In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the dynamical symmetry refers to that the time evolution of certain observables are symmetric between the repulsive and attractive Hubbard models. We demonstrate our theorem with three different examples in which the symmetry involves bipartite lattice symmetry, reflection symmetry and translation symmetry, respectively. Each of these examples relates to one recent cold atom experiment on the dynamics in the optical lattices where such a dynamical symmetry is manifested. These experiments include expansion dynamics of cold atoms, chirality of atomic motion within a synthetic magnetic field and melting of charge-density-wave order. Therefore, our theorem provides a unified view of these seemingly disparate phenomena.
We investigate an unconventional symmetry in time-periodically driven systems, the Floquet dynamical symmetry (FDS). Unlike the usual symmetries, the FDS gives symmetry sectors that are equidistant in the Floquet spectrum and protects quantum coherence between them from dissipation and dephasing, leading to two kinds of time crystals: the discrete time crystal and discrete time quasicrystal that have different periodicity in time. We show that these time crystals appear in the Bose- and Fermi-Hubbard models under ac fields and their periodicity can be tuned only by adjusting the strength of th…
Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The paradigmatic model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain. Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterised by vanishing two-point spin correlations, gapped excitations, and a characteristic non-local order parameter. More recently it was understood that the Haldane chain forms a specific example o…
Utilizing the Fermi gas microscope, recently the MIT group has measured the spin transport of the Fermi Hubbard model starting from a spin-density-wave state, and the Princeton group has measured the charge transport of the Fermi Hubbard model starting from a charge-density-wave state. Motivated by these two experiments, we prove a theorem that shows under certain conditions, the spin and charge transports can be equivalent to each other. The proof makes use of the particle-hole transformation of the Fermi Hubbard model and a recently discovered symmetry protected dynamical symmetry. Our resul…
We show that the non-equilibrium time-evolution after interaction quenches in the one dimensional, integrable Hubbard model exhibits a dynamical transition in the half-filled case. This transition ceases to exist upon doping. Our study is based on systematically extended equations of motion. Thus it is controlled for small and moderate times; no relaxation effects are neglected. Remarkable similarities to the quench dynamics in the infinite dimensional Hubbard model are found suggesting dynamical transitions to be a general feature of quenches in such models.
We study a two dimensional super-lattice Bose-Hubbard model with alternating hoppings in the limit of strong on-site interactions. We evaluate the phase diagram of the model around half-filling using the density matrix renormalization group method and find two gapped phases separated by a gapless superfluid region. We demonstrate that the gapped states realize two distinct higher order symmetry protected topological phases, which are protected by a combination of charge conservation and $C_4$ lattice symmetry. The phases are distinguished in terms of a quantized fractional corner charge and a …
In their preprint Anders et al. [arXiv:1004.0510] propose a crucial modification of the Bosonic Dynamical Mean-Field Theory (B-DMFT) derived by us [Phys. Rev. B 77, 235106 (2008)]. Here we show that the modification consists of two steps which, in fact, cancel each other. Consequently their self-consistency equations are identical to ours.
We present the effective action and self-consistency equations for the bosonic dynamical mean field (B-DMFT) approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.
We use cellular dynamical mean-field theory with extended unit cells to study the ground state of the two-dimensional repulsive Hubbard model at finite doping. We calculate the energy of states with d-wave superconductivity coexisting with spatially uniform magnetic order and find that they are energetically favoured in a large doping region as compared to the uniform solution. We study the spatial form of the superconducting and magnetic order parameters at different doping values.
We propose that ultracold alkaline-earth-like atoms confined in one-dimensional optical lattice can realize a Kondo lattice model which hosts a symmetry-protected topological (SPT) phase and an associated quantum phase transition in a controllable manner. The symmetry protection of the phase transition is discussed from two different viewpoints: topological properties related to spatial patterns of Kondo singlets, and symmetry eigenvalues of the spin states. We uncover the role of various symmetries in the phase diagram of this system by combining a weak-coupling approach by Abelian bosonizati…
We apply the dynamical mean-field approach to the four-component SU(4)-symmetric Fermi-Hubbard model to study transitions between different magnetically ordered phases as well as the hysteresis behavior in the unordered regime. At quarter filling (one particle per site) on the square lattice we identify both the two-sublattice and plaquette-ordered antiferromagnetic phases with the corresponding entropy-driven hierarchy for critical temperatures. We also analyze the behavior of thermodynamic characteristics: the local double occupancy, compressibility, and entropy per particle, which are relev…
We study the off-equilibrium dynamics of the infinite dimensional Bose Hubbard Model after a quantum quench. The dynamics can be analyzed exactly by mapping it to an effective Newtonian evolution. For integer filling, we find a dynamical transition separating regimes of small and large quantum quenches starting from the superfluid state. This transition is very similar to the one found for the fermionic Hubbard model by mean field approximations.
We study strongly correlated Hubbard systems extended to symmetric $N$-component fermions. We focus on the intermediate-temperature regime between magnetic superexchange and interaction energy, which is relevant to current ultracold fermionic atom experiments. The $N$-component fermions are represented by slave particles, and, by using a diagrammatic technique based on the atomic limit, spectral functions are analytically obtained as a function of temperature, filling factor and the component number $N$. We also apply this analytical technique to the calculation of lattice modulation experimen…
We study the decay of bosonic many-body states in the three well Bose-Hubbard chain where bosons in the central well can escape into a reservoir. For vanishing inter-particle interaction this system supports a non-decaying many-body state which is the antisymmetric Bose-Einstein condensate with particles occupying only the edge wells. In the classical approach this quantum state corresponds to a symmetry protected non-decaying state which is stable even at finite interaction below a certain intensity threshold. Here we demonstrate that despite the classical counterpart is stable the antisymmet…
We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated b…
We investigate the use of programmable optical lattices for quantum simulation of Hubbard models, determining analytic expressions for the hopping and Hubbard U, finding that they are suitable for emulating strongly correlated systems with arbitrary structures, including those with multiple site basis and impurities. Programmable potentials are highly flexible, with the ability to control the depth and shape of individual sites in the optical lattice dynamically. Quantum simulators of Hubbard models with (1) arbitrary basis are required to represent many real materials of contemporary interest…
We numerically study a Bose-Hubbard ring of finite size with disorder containing a finite number of bosons that are subject to an on-site two-body interaction. Our results show that moderate interactions induce dynamical thermalization in this isolated system. In this regime the individual many-body eigenstates are well described by the standard thermal Bose-Einstein distribution for well-defined values of the temperature and the chemical potential which depend on the eigenstate under consideration. We show that the dynamical thermalization conjecture works well both at positive and negative t…
We perform an ab-initio comparison between nonequilibrium dynamical mean-field theory and optical lattice experiments by studying the time evolution of double occupations in the periodically driven Fermi-Hubbard model. For off-resonant driving, the range of validity of a description in terms of an effective static Hamiltonian is determined and its breakdown due to energy absorption close to resonance is demonstrated. For near-resonant driving, we investigate the response to a change in driving amplitude and discover an asymmetric excitation spectrum with respect to the detuning. In general, we…
We introduce a new class of exchange-correlation potentials for a static and time-dependent Density Functional Theory of strongly correlated systems in 3D. The potentials are obtained via Dynamical Mean Field Theory and, for strong enough interactions, exhibit a discontinuity at half filling density, a signature of the Mott transition. For time-dependent perturbations, the dynamics is described in the adiabatic local density approximation. Results from the new scheme compare very favorably to exact ones in clusters. As an application, we study Bloch oscillations in the 3D Hubbard model.
This is a preprint from 1990, in which it is explained how non-Abelian gauge magnets originate as effective dynamics in models of hopping particles. In particular, an explicit model is discussed in which both link and plaquette terms appear. The motivation (as explained in a brief apology) to reintroduce the idea is some recent theoretical progress on the topic of optical lattices.
In quantum magnetism, the virtual exchange of particles mediates an interaction between spins. Here, we show that an inelastic Hubbard interaction fundamentally alters the magnetism of the Hubbard model due to dissipation in spin-exchange processes, leading to sign reversal of magnetic correlations in dissipative quantum dynamics. This mechanism is applicable to both fermionic and bosonic Mott insulators, and can naturally be realized with ultracold atoms undergoing two-body inelastic collisions. The dynamical reversal of magnetic correlations can be detected by using a double-well optical lat…
Dynamical quantum phase transitions (DQPTs) are topologically characterized in quantum quench dynamics in topological systems. In this paper, we study Loschmidt amplitudes and DQPTs in quantum quenches in mirror-symmetric topological phases. Based on the topological classification of mirror-symmetric insulators, we show that mirror symmetry creates symmetry-protected DQPTs. If mirror symmetry is present, topologically robust DQPTs can occur in quantum quenches, even in high-dimensional time-reversal invariant systems. Then, we also show that symmetry-protected DQPTs occur in quenches in two-di…
We study the dynamical instabilities of superfluid flows in the S=1 Bose-Hubbard model. The time evolution of each spin component in a condensate is calculated based on the dynamical Gutzwiller approximation for a wide range of interactions, from a weakly correlated regime to a strongly correlated regime near the Mott-insulator transition. Owing to the spin-dependent interactions, the superfluid flow of the spin-1 condensate decays at a different critical momentum from a spinless case when the interaction strength is the same. We furthermore calculate the dynamical phase diagram of this model …
We study the dynamics of magnetic correlations in the half-filled fermionic Hubbard model following a fast ramp of the repulsive interaction. We use Schwinger-Keldysh self-consistent second-order perturbation theory to investigate the evolution of single-particle Green's functions and solve the non-equilibrium Bethe-Salpeter equation to study the dynamics of magnetic correlations. This approach gives us new insights into the interplay between single-particle relaxation dynamics and the growth of antiferromagnetic correlations. Depending on the ramping time and the final value of the interactio…
We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians with pure loss terms possess parity-time ($\mathcal{PT}$) symmetry if we compensate the system additionally an overall gain term. By solving the two-site Lindblad equation with fixed dissipation exactly, we find that the dynamics of rescaled density matrix shows an instability as the interaction increases over a threshold, which can be equivalently described in…
We study a dissipative Bose-Hubbard chain subject to an engineered bath using a superoperator approach based on matrix product operators. The dissipation is engineered to stabilize a BEC condensate wave function in its steady state. We then characterize the steady state emerging from the interplay between incompatible Hamiltonian and dissipative dynamics. While it is expected that interactions lead to this competition, even the kinetic energy in an open boundary condition setup competes with the dissipation, leading to a non-trivial steady state. We also present results for the transient dynam…
Fermionic atoms in a periodic optical lattice provide a realization of the single-band Hubbard model. Using Quantum Monte Carlo simulations along with the Maximum Entropy Method, we evaluate the effect of a time-dependent perturbative modulation of the optical lattice amplitude on atomic correlations, revealed in the fraction of doubly-occupied sites. Our treatment extends previous approaches which neglected the time dependence of the on-site interaction, and shows that this term changes the results in a quantitatively significant way. The effect of modulation depends strongly on the filling--…
A superfluid flow beyond a critical momentum in an optical lattice decays drastically by the interplay between nonlinearity due to the interparticle interactions in Bose-Einstein condensate and periodicity of the lattice; this instability is called dynamical instability. The complex density modulational profiles after the condensate becomes unstable observed experimentally is not completely understood, while the dynamical instability has been studied theoretically and experimentally. In this paper, we analyze the density modulation of condensates as a precursor of the dynamical instability in …
We propose a spinless Bose-Hubbard model in an one-dimensional (1D) double-chain tilted lattice at unit filling per cell. A subspace of this model can be faithfully mapped to the 1D transverse Ising model through superexchange interaction with second-order perturbation theory. At a valid parameter region, numerical results show good agreement of these two models both on energy spectrums and correlation functions. And we show that the dynamical quantum phase transition of the effective 1D transverse Ising model can be simulated. With carefully designed procedures for producing the dynamical qua…
Weyl semimetals are three-dimensional, topologically protected, gapless phases which show exotic phenomena such as Fermi arc surface states or negative magnetoresistance. It is an open question whether interparticle interactions can turn the topological semimetal into a topologically nontrivial Mott insulating phase. We investigate an experimentally motivated model for Weyl physics of cold atoms in optical lattices, with the main focus on interaction effects and topological properties by means of dynamical mean-field theory (DMFT). We characterize topological phases by numerically evaluating t…
We present the quantum and classical study of a four-well trapped Bose-Einstein condensate (BEC) modeled by the Bose-Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamica…
In the strongly interacting limit of the Hubbard model localized double-occupancies form effective hard-core bosonic excitations, called a doublons, which are long-lived due to energy conservation. Using time-dependent density-matrix renormalisation group we investigate numerically the dynamics of doublons arising from the sudden expansion of a spatially confined band-insulating state in one spatial dimension. By analysing the occupation scaling of the natural orbitals within the many-body state, we show that doublons dynamically quasicondense at the band edges, consistent with the spontaneous…
We provide evidence that a clean kicked Bose-Hubbard model exhibits a many-body dynamically localized phase. This phase shows ergodicity breaking up to the largest sizes we were able to consider. We argue that this property persists in the limit of large size. The Floquet states violate eigenstate thermalization and then the asymptotic value of local observables depends on the initial state and is not thermal. This implies that the system does not generically heat up to infinite temperature, for almost all the initial states. Differently from many-body localization here the entanglement entrop…
The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and t…
The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this work, we investigate the potential of this approach from three perspectives. First, we consider a double-well system in the classical large-atom-number limit, deriving the exact equations of motion in the presence of feedback. Second, we consider the same system in the limit of small atom number, revealing the effect that quantum fluctuations have on the feedback scheme. Finally, we explore the behavior of modest sized Hubb…
Dynamical structure factor and a new method to measure the pairing gap in two-dimensional attractive Fermi-Hubbard model
Centre for Theoretical and Computational Physics, College of Physics, Qingdao University（青岛大学物理学院理论计算物理中心）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）
This work presents a theoretical study of a protocol for dynamical generation and storage of the durable, highly entangled Greenberger-Horne-Zeilinger (GHZ) state in a system composed of bosonic atoms loaded into a one-dimensional optical lattice potential. A method of indicating entanglement in the system is also presented. The system ground-state can be either in the superfluid phase or in the Mott insulator phase. The wave functions of atoms in the superfluid phase are delocalised over the whole lattice and overlap. In the Mott phase, the wave functions are localised around lattice sites. T…
We investigate the non-equilibrium behavior of a fully-connected (or all-to-all coupled) Bose-Hubbard model after a Mott to superfluid quench, in the limit of large boson densities and for an arbitrary number $V$ of lattice sites, with potential relevance in experiments ranging from cold atoms to superconducting qubits. By means of the truncated Wigner approximation, we predict that crossing a critical quench strength the system undergoes a dynamical phase transition between two regimes that are characterized at long times either by an inhomogeneous population of the lattice (i.e. macroscopica…
