly correlated bosons in the Harper-Hofstadter-Mott model

Using an efficient cluster approach, we study the physics of two-dimensional lattice bosons in a strong magnetic field in the regime where the tunneling is much weaker than the on-site interaction strength. We study both dilute, hard core bosons at filling factors much smaller than unity occupation per site, and the physics in the vicinity of the superfluid-Mott lobes as the density is tuned away from unity. For hardcore bosons, we carry out extensive numerics for a fixed flux per plaquette $\phi=1/5$ and $\phi = 1/3$. At large flux, the lowest energy state is a strongly correlated superfluid, analogous to He-$4$, in which the order parameter is dramatically suppressed, but non-zero. At filling factors $\nu=1/2,1$, we find competing incompressible states which are metastable. These appear to be commensurate density wave states. For small flux, the situation is reversed, and the ground state at $\nu = 1/2$ is an incompressible density-wave solid. Here, we find a metastable lattice supersolid phase, where superfluidity and density-wave order coexist. We then perform careful numerical studies of the physics near the vicinity of the Mott lobes for $\phi = 1/2$ and $\phi = 1/4$. At $\phi = 1/2$, the superfluid ground state has commensurate density-wave order. At $\phi = 1/4$, incompressible phases appear outside the Mott lobes at densities $n = 1.125$ and $n = 1.25$, corresponding to filling fractions $\nu = 1/2$ and $1$ respectively. These phases, which are absent in single-site mean-field theory are metastable, and have slightly higher energy than the superfluid, but the energy difference between them shrinks rapidly with increasing cluster size, suggestive of an incompressible ground state. We thus explore the interplay between Mott physics, magnetic Landau levels, and superfluidity, finding a rich phase diagram of competing compressible and incompressible states.

Fluctuation Effects in Phase-Frustrated Multiband Superconductors

In this paper, we compute the phase diagrams of an effective model of a three-dimensional multiband superconductor which is phase-frustrated by interband Josephson couplings. Four different computations are performed and compared: (i) standard mean field theory, (ii) cluster mean field theory, (iii) large-scale Monte Carlo computations including phase fluctuations but no gauge field fluctuations, and (iv) large-scale Monte Carlo computations including phase fluctuations and gauge field fluctuations. Here, phase fluctuations refer to fluctuations in the phases of the components of the superconducting order parameter. Our findings may be summarized as follows: (i) The standard mean field theory treatment fails in locating correctly the positions of the phase transitions, as well as the character of the transitions between the different states. (ii) A cluster mean field calculations taking into account order parameter fluctuations in a local environment improves the results considerably. This shows that phase fluctuations in the superconducting order parameter are important in these three-dimensional systems. The origin of the strong phase fluctuations is frustration due to interband Josephson couplings. However, a novel chiral metallic phase found in previous works using large-scale Monte Carlo computations is not obtained either within the single-site mean field theory or the improved cluster mean field theory of order parameter fluctuations. (iii) Including all phase fluctuations, but no gauge field fluctuations, in the effective model in large-scale Monte Carlo computations yields results essentially in agreement with the cluster mean field calculations. (iv) Including all phase fluctuations and gauge field fluctuations in the effective model in large-scale Monte Carlo computations shows that the inclusion of gauge field fluctuations is crucial in bringing about the novel chiral metallic state in three dimensions.

Exotic spin orders driven by orbital fluctuations in the Kugel-Khomskii model

We study zero temperature phase diagram of the three-dimensional Kugel-Khomskii model on a cubic lattice using the cluster mean field theory and different perturbative expansions in the orbital sector. The phase diagram is rich, goes beyond the single-site mean field theory due to spin-orbital entanglement. In addition to the antiferromagnetic (AF) and ferromagnetic (FM) phases, one finds also a plaquette valence-bond phase with singlets ordered either on horizontal or vertical bonds. More importantly, for increasing Hund's exchange we identify three phases with exotic magnetic order stabilized by orbital fluctuations in between the AF and FM order: (i) an AF phase with two mutually orthogonal antiferromagnets on two sublattices in each $ab$ plane and AF order along the c axis (ortho-$G$-type phase), (ii) a canted-$A$-type AF phase with a non-trivial canting angle between nearest neighbor FM layers along the c axis, and (iii) a striped-AF phase with anisotropic AF order in the $ab$ planes. We elucidate the mechanism responsible for each of the above phases by deriving effective spin models which involve second and third neighbor Heisenberg interactions as well as four-site spin interactions going beyond Heisenberg physics, and explain how the entangled nearest neighbor spin-orbital superexchange generates spin interactions between more distant spins.

Ab Initio Study of Lattice Site Occupancies in Binary Sigma Phases Using a Single-Site Mean Field Model

The site occupation of binary Fe-Cr, Co-Cr, Re-W and Fe-V sigma phases is studied in the present work with a first-principles-based single-site mean field theory. We show that the alloy components in these systems exhibit similar site preferences except for the Re-W system, where the occupation of two sites is reversed in agreement with previously published works. In case of the FeV sigma phase, for which the size mismatch between the alloy components is large, we also include into our consideration the effect of local lattice relaxations. The obtained results are found in good agreement with the experimental data and previous theoretical studies.

Application of a multisite mean-field theory to the disordered Bose-Hubbard model

We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose glass-to-superfluid transition, one an approximation based on the behaviour of the condensate fraction, and one of which relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non self-averaging is discussed.

Some aspects of the theory of magnets with competing double exchange and superexchange interactions

In the CMR materials, ferromagnetic double exchange (DE) presumably coexists with a direct nearest-neighbour antiferromagnetic interaction. We construct a single-site mean field theory that explicitly takes into account the different nature of carrier-mediated ferromagnetism vs. Heisenberg-like superexchange. We find, in contrast to previous results in the literature, that the competition between these two exchange interactions leads to ferro- or antiferromagnetic order with incomplete saturation of the magnetization (or sublattice magnetization), rather than spin canting. The associated experimental implications are discussed.

A mean field theory of magnets with competing double exchange and superexchange interactions

We study the competition between ferromagnetic double exchange (DE) and direct nearest-neighbor antiferromagnetic exchange JAF in two-dimensional colossal magnetoresistance materials. Towards this end, a single site mean field theory is proposed which incorporates the hopping-mediated nature of the DE contribution. The canted state appears only under highly restricted conditions. Instead, in the regime where the antiferromagnetic and DE ferromagnetic interactions are of comparable scale (and in the classical limit), the system exhibits ferro- or antiferromagnetic order with incomplete saturation of the lattice or sublattice magnetization. We interpret these results as an indication that spin fluctuations remain strong even at low temperatures and discuss the associated experimental implications.