Single-site Mean Field Research Articles

Finite temperature phases and excitations of bosons on a square lattice: a cluster mean field study

We study the finite temperature phases and collective excitations of hardcore as well as softcore bosons on a square lattice with nearest and next nearest neighbor interactions, focusing on the formation of various types of supersolid (SS) phases and their stability under thermal fluctuations. The interplay between the on-site, nearest, and next nearest neighbor interactions leads to various density ordering and structural transitions, which we have plotted out. Thermodynamic properties and phase diagrams are obtained by cluster mean field theory at finite temperatures, which includes quantum effects systematically, and they are compared with the single-site mean field (MF) results. We investigate the melting process of the SS phase to normal fluid (NF), which can occur in at least two steps due to the presence of two competing orders in the SS. A tetra-critical point exists at finite temperature and exhibits intriguing behavior, which is analyzed for different regimes of interactions. The phase diagrams reveal the different pathways of the thermal transition of SSs to the NF phase, for different interaction regimes, which can be accessible by thermal quench protocols used in recent experiments. We show how the phases and the transitions between them can be identified from the characteristic features of the excitation spectrum. We analyze the appearance of a low-energy gapped mode apart from the gapless sound mode in the SS phase, which is analogous to the gapped mode recently studied for dipolar SS phases. Finally, we discuss the relevance of the results of the present work in the context of ongoing experiments on ultracold atomic gases and newly observed SS phases.

Vacancy formation energy in CuNiCo equimolar alloy and CuNiCoFe high entropy alloy: ab initio based study

In this research, the interaction between the composing elements of CuNiCoFe high entropy alloy with vacancies was investigated employing EMTO-LSGF and EMTO-CPA codes based on DFT calculations. In this regard, for the equimolar CuNiCo and CuNiCoFe alloys with the face center cubic structure, variation of vacancy formation energy was calculated as a function of the number of the nearest neighbors of composing elements. The results reveal that copper atoms have the strongest interaction with vacancy among all elements in both CuNiCo and CuNiCoFe equimolar alloys. The mean local vacancy formation energy (<Ef>) was calculated based on its distribution function for both alloys. Since the differences between the interaction energy of Cu-vacancy and other metal-vacancies in these two equimolar alloys was significant, to calculate the distribution function of vacancy formation energy and its dependence to temperature, equimolar CuNiCo and CuNiCoFe were estimated by a quasi-binary alloy. In this quasi-binary alloy copper is one of the components and other elements could be other components. The results show that <Ef> of equimolar CuNiCoFe is 0.176 eV greater than that for CuNiCo equimolar alloy. The dependence of effective vacancy formation energy (E¯f) and renormalized vacancy formation energy (E˜f) to temperature is estimated using the single-site mean field approximations with energy parameters obtained in ab initio calculations. In these calculations, the alloy configurational entropy was used. The results indicate higher E¯f and E˜f values with increasing temperature from 400 to 2500K in both alloys. The values of E¯f and E˜f for CuNiCoFe are greater than those in CuNiCo within this range of temperature.

Cluster mean-field signature of entanglement entropy in bosonic superfluid-insulator transitions

Entanglement entropy (EE), a fundamental conception in quantum information for characterizing entanglement, has been extensively employed to explore quantum phase transitions (QPTs). Although the conventional single-site mean-field (MF) approach successfully predicts the emergence of QPTs, it fails to include any entanglement. Here, for the first time, in the framework of a cluster MF treatment, we extract the signature of EE in the bosonic superfluid-insulator transitions. We consider a trimerized Kagome lattice of interacting bosons, in which each trimer is treated as a cluster, and implement the cluster MF treatment by decoupling all inter-trimer hopping. In addition to superfluid and integer insulator phases, we find that fractional insulator phases appear when the tunneling is dominated by the intra-trimer part. To quantify the residual bipartite entanglement in a cluster, we calculate the second-order Renyi entropy, which can be experimentally measured by quantum interference of many-body twins. The second-order Renyi entropy itself is continuous everywhere, however, the continuousness of its first-order derivative breaks down at the phase boundary. This means that the bosonic superfluid-insulator transitions can still be efficiently captured by the residual entanglement in our cluster MF treatment. Besides to the bosonic superfluid-insulator transitions, our cluster MF treatment may also be used to capture the signature of EE for other QPTs in quantum superlattice models.

Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems

We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1=2 on a lattice interacting through an XYZ Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.

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.

Response of electrically coupled spiking neurons: A cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate vs. stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by n-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is alpha=1, while for deterministic spike propagation we obtain alpha=1/2, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.

Screened Coulomb interactions in metallic alloys. I. Universal screening in the atomic-sphere approximation

We have used the locally self-consistent Green's function (LSGF) method in supercell calculations to establish the distribution of the net charges assigned to the atomic spheres of the alloy components in metallic alloys with different compositions and degrees of order. This allows us to determine the Madelung potential energy of a random alloy in the single-site mean field approximation which makes the conventional single-site density-functional- theory coherent potential approximation (SS-DFT-CPA) method practically identical to the supercell LSGF method with a single-site local interaction zone that yields an exact solution of the DFT problem. We demonstrate that the basic mechanism which governs the charge distribution is the screening of the net charges of the alloy components that makes the direct Coulomb interactions short-ranged. In the atomic sphere approximation, this screening appears to be almost independent of the alloy composition, lattice spacing, and crystal structure. A formalism which allows a consistent treatment of the screened Coulomb interactions within the single-site mean-filed approximation is outlined. We also derive the contribution of the screened Coulomb interactions to the S2 formalism and the generalized perturbation method.

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.