We investigate spin-order of ultracold bosons in an optical lattice by means of Dynamical Mean-Field Theory. A rich phase diagram with anisotropic magnetic order is found, both for the ground state and at finite temperatures. Within the Mott insulator, a ferromagnetic to antiferromagnetic transition can be tuned using a spin-dependent optical lattice. In addition we find a supersolid phase, in which superfluidity coexists with antiferromagnetic spin order. We present detailed phase diagrams at finite temperature for the experimentally realized heteronuclear 87 Rb -41 K mixture in a three-dimensional optical lattice.

We apply Dynamical Mean-Field Theory to strongly interacting fermions in an inhomogeneous environment. With the help of this Real-Space Dynamical Mean-Field Theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions with spin 1 2 in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.Submitted to: New J. Phys.

We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized DMFT scheme, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.PACS numbers: 03.75. Lm, 32.80.Pj, 67.40.Vs Ultracold atomic gases confined in optical lattices provide a new laboratory for investigating quantum manybody problems with high precision and tunability [1,2]. In this way new light can be shed on notoriously difficult problems in condensed matter physics [3]. One of the intriguing aspects of cold atoms is that the atomic quantum statistics can be controlled. In particular, cold atomic gases offer the possibility to realize mixtures of fermions and bosons [4,5,6,7,8], recently also in an optical lattice [9,10]. It is thus possible to create physical systems without analog in conventional solid state physics.An exotic quantum phase that has intrigued researchers for a while is the supersolid with superfluid order, i.e. broken U (1) symmetry, and coexisting particle density wave order. It is still an open question whether a supersolid has been realized in recent experiments on 4 He [11]. While in single-component quantum gases supersolids can only be stabilized by including nearest neighbor repulsion between the particles [12], they can be conveniently realized in Bose-Fermi mixtures with on-site repulsion as we show in this Letter. Earlier theoretical studies already suggested that Bose-Fermi mixtures can be unstable against charge density wave (CDW) and supersolid order or phase separation (PS). However, so far all theoretical approaches either dealt with onedimensional systems [13,14,15,16,17,18,19], or relied on weak-coupling approximations [20,21,22].Here we introduce and apply a generalized dynamical mean-field theory (GDMFT) that treats this problem in a fully non-perturbative way. In this method the fermions are described by dynamical mean field theory (DMFT) [23], into which the bosons are incorporated by means of the static Gutzwiller decoupling approximation [24] of the hopping. This approach therefore reproduces the strong coupling behavior of both the fermions and the bosons. In particular it is able to describe the formation of a bosonic Mott insulator state for strong repulsion between the bosons at integer filling. Here we restrict ourselves to half filling for both the bosons and fermions ( n b = n f = 1 2 ). For weak interspecies repulsion we predict the formation of a supersolid phase, in which the bosons form a superfluid with spatially modulated density and the fermions form a CDW. For stronger r...

A gene signature specific for intestinal stem cells (ISCs) has recently been shown to predict relapse in colorectal cancer (CRC) but the tumorigenic role of individual signature genes remains poorly defined. A prominent ISC-signature gene is the cancer stem cell marker CD44, which encodes various splice variants comprising a diverse repertoire of adhesion and signaling molecules. Using Lgr5 as ISC marker, we have fluorescence-activated cell sorting-purified ISCs to define their CD44 repertoire. ISCs display a specific set of CD44 variant isoforms (CD44v), but remarkably lack the CD44 standard (CD44s) isoform. These CD44v also stand-out in transformed human ISCs isolated from microadenomas of familial adenomatous polyposis patients. By employing knock-in mice expressing either CD44v4-10 or CD44s, we demonstrate that the CD44v isoform, but not CD44s, promotes adenoma initiation in Apc(Min/+)mice. Our data identify CD44v as component of the ISCs program critical for tumor initiation, and as potential treatment target in CRC.