Many-body effects are at the very heart of diverse phenomena found in condensed-matter physics. One striking example is the Mott insulator phase where conductivity is suppressed as a result of a strong repulsive interaction. Advances in cold atom physics have led to the realization of the Mott insulating phases of atoms in an optical lattice, mimicking the corresponding condensed matter systems. Here, we explore an exotic strongly-correlated system of Interacting Dual Mott Insulators of bosons and fermions. We reveal that an inter-species interaction between bosons and fermions drastically modifies each Mott insulator, causing effects that include melting, generation of composite particles, an anti-correlated phase, and complete phase-separation. Comparisons between the experimental results and numerical simulations indicate intrinsic adiabatic heating and cooling for the attractively and repulsively interacting dual Mott Insulators, respectively.

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The reduced density matrix (RDM) method, which is a variational calculation based on the second-order reduced density matrix, is applied to the ground state energies and the dipole moments for 57 different states of atoms, molecules, and to the ground state energies and the elements of 2-RDM for the Hubbard model. We explore the well-known N-representability conditions (P, Q, and G) together with the more recent and much stronger T1 and T2(') conditions. T2(') condition was recently rederived and it implies T2 condition. Using these N-representability conditions, we can usually calculate correlation energies in percentage ranging from 100% to 101%, whose accuracy is similar to CCSD(T) and even better for high spin states or anion systems where CCSD(T) fails. Highly accurate calculations are carried out by handling equality constraints and/or developing multiple precision arithmetic in the semidefinite programming (SDP) solver. Results show that handling equality constraints correctly improves the accuracy from 0.1 to 0.6 mhartree. Additionally, improvements by replacing T2 condition with T2(') condition are typically of 0.1-0.5 mhartree. The newly developed multiple precision arithmetic version of SDP solver calculates extraordinary accurate energies for the one dimensional Hubbard model and Be atom. It gives at least 16 significant digits for energies, where double precision calculations gives only two to eight digits. It also provides physically meaningful results for the Hubbard model in the high correlation limit.

Anorexia nervosa (AN) results in gut dysbiosis, but whether the dysbiosis contributes to AN-specific pathologies such as poor weight gain and neuropsychiatric abnormalities remains unclear. To address this, germ-free mice were reconstituted with the microbiota of four patients with restricting-type AN (gAN mice) and four healthy control individuals (gHC mice). The effects of gut microbes on weight gain and behavioral characteristics were examined. Fecal microbial profiles in recipient gnotobiotic mice were clustered with those of the human donors. Compared with gHC mice, gAN mice showed a decrease in body weight gain, concomitant with reduced food intake. Food efficiency ratio (body weight gain/food intake) was also significantly lower in gAN mice than in gHC mice, suggesting that decreased appetite as well as the capacity to convert ingested food to unit of body substance may contribute to poor weight gain. Both anxiety-related behavior measured by open-field tests and compulsive behavior measured by a marble-burying test were increased only in gAN mice but not in gHC mice. Serotonin levels in the brain stem of gAN mice were lower than those in the brain stem of gHC mice. Moreover, the genus Bacteroides showed the highest correlation with the number of buried marbles among all genera identified. Administration of Bacteroides vulgatus reversed compulsive behavior but failed to exert any substantial effect on body weight. Collectively, these results indicate that AN-specific dysbiosis may contribute to both poor weight gain and mental disorders in patients with AN.