We perform a theoretical study of a fermionic gas with two hyperfine states confined to an optical lattice. We derive a generic state diagram as a function of interaction strength, particle number, and confining potential. We discuss the central density, the double occupancy and their derivatives as probes for the Mott state, connecting our findings to the recent experiment of Jördens et al. Using entropic arguments we compare two different strategies to reach the antiferromagnetic state in the presence of a trapping potential.
Successive quantum transitions in an intermediate regime are shown to exist between the superfluid and Mott insulating states for interacting bosonic atoms in one dimension with a trapping potential. These transitions, which are caused by the interplay of the trapping potential with the competition between the kinetic energy and the interaction, reveal novel many-body effects as reflected by low-lying excitation behavior, unconventional long-range correlations and an even-odd alternating squeezing process of superfluid bosons into the Mott insulating state. These features, most likely being ge…
We study the competition between a random potential and a commensurate potential on interacting fermionic and bosonic systems using a variety of methods. We focus on one dimensional interacting fermionic systems but higher dimensional bosonic and fermionic extensions, as well as classical equivalents are also discussed. Our methods which include bosonization, replica variational method, functional renormalization group (RG) and perturbation around the atomic limit, go beyond conventional perturbative expansions around the Luttinger liquid in one dimension. All these methods agree on the predic…
The Mott critical point between a metal and a correlated insulator has usually been studied via density or spin density bosonic mode fluctuations according to the standard Ginzburg-Landau-Wilson phase transition paradigm. A moment's reflection leads to increasing doubts that such an approach should work as the transition is nonmagnetic, voiding the relevance of spin density modes. Charge density modes are irrelevelant since the long range Coulomb interaction leads to a large plasmon gap and their incompressibility. In solidarity with these doubts, recent measurements of the Mott critical point…
We study various Mott insulating phases of interacting spin-3/2 fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole/spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations and topological characterizations. Near the SU(4) symmetric point, a quantum cr…
Comment on the paper "Absence of the Mott Glass Phase in 1D Disordered Fermionic Systems" by T. Nattermann, A. Petkovic, Z. Ristivojevic, and F. Schutze, Phys. Rev. Lett. 99, 186402 (2007).
We study theoretically the Mott metal-insulator transition for a system of fermionic atoms confined in a three-dimensional optical lattice and a harmonic trap. We describe an inhomogeneous system of several thousand sites using an adaptation of dynamical mean field theory solved efficiently with the numerical renormalization group method. Above a critical value of the on-site interaction, a Mott-insulating phase appears in the system. We investigate signatures of the Mott phase in the density profile and in time-of-flight experiments.
We show that a new state of matter, the d-wave Mott-insulator state (d-Mott state) (introduced recently by [H. Yao, W. F. Tsai, and S. A. Kivelson, Phys. Rev. B 76, 161104 (2007)]), which is characterized by a non-zero expectation value of a local plaquette operator embedded in an insulating state, can be engineered using ultra-cold atomic fermions in two-dimensional double-well optical lattices. We characterize and analyze the parameter regime where the $d$-Mott state is stable. We predict the testable signatures of the state in the time-of-flight measurements.
We investigate the continuous variation of electronic states from a Fermi liquid to a quantum spin liquid induced by chemical substitution in the organic dimer-Mott system of $κ$-[(BEDSe-TTF)$_x$(BEDT-TTF)$_{1-x}$]$_2$Cu[N(CN)$_2$]Br. Electrical transport measurements reveal that the mixing of BEDSe-TTF into the BEDT-TTF layers induces a quantum Mott transition around $x$=0.10. Although a charge gap disappears at this point, magnetic susceptibility and heat capacity measurements indicate that fermionic low-energy excitations remain in the insulating salts, suggesting that fermionic spin excita…
We calculate the rate of creation of double occupancies in a 3D Fermionic Mott insulator near half-filling by modulation of optical lattice potential. At high temperatures, incoherent holes lead to a broad response peaked at the Hubbard repulsion $U$. At low temperatures, antiferromagnetic order leads to a coherent peak for the hole along with broad features representing spin wave shake-off processes. This is manifested in the doublon creation rate as a sharp absorption edge and oscillations as a function of modulating frequency. Thus, modulation spectroscopy can be used as a probe of antiferr…
We study transport properties of the half-filled two-dimensional (2D) Hubbard model with spatially varying interactions, where a pattern of interacting and non-interacting sites is formed. We use Determinantal Quantum Monte Carlo method to calculate the double occupation, effective hopping and Drude weight. These data point to two phase transitions, driven by fermionic correlations. The first is the expected metal to a Mott insulating state. The second one, is an exotic transition from a Mott insulating state to a highly anisotropic metal, that takes place at large values of the fermion-fermio…
We use quantum Monte Carlo and exact diagonalization calculations to study the Mott-insulator to superconductor quantum phase transition in a two-dimensional fermionic Hubbard model with attractive interactions in the presence of a superlattice potential. The model introduced offers unique possibilities to study such transitions in optical lattice experiments. We show that, in regimes with moderate to strong interactions, the transition belongs to the 3D-XY universality class. We also explore the character of the lowest energy charge excitations in the insulating and superconducting phases and…
We study a class of SU(N) Heisenberg models, describing Mott insulators of fermionic ultra-cold alkaline earth atoms on the three-dimensional simple cubic lattice. Based on an earlier semiclassical analysis, magnetic order is unlikely, and we focus instead on a solvable large-N limit designed to address the competition among non-magnetic ground states. We find a rich phase diagram as a function of the filling parameter k, composed of a variety of ground states spontaneously breaking lattice symmetries, and in some cases also time reversal symmetry. One particularly striking example is a state …
Hall and optical conductivity experiments on the cuprates indicate that the low-energy fermionic degrees of freedom in a doped Mott insulator posess a component that is dynamcially generated and hence determined by the temperature. We show explicitly how the spectrum in the lower Hubbard band should be partitioned to describe such dynamically generated charge degrees of freedom and corroborate this picture with the results from the exact low-energy theory of the Hubbard model. A consequence of such dynamics is that the Landau one-to-one correspondence between bare electrons and the effective f…
In a solid material strong interactions between the electrons can lead to surprising properties. A prime example is the Mott insulator, where the suppression of conductivity is a result of interactions and not the consequence of a filled Bloch band. The proximity to the Mott insulating phase in fermionic systems is the origin for many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. Therefore it is highly desirable to use the novel experimental tools developed in atomic physics to access this regime. Indeed, the Hubbard model, which encompasses…
We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.
We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu$^\ast$ universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a $t$-…
We consider the fermionic SU($3$) Hubbard model on the triangular lattice in the presence of a three-sublattice staggered potential which provides the possibility to investigate the competition of charge and magnetic order in three-component systems. We show that depending on the strength of the staggered potential $Δ$, the Hubbard interaction $U$ destabilizes the band insulator (BI) at small $U$ into the Mott insulator (MI) at large $U$ in three different ways with different intermediate phases. This leads to a rich phase diagram in the $U$-$Δ$ plane. Our results indicate that multi-component…
We investigate the effect of mass imbalance in binary Fermi mixtures loaded in optical lattices. Using dynamical mean-field theory, we study the transition from a fluid to a Mott insulator driven by the repulsive interactions. For almost every value of the parameters we find that the light species with smaller bare mass is more affected by correlations than the heavy one, so that their effective masses become closer than their bare masses before a Mott transition occurs. The strength of the critical repulsion decreases monotonically as the mass imbalance grows so that the minimum is realized w…
The variational cluster approximation is used to study the ground-state properties and single-particle spectra of the three-component fermionic Hubbard model defined on the two-dimensional square lattice at half filling. First, we show that either a paired Mott state or color-selective Mott state is realized in the paramagnetic system, depending on the anisotropy in the interaction strengths, except around the SU(3) symmetric point, where a paramagnetic metallic state is maintained. Then, by introducing Weiss fields to observe spontaneous symmetry breakings, we show that either a color-density…
We report on the site-resolved observation of characteristic states of the two-dimensional repulsive Fermi-Hubbard model, using ultracold $^{40}$K atoms in an optical lattice. By varying the tunneling, interaction strength, and external confinement, we realize metallic, Mott-insulating, and band-insulating states. We directly measure the local moment, which quantifies the degree of on-site magnetization, as a function of temperature and chemical potential. Entropies per particle as low as $0.99(6)\,k_B$ indicate that nearest-neighbor antiferromagnetic correlations should be detectable using sp…
Non-equilibrium quantum phenomena are ubiquitous in nature. Yet, theoretical predictions on the real-time dynamics of many-body quantum systems remain formidably challenging, especially for high dimensions, strong interactions or disordered samples. Here we consider a notable paradigm of strongly correlated Fermi systems, the Mott phase of the Hubbard model, in a setup resembling ultracold-gases experiments. We study the three-dimensional expansion of a cloud into an optical lattice after removing the confining potential. We use time-dependent density-functional theory combined with dynamical …
Here the line shape of the up- and down-spin one-particle spectral functions at and in the (k,energy)-plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved non-perturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates th…
We study analytically and with the numerical time-evolving block decimation method the dynamics of an impurity in a bath of spinless fermions with nearest-neighbor interactions in a one-dimensional lattice. The bath is in a Mott insulator state with alternating sites occupied and the impurity interacts with the bath by repulsive on-site interactions. We find that when the magnitudes of the on-site and nearest-neighbor interactions are close to each other, the system shows excitations of two qualitatively distinct types. For the first type, a domain wall and an anti-domain wall of density propa…
The spectra and role in the spin dynamical properties of bound states of elementary magnetic excitations named Bethe strings that occur in some integrable spin and electronic one-dimensional models have recently been identified and realized in several materials by experiments. Corresponding theoretical studies have usually relied on the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field. At the isotropic point, it describes the large onsite repulsion U limit of the spin degrees of freedom of the one-dimensional fermionic Hubbard model with one electron per site in a magnet…
We study the asymmetric Hubbard model at half-filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use Dynamical Mean Field Theory to obtain the paramagnetic phase diagram of the model as function of temperature, interaction strength and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi-liquid, qualitatively analogous to the Fermi liquid state of the symmetric Hubbard m…
We study interaction-induced Mott insulators, and their topological properties in a 1D non-Hermitian strongly-correlated spinful fermionic superlattice system with either nonreciprocal hopping or complex-valued interaction. For the nonreciprocal hopping case, the low-energy neutral excitation spectrum is sensitive to boundary conditions, which is a manifestation of the non-Hermitian skin effect. However, unlike the single-particle case, particle density of strongly correlated system does not suffer from the non-Hermitian skin effect due to the Pauli exclusion principle and repulsive interactio…
We study the double occupancy in a fermionic Mott insulator at half-filling generated via a dynamical periodic modulation of the hopping amplitude. Tuning the modulation amplitude, we describe a crossover in the nature of doublon-holon excitations from a Fermi Golden Rule regime to damped Rabi oscillations. The decay time of excited states diverges at a critical modulation strength, signaling the transition to a dynamically bound non-equilibrium state of doublon-holon pairs. A setup using a fermionic quantum gas should allow to study the critical exponents.
The zero-temperature phase diagram of $p$-orbital two-component fermionic system loaded into a one-dimensional optical lattice is mapped out by means of analytical and numerical techniques. It is shown that the $p$-band model away from half-filling hosts various competing superconducting phases for attractive and repulsive interactions. At quarter filling, we analyze the possible formation of incompressible Mott phases and in particular for repulsive interactions, we find the occurrence of a Mott transition with the formation of fully gapped bond-ordering waves.
We use the two-step density-matrix renormalization group method to elucidate the long-standing issue of the universality class of the Mott transition in the Hubbard model in two dimensions. We studied a spatially anisotropic two-dimensional Hubbard model with a non-perfectly nested Fermi surface at half-filling. We find that unlike the pure one-dimensional case where there is no metallic phase, the quasi one-dimensional modeldisplays a genuine metal-insulator transition at a finite value of the interaction. The critical exponent of the correlation length is found to be $ν\approx 1.0$. This imp…
We study the spectral and transport properties of a Mott insulator driven by a static electric field into a non-equilibrium steady state. For the dissipation, we consider two mechanisms: Wide-band fermion reservoirs and phonons included within the Migdal approximation. The electron correlations are treated via non-equilibrium dynamical mean field theory with an impurity solver suitable for strong correlations. We find that dissipation via phonons is limited to restricted ranges of field values around Wannier-Stark resonances. To cover the full range of field strengths, we allow for a small cou…
An ultracold gas of interacting fermionic atoms in a three-dimensional optical lattice is considered, where the lattice potential strength is periodically modulated. This non-equilibrium system is non-perturbatively described by means of a Keldysh-Floquet-Green's function approach for Mott-Hubbard systems employing a generalized dynamical mean field theory (DMFT). Strong repulsive interactions between different atoms lead to a Mott insulator state for the equilibrium system, but the additional external driving at zero temperature yields a non-equilibrium quantum critical behavior, where an inf…
Motivated by recent work of Mross and Senthil [Phys. Rev. B \textbf{84}, 165126 (2011)] which provides a dual description for Mott transition from Fermi liquid to quantum spin liquid in two space dimensions, we extend their approach to higher dimensional cases, and we provide explicit formalism in three space dimensions. Instead of the vortices driving conventional Fermi liquid into quantum spin liquid states in 2D, it is the vortex lines to lead to the instability of Fermi liquid in 3D. The extended formalism can result in rich consequences when the vortex lines condense in different degrees …
A link is established between the spin-fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-N approximation in the SF model. It is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped d-Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence the SF model p…
We study the competition between interactions and disorder in two dimensions. Whereas a noninteracting system is always Anderson localized by disorder in two dimensions, a pure system can develop a Mott gap for sufficiently strong interactions. Within a simple model, with short-ranged repulsive interactions, we show that, even in the limit of strong interaction, the Mott gap is completely washed out by disorder for an infinite system for dimensions $D\le 2$. The probability of a nonzero gap falls onto a universal curve, leading to a glassy state for which we provide a scaling function for the …
Quantum phase transition of fermionic atoms in anisotropic triangular optical lattice was investigated by dynamical cluster approximation combining with continuous time quantum Monte Carlo algorithm. The temperature-interaction phase diagram for different hoping terms and the competition between the anisotropic parameter and interaction is presented. Our results show that the system undergoes Mott transition from Fermi liquid to Mott insulator while the repulsive interaction reach the critical value. The Kondo metal characterized by Kondo peak in the density of states is found in this systems …
Based on a generalized one-band Hubbard model, we study magnetic properties of Mott insulating states for ultracold spin-3/2 fermionic atoms in optical lattices. When the \textit{s}-wave scattering lengths for the total spin $S=2,0$ satisfy conditions $a_{2}>a_{0}>0$, we apply a functional integral approach to the half filled case, where the spin-quadrupole fluctuations dominate. On a 2D square lattice, the saddle point solution yields a staggered spin-quadrupole ordering at zero temperature with symmetry breaking from SO(5) to SO(4). Both spin and spin-quadrupole static structure factors are …
We investigate the excitation spectrum of a two-dimensional resonating valence bond (RVB) state. Treating the $pi$-flux phase with antiferromagnetic correlations as a variational ground state, we recover the long wavelength magnon as an "RVB exciton". However, we find that this excitation does NOT exhaust the entire spectral weight and the high energy spectrum is dominated by fermionic excitations. The latter can be observed directly by inelastic neutron scattering and we predict their characteristic energy scales along different high symmetry directions in the magnetic Brillouin zone. We also…
We examine the phase diagram of a simple-cubic optical lattice half-filled by two species of fermionic atoms with a repulsive s-wave contact interaction. We use the Hartree approximation in the regime of weaker interactions, and a Hubbard model approximation in the Mott insulating phase. The regime where the Neel phase of this system is likely to be most accessible to experiments is at intermediate lattice strengths and interactions, and our two approximations agree fairly well in this regime. We discuss the various issues that may determine where in this phase diagram the Neel phase is first …
The physical properties of arbitrary half-integer spins F = N - 1/2 fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for F \ge 3/2: A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of Z_N parafermionic degrees of freedom. The quantum phase transition for F=3/…
We propose a method to directly measure the temperature of a gas of weakly interacting fermionic atoms loaded into an optical lattice. This technique relies on Raman spectroscopy and is applicable to experimentally relevant temperature regimes. Additionally, we show that a similar spectroscopy scheme can be used to obtain information on the quasiparticle properties and Hubbard bands of the metallic and Mott-insulating states of interacting fermionic spin mixtures. These two methods provide experimentalists with novel probes to accurately characterize fermionic quantum gases confined to optical…
We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice, that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the inter-atom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator", has yet to be realized in solid-state systems, since this requires, in the tight-binding model, large offsite interactions on top of a small onsite interaction. Here we overcome the difficulty by introducing a spin-dependent potential, where a spin-se…
Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal, repulsive on-site interactions U>0. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory using multigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., should be accessible to experiments. In addition, we present spectral functions and discu…
We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical point by use of the representation theory of the q-oscillator and Weyl algebras. The transition is further characterized by the ground state modification. The explicit mapping provides a new tool to further probe and test the detailed physical properties of the fermionic lattice model considered here and to enhance our understanding of the Mott transition(s).
The phase diagram of one-dimensional earth-alkaline fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings.
A gas of strongly interacting spinless p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or Kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degree model. We determine the orbital ordering on the Kagome lattice, and show how orbital wave fluctuations select ground states via the order by di…
We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $π$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the cr…
In this work we consider a system of spinless fermions with nearest and next-to-nearest neighbor repulsive Hubbard interactions on a honeycomb lattice, and propose and analyze a realistic scheme for analog quantum simulation of this model with cold atoms in a two-dimensional hexagonal optical lattice. To this end, we first derive the zero-temperature phase diagram of the interacting model within a mean-field theory treatment. We show that besides a semi-metallic and a charge-density-wave ordered phase, the system exhibits a quantum anomalous Hall phase, which is generated dynamically, i.e. pur…
We investigate the dynamics of Mott-insulating regions of a trapped bosonic gas as the interaction strength is changed linearly with time. The bosonic gas considered is loaded into an optical lattice and confined to a parabolic trapping potential. Two situations are addressed: the formation of Mott domains in a superfluid gas as the interaction is increased, and their melting as the interaction strength is lowered. In the first case, depending on the local filling, Mott-insulating barriers can develop and hinder the density and energy transport throughout the system. In the second case, the de…
Cold atoms provide a unique arena to study many-body systems far from equilibrium. Furthermore, novel phases in cold atom systems are conveniently investigated by dynamical probes pushing the system out of equilibrium. Here, we discuss the pumping of doubly-occupied sites in a fermionic Mott insulator by a periodic modulation of the hopping amplitude. We show that deep in the insulating phase the many-body system can be mapped onto an effective two-level system which performs coherent Rabi oscillations due to the driving. Coupling the two-level system to the remaining degrees of freedom render…
We observe a localized phase of ultracold bosonic quantum gases in a 3-dimensional optical lattice induced by a small contribution of fermionic atoms acting as impurities in a Fermi-Bose quantum gas mixture. In particular we study the dependence of this transition on the fermionic 40K impurity concentration by a comparison to the corresponding superfluid to Mott insulator transition in a pure bosonic 87Rb gas and find a significant shift in the transition parameter. The observed shift is larger than expected based on a mean-field argument, which is a strong indication that disorder-related eff…
Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulating region. A local compressibility defined to characterize the Mott-insulating phase has a non-trivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We determine a generic phase diagram, that allows the prediction of the phases to be observed in experiments with ultracold fermionic atoms trapped on optical …
The physical properties of arbitrary half-integer spins $F = N - 1/2$ fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for $F \ge 3/2$ depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular superfluid instability made of $2N$ fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the $Z_N$ generaliz…
The phase diagram of spin-3/2 fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repu…
Various topics at the interface between condensed matter physics and the physics of ultra-cold fermionic atoms in optical lattices are discussed. The lectures start with basic considerations on energy scales, and on the regimes in which a description by an effective Hubbard model is valid. Qualitative ideas about the Mott transition are then presented, both for bosons and fermions, as well as mean-field theories of this phenomenon. Antiferromagnetism of the fermionic Hubbard model at half-filling is briefly reviewed. The possibility that interaction effects facilitate adiabatic cooling is disc…
Phase transitions and their associated crossovers are imprinted in the behavior of fluctuations. Motivated by recent experiments on ultracold atoms in optical lattices, we compute the thermodynamic density fluctuations $δN^2$ of the two-dimensional fermionic Hubbard model with plaquette cellular dynamical mean-field theory. To understand the length scale of these fluctuations, we separate the local from the nonlocal contributions to $δN^2$. We determine the effects of particle statistics, interaction strength $U$, temperature $T$ and density $n$. At high temperature, our theoretical framework …
