We study the equilibrium and nonequilibrium formation of four-particle complexes in a balanced two-species Bose-Hubbard model with repulsive intraspecies and attractive interspecies interactions. Using exact diagonalization, we characterize the transition from weakly to strongly correlated dimer and tetramer states along the one- to two-dimensional crossover in coupled-chain geometries by combining local correlation signatures with global diagnostics such as the binding energy and interspecies entanglement entropy. We show that transverse connectivity between chains qualitatively reshapes the phase diagram, substantially enlarging the tetramer region and, in particular, stabilizing weakly bound tetramers when compared to the one-dimensional chains. By tuning the interchain hopping, we identify a transition from a degenerate manifold of spatially separated dimers to a localized tetramer ground state, driven by the lifting of one-dimensional configurational degeneracies and an associated kinetic-energy gain. By extending our analysis to larger complexes of six and eight particles, we reveal that these binding mechanisms are robust and suggest a general pathway for the formation of higher-order complexes. Finally, we demonstrate interaction and geometric quench protocols to dynamically prepare these complexes with high fidelity. Our results provide a microscopic framework for engineering and probing few-body bosonic bound states in tunable lattice geometries.
Motivated by the recent realization of the Haldane model in shaking optical lattice, we investigate the effects of attractive interaction and BEC-BCS crossover in this model at and away from half filling. We show that, contrary to the usual s-wave BEC-BCS crossover in the lattice, a topological superfluid with Chern number C=2 appears in an extended region of phase space for intermediate strength of the attractive interaction in the interaction-density plane. When inversion symmetry is broken, a new gapless topological state is realized. We also investigate the fluctuations in these superfluid…
The Fermi-Hubbard model (FHM) is a cornerstone of modern condensed matter theory. Developed for interacting electrons in solids, which typically exhibit SU($2$) symmetry, it describes a wide range of phenomena, such as metal to insulator transitions and magnetic order. Its generalized SU($N$)-symmetric form, originally applied to multi-orbital materials such as transition-metal oxides, has recently attracted much interest owing to the availability of ultracold SU($N$)-symmetric atomic gases. Here we report on a detailed experimental investigation of the SU($N$)-symmetric FHM using local probin…
The $2d$ Hubbard model with nearest-neighbour hopping on the square lattice and an average of one electron per site is known to undergo an extended crossover from metallic to insulating behavior driven by proliferating antiferromagnetic correlations. We study signatures of this crossover in spin and charge correlation functions and present results obtained with controlled accuracy using diagrammatic Monte Carlo in the range of parameters amenable to experimental verification with ultracold atoms in optical lattices. The qualitative changes in charge and spin correlations associated with the cr…
Dissipation is ubiquitous in nature and plays a crucial role in quantum systems such as causing decoherence of quantum states. Recently, much attention has been paid to an intriguing possibility of dissipation as an efficient tool for preparation and manipulation of quantum states. Here we report the realization of successful demonstration of a novel role of dissipation in a quantum phase transition using cold atoms. We realize an engineered dissipative Bose-Hubbard system by introducing a controllable strength of two-body inelastic collision via photo-association for ultracold bosons in a thr…
We investigate the trion formation and the effective trionic properties in the attractive Hubbard model with three fermionic colors using exact diagonalization. The crossover to the trionic regime with colorless compound fermions upon increasing strength of the onsite attraction parameter U features smoothly evolving ground state properties and exhibits clear similarities to the BCS/BEC-crossover for two colors. In the excitation spectrum, there is a clear gap opening between a band of well-defined trions and excitations of broken-up trions at U_c ~ 1.8t. This picture remains the same away fro…
We study the Renyi entropy in the finite temperature crossover regime of a Hubbard chain using quantum Monte Carlo. The ground state entropy has characteristic features such as a logarithmic divergence with block size and $2\kF$ oscillations that are a hallmark of its Luttinger liquid nature. The interplay between the (extensive) thermal entropy and the ground state features is studied and we analyze the temperature induced decay of the amplitude of the oscillations as well as the scaling of the purity. Furthermore, we show how the spin and charge velocities can be extracted from the temperatu…
We study properties of the lowest energy states at non-zero total momentum (yrast states) of the Hubbard model for spin-1/2 fermions in the quantum ring configuration with attractive on-site interaction at low density. In the one-dimensional (1D) case we solve the Hubbard model using the Bethe ansatz, while for the crossover into the 2D regime we use the Full-Configuration-Interaction Quantum Monte-Carlo method (FCIQMC) to obtain the yrast states for the spin-balanced Fermi system. We show how the yrast excitation spectrum changes from the 1D to the 2D regime and how pairing affects the yrast …
The influence of the Zeeman magnetic field ($h$) on the ground state evolution of superfluid properties from the weak coupling (BCS like) to the strong coupling limit of tightly bound local pairs (LP) with increasing attraction has been studied. The analysis was carried out within the spin-polarized attractive Hubbard model, for a fixed number of particles and a $d=3$ simple cubic lattice. The broken symmetry Hartree approximation was used. For strong attraction and in the dilute limit, the homogeneous magnetized superconducting phase (SC$_M$) was found in the $(h-|U|)$ and ($P-|U|$) diagrams.
We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrat…
Recent experiments with ultracold fermionic atoms in optical lattices have provided a tuneable and clean realization of the attractive Hubbard model (AHM). In view of this, several physical properties may be thoroughly studied across the crossover between weak (Bardeen-Cooper-Schrieffer, BCS) and strong (Bose-Einstein condensation, BEC) couplings. Here we report on extensive determinant Quantum Monte Carlo (DQMC) studies of the AHM on a square lattice, from which several different quantities have been calculated and should be useful as a roadmap to experiments. We have obtained a detailed phas…
We analyze the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP's) in the 2D asymmetric attractive Hubbard model, in the presence of the Zeeman magnetic field ($h$). The broken symmetry Hartree approximation is used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. We obtain that for the spin dependent hopping integrals ($t^{\uparrow}\neq t^{\downarrow}$) the homogeneous polarized superfluid (SC$_M$) phase in the ground state for the strong attraction and lower filling can be stabil…
The properties of a phase with large correlation length can be strongly influenced by the underlying normal phase. We illustrate this by studying the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo. Sharp crossovers in the mechanism that favors antiferromagnetic correlations and in the corresponding local density of states are observed. These crossovers occur at values of the interaction strength $U$ and temperature $T$ that are controlled by the underlying normal-state Mott transition.
The problem of a single down spin particle interacting with a Fermi sea of up spin particles is of current interest in the field of cold atoms. The Hubbard model, appropriate to atoms in an optical lattice potential, is considered in parallel with a gas model. As the strength of an attractive short-range interaction is increased there is a crossover from "polaron" behaviour, in which the Fermi sea is weakly perturbed, to "molecule" behaviour in which the down spin particle is bound to a single up spin particle. It is shown that this is a smooth crossover, not a sharp transition as claimed by m…
We consider a quasi-one-dimensional model of a two-component Fermi gas at zero temperature on one, two and three-leg attractive-U Hubbard ladders. We construct the grand canonical phase diagram of a two-component spin-polarized gas. We find that the structure of the phase diagram of the attractive-U Hubbard model for two and three leg ladders significantly differs q from the structure of the phase diagram of a single chain. We argue that the single chain model is a special case, and that multichain ladders display qualitative features of the 1D-to-3D crossover, observed in experiments with tra…
We present a non-perturbative renormalization-group approach to the Bose-Hubbard model. By taking as initial condition of the RG flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial way. This approach yields a phase diagram in very good quantitative agreement with the quantum Monte Carlo results and reproduces the two universality classes of the superfluid--Mott-insulator transition with a good estimate of the critical exponents. Furthermore, it reveals the crucial role of the "Ginzburg length" as a crossover length between a…
The recent experimental implementation of condensed matter models in optical lattices has motivated research on their nonequilibrium behavior. Predictions on the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective BCS Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics, and (ii) overheating beyond the critical temperature of supe…
We study thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half-filling: a maximum in the entropy at non-zero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crosso…
We propose a scheme where strongly correlated photons generated inside a hollow-core one-dimensional fiber filled with two cold atomic species can be used to simulate the BCS-BEC crossover. We first show how stationary light-matter excitations (polaritons) in the system can realize an optically tunable two component Bose-Hubbard model, and then analyze the optical parameters regime necessary to generate an effective Fermi-Hubbard model of photons exhibiting Cooper pairing. The characteristic correlated phases of the system can be efficiently observed due to the {\it in situ} accessibility of t…
In quantum many-body system, dimensionality plays a critical role on type of the quantum phase transition. In order to study the quantum system during dimensional crossover, we studied the Bose-Hubbard model on cubic lattice with anisotropic hopping by using the high order symbolic strong coupling expansion method. The analytic series expanded boundaries between the Mott-insulator and superfluid phase up to eighth order are calculated. The critical exponents are extracted by Padé re-summation method, which clearly shows the dimensional crossover behavior. Meanwhile, the critical points at comm…
The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using Determinant Quantum Monte Carlo, a simple realization of anisotropy in the 3D …
Motivated by recent experiments on interacting bosons in quasi-one-dimensional optical lattice [Nature {\bf 573}, 385 (2019)] we analyse theoretically properties of the system in the crossover between delocalized and localized regimes. Comparison of time dynamics for uniform and density wave like initial states enables demonstration of the existence of the mobility edge. To this end we define a new observable, the mean speed of transport at long times. It gives us an efficient estimate of the critical disorder for the crossover. We also show that the mean velocity growth of occupation fluctuat…
Intertwining of spin, charge and pairing correlations in the repulsive two-dimensional Hubbard model is shown through unrestricted variational calculations, with projected wavefunctions free of symmetry breaking. A crossover from incommensurate antiferromagnetism to stripe order naturally emerges in the hole-doped region when increasing the on-site coupling. Although effective pairing interactions are identified, they are strongly fragmented in several modes including d-wave pairing and more exotic channels related to an underlying stripe. We demonstrate that the entanglement of a mean-field w…
We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly-bound Cooper pairs to the Bose-Einstein Condensate (BEC) of strongly-bound molecular dimers in a gas of ultracold atoms loaded on a two-dimensional optical lattice. By using the the mean-field BCS equations of the emerging Hubbard model and the concept of off-diagonal-long-range-order for fermions we calculate analytically and numerically the pair binding energy, the energy gap and the condensate fraction of Cooper pairs as a function of interaction strength and filling fractor of atoms in the lattice at zero…
We show that the dilute Fermi gas quantum critical universality class quantitatively describes the Mott/metal crossover of the two-dimensional Hubbard model for temperatures somewhat less than (roughly half) the tunneling but much greater than (roughly twice) the superexchange energy. We calculate the observables expected to be universal near the transition --- density and compressibility --- with numerically exact determinantal quantum Monte Carlo. We find they are universal functions of the chemical potential. Despite arising from the strongly correlated regime of the Hubbard model, these fu…
We investigate finite size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy-scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground-states. Both criteria can be computed using ground-state techniques that work for larger system sizes than full spectrum diagonalization. As examples, two models are s…
Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Motivated by recent cold atom experiments, which are now able to measure the corresponding information-theoretic quantities, we study the Mott transition in the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory, and focus on two key measures of quantum correlations: entanglement entropy and mutual information. We show that they detect the first-order nature of the transition, the universality class of the endpoint, and the crossover emanating from the endpoint.
We investigate the ground state of a few-body Bose-Fermi mixture in a one-dimensional harmonic trap with varying interaction strengths and mass ratio. A bunching-antibunching crossover of the bosonic species for increasing interspecies' repulsion is observed within our fully correlated \textit{ab~initio} studies. Interestingly, this crossover is suppressed if the bosonic repulsion exceeds a critical value which strongly depends on the mass ratio. In order to unveil the physical origin of this crossover, we employ different levels of approximations: while a species mean-field approach can accou…
We present a full phase diagram for the one-dimensional (1D) to three-dimensional (3D) crossover of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in an attractive Hubbard model of 3D-coupled chains in a har- monic trap. We employ real-space dynamical mean-field theory which describes full local quantum fluctuations beyond the usual mean-field and local density approximation. We find strong dimensionality effects on the shell structure undergoing a crossover between distinctive quasi-1D and quasi-3D regimes. We predict an optimal regime for the FFLO state that is considerably extended to in…
We study a possible superconductivity in quasiperiodic systems, by portraying the issue within the attractive Hubbard model on a Penrose lattice. Applying a real-space dynamical mean-field theory to the model consisting of 4181 sites, we find a superconducting phase at low temperatures. Reflecting the nonperiodicity of the Penrose lattice, the superconducting state exhibits an inhomogeneity. According to the type of the inhomogeneity, the superconducting phase is categorized into three different regions which cross over each other. Among them, the weak-coupling region exhibits spatially extend…
