Mott Insulator Regime Research Articles

Spectral statistics of driven Bose-Hubbard models

We study the spectral statistics of a one-dimensional Bose–Hubbard model subjected to kinetic driving; a form of Floquet engineering where the kinetic energy is periodically driven in time with a zero time-average. As the amplitude of the driving is increased, the ground state of the resulting flat-band system passes from the Mott insulator regime to an exotic superfluid. We show that this transition is accompanied by a change in the system’s spectral statistics from Poisson to GOE-type. Remarkably, and unlike in the conventional Bose–Hubbard model which we use as a benchmark, the details of the GOE statistics are sensitive to the parity of both the particle number and the lattice sites. We show how this effect arises from a hidden symmetry of the Hamiltonian produced by this form of Floquet driving.

Heteronuclear Magnetisms with Ultracold Spinor Bosonic Gases in Optical Lattices

Motivated by recent realizations of spin-1 NaRb mixtures in the experiments [Phys. Rev. Lett. 114, 255301 (2015); Phys. Rev. Lett. 128, 223201 (2022)], we investigate heteronuclear magnetism in the Mott-insulating regime. Different from the identical mixtures where the boson statistics only admits even parity states from angular momentum composition, for heteronuclear atoms in principle all angular momentum states are allowed, which can give rise to new magnetic phases. While various magnetic phases can be developed over these degenerate spaces, the concrete symmetry breaking phases depend on not only the degree of degeneracy but also the competitions from many-body interactions. We unveil these rich phases using the bosonic dynamical mean-field theory approach. These phases are characterized by various orders, including spontaneous magnetization order, spin magnitude order, singlet pairing order, and nematic order, which may coexist specially in the regime with odd parity. Finally we address the possible parameter regimes for observing these spin-ordered Mott phases.

The Mott transition in the 5d[formula omitted] compound Ba[formula omitted]NaOsO[formula omitted]: A DFT+DMFT study with PAW spinor projectors

Spin–orbit coupling has been reported to be responsible for the insulating nature of the 5d1 osmate double perovskite Ba2NaOsO6 (BNOO). However, whether spin–orbit coupling indeed drives the metal-to-insulator transition (MIT) in this compound is an open question. In this work we investigate the impact of relativistic effects on the electronic properties of BNOO via density functional theory plus dynamical mean-field theory calculations in the paramagnetic regime, where the insulating phase is experimentally observed. The correlated subspace is modeled with spinor projectors of the projector augmented wave method (PAW) employed in the Vienna Ab Initio Simulation Package (VASP), suitably interfaced with the TRIQS package. The inclusion of PAW spinor projectors in TRIQS enables the treatment of spin–orbit coupling effects fully ab-initio within the dynamical mean-field theory framework. In the present work, we show that spin–orbit coupling, although assisting the MIT in BNOO, is not the main driving force for its gapped spectra, placing this material in the Mott insulator regime. Relativistic effects primarily impact the correlated states’ character, excitations, and magnetic ground-state properties.

Electromagnetic signatures of a chiral quantum spin liquid

Quantum spin liquids (QSL) have emerged as a captivating subject within interacting spin systems that exhibit no magnetic ordering even at the lowest temperature accessible experimentally. However, definitive experimental evidence remains elusive. In light of the recent surge in theoretical and experimental interest in the half-filled Hubbard model on a triangular lattice, which offers the potential for stabilizing a chiral QSL, we investigate the electromagnetic signatures of this phase to facilitate experimental detection. Utilizing a combination of parton mean-field theory and unbiased density-matrix renormalization group calculations, we systematically examine the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL. Additionally, we calculate the longitudinal and transverse optical conductivities below the Mott gap. Furthermore, employing quantum field theory analysis, we unravel the connection between spinon excitations and emergent as well as physical gauge fields. Our results demonstrate that the chiral QSL phase exhibits a distinct electromagnetic response, even within a Mott insulator regime. This finding holds great potential for enabling the experimental detection of this long-sought-after phase.

Emergent Mott insulators at noninteger fillings and devil's staircase induced by attractive interaction in many-body polarons

We investigate the ground-state properties of an ultracold-atom system consisting of many-body polarons, quasiparticles formed by impurity atoms in optical lattices immersed in a Bose-Einstein condensate. We find the nearest-neighbor attractive interaction between polarons can give rise to rich physics that is peculiar to this system. In a relatively shallow optical lattice, the attractive interaction can drive the system to be in a self-bound superfluid phase, with its particle density distribution manifesting a self-concentrated structure. However, in a relatively deep optical lattice, the attractive interaction can drive the system, leading to the Mott-insulator phase even though the global filling factor is not an integer. Interestingly, in the Mott-insulator regime, the system can support a series of different Mott insulators, with their effective density manifesting a devil's-staircase structure with respect to the strength of the attractive interaction. A detailed estimation of the relevant experimental parameters shows that these rich physics can be readily observed in current experimental setups.

Thermal fluctuations of the extended Bose-Hubbard model at finite temperature

We consider the finite-temperature effects of the extended Bose-Hubbard model, especially in the Haldane insulator regime. We show the quantum-to-thermal (normal) crossover temperatures reveal signatures of the zero-temperature quantum phase transition. By studying the heat capacity of the system, we find a qualitative difference between the Mott insulator regimes and the other two regimes for small system sizes. We attribute these effects to the thermal energy fluctuations and find characteristic behaviors of this fluctuation in the Haldane insulator regime. We hope these results will provide insights into further research in this system.

Mott-moiré excitons

We develop a systematic theory for excitons subject to Fermi-Hubbard physics in moir\'e twisted transition metal dichalcogenides (TMDs). Specifically, we consider excitons in moir\'e systems for which the valence band is in the Mott-insulating regime. These "Mott-moir\'e excitons", which are achievable in twisted TMD heterobilayers, are bound states of a magnetic polaron in the valence band and a free electron in the conduction band. We find significantly narrower exciton bandwidths in the presence of Hubbard physics, serving as a potential experimental signature of strong correlations. We also demonstrate the high tunability of Mott-moir\'e excitons through the dependence of their binding energies, diameters, and bandwidths on the moir\'e period. Our work provides guidelines for future exploration of strongly correlated excitons in twisted TMD heterobilayers.

Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU(N) Hubbard models

It is well established that the noise correlations measured by time-of-flight imaging in cold-atom experiments, which correspond to the density-density correlations in the momentum space of trapped atomic gases, can probe the spin structure factor deep in the Mott-insulating regime of SU(2) Hubbard models. We explicitly derive the mathematical relation between the noise correlations and the spin structure factor in the strong-interaction limit of SU$(N)$ Hubbard models at any integer filling $\rho$. By calculating the ground states of one-dimensional SU$(N)$ Fermi-Hubbard models for $2\leq N\leq 6$ with use of the density-matrix renormalization-group method, we confirm the relation numerically in the regime of strong interactions $U \gg t$, where $U$ and $t$ denote the onsite interaction and the hopping energy. We show that the deviation between the actual noise correlations and those obtained from the spin structure factor scales as approximately $(t/U)^2$ for $\rho=1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments.

Quantum phases of spin-orbital-angular-momentum–coupled bosonic gases in optical lattices

Spin-orbit coupling plays an important role in understanding exotic quantum phases. In this work, we present a scheme to combine spin-orbital-angular-momentum (SOAM) coupling and strong correlations in ultracold atomic gases. Essential ingredients of this setting is the interplay of SOAM coupling and Raman-induced spin-flip hopping, engineered by lasers that couples different hyperfine spin states. In the presence of SOAM coupling only, we find rich quantum phases in the Mott-insulating regime, which support different types of spin defects such as spin vortex and composite vortex with antiferromagnetic core surrounded by the outer spin vortex. Based on an effective exchange model, we find that these competing spin textures are a result of the interplay of Dzyaloshinskii-Moriya and Heisenberg exchange interactions. In the presence of both SOAM coupling and Raman-induced spin-flip hopping, more many-body phases appear, including canted-antiferromagnetic and stripe phases. Our prediction suggests that SOAM coupling could induce rich exotic many-body phases in the strongly interacting regime.

Emergent flat-band physics in d9−δ multilayer nickelates

Recent experiments showed that the reduced multilayer rare-earth (RE) nickel oxides of form $\mathrm{R}{\mathrm{E}}_{p+1}{\mathrm{Ni}}_{p}{\mathrm{O}}_{2p+2}$ may belong to the novel family of superconducting lanthanide nickelates. Here, the correlated electronic structure of ${\mathrm{Pr}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{8}$ and ${\mathrm{Nd}}_{6}{\mathrm{Ni}}_{5}{\mathrm{O}}_{12}$ is studied by means of an advanced realistic many-body framework. It is revealed that the low-energy physics of both systems is dominated by an interplay of Ni-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and Ni-${d}_{{z}^{2}}$ degrees of freedom. While the Ni-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals are always highly correlated near a (orbital-selective) Mott-insulating regime, the Ni-${d}_{{z}^{2}}$ orbitals give rise to intriguing nondispersive features. At low temperature, the Pr compound still displays quasiparticle-like Ni-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-derived states at the Fermi level, but the interacting fermiology of the Nd compound is outshined by an emergent Ni-${d}_{{z}^{2}}$-controlling flat band. These findings translate well to the previous characterization of doped infinite-layer nickelates, and hence further make the case for a mechanism of unconventional superconductivity, which is distinct from the one in high-${T}_{\mathrm{c}}$ cuprates.

Mott insulator of strongly interacting two-dimensional semiconductor excitons

In condensed-matter physics, Mott insulators are an important phase involving strongly interacting electrons because of their intricate relationship with high-temperature superconductors1,2. Mott phases were recently observed for both bosonic and fermionic species in atomic systems3–9. However, in the solid state, the fingerprint of a Mott insulator implemented with bosons has yet to be found. Here we demonstrate such signature by exploring the Bose–Hubbard model using semiconductor excitons confined in a two-dimensional lattice. We emphasize the regime where on-site interactions are comparable to the energy separation between lattice-confined states. We then observe that a Mott phase is accessible, with at most two excitons uniformly occupying each lattice site. The technology introduced here allows us to programme the geometry of the lattice that confines the excitons. This versatility, combined with the long-range nature of dipolar interactions between excitons, provides a route to explore many-body phases that spontaneously break the lattice symmetry10,11. A semiconductor platform for experimentally investigating the multiorbital Bose–Hubbard model with long-range interactions is demonstrated. The interactions between the excitons are strong enough to reach the Mott insulator regime.

Quantum Simulation of Antiferromagnetic Heisenberg Chain with Gate-Defined Quantum Dots

Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted. Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers. To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required. Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array. We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met. Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian. Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein. The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

Persistent currents in Bose–Bose mixtures after an interspecies interaction quench

We study the persistent currents and interspecies entanglement generation in a Bose–Bose mixture formed by two atomic gases (hereafter labeled by the letters A and B) trapped in a one-dimensional ring lattice potential with an artificial gauge field after a sudden quench from zero to strong interactions between the two gases. Assuming that the strength of these interactions is much larger than the single species energies and that the gas A is initially in the Mott-insulator regime, we show that the current of the gas B is reduced with respect to its value prior the interaction quench. Averaging fast oscillations out, the relative decrease of this current is independent of the initial visibility and Peierls phase of the gas B and behaves quadratically with the visibility of the gas A. The second Rényi entropy of the reduced state measuring the amount of entanglement between the two gases is found to scale linearly with the number of sites and to be proportional to the relative decrease of the current.

Superconductor-like effects in an ac-driven normal Mott-insulating quantum dot array

We study the current response of an AC driven dissipative Mott insulator system, a normal quantum dot array, using an analytical Keldysh field theory approach. Deep in the Mott insulator regime, the nonequilibrium steady state (NESS) response resembles a resistively shunted Josephson array, with a nonequilibrium Mott insulating to conductor transition as the drive frequency {\Omega} is increased. The diamagnetic component of the NESS in the conducting phase is anomalous, implying negative inductance, strikingly reminiscent of the {\eta}-pairing phase of a Josephson array with negative phase stiffness. However in the presence of an additional DC field the signature of supercurrent - Shapiro steps - is completely absent. We interpret these properties as number-phase fluctuation effects shared with Josephson systems rather than superconductivity.

Quantum simulation of the two-site Hubbard Hamiltonian

We present an experimental quantum simulation of the two-site Hubbard Hamiltonian, using the NMR technique. By varying the ratio between the Coulomb interaction U and the kinetic energy Jh (U/Jh), it was possible to observe changes in the behavior of the system, showing that the simulation carries the physics of the Hubbard model, such as the occurrence of an analog of the crossover from a metallic to a Mott-insulator regime in the limit U ​≫Jh. The experimental results were compared with the theoretic predictions, showing good fidelity. The problem is relevant to the areas of Quantum Computation and Solid State Physics, and establishes a possible new approach to treat the model.

Hidden Anderson localization in disorder-free Ising–Kondo lattice**Project supported in part by the National Natural Science Foundation of China (Grant Nos. 11704166, 11834005, and 11874188).

Anderson localization (AL) phenomena usually exist in systems with random potential. However, disorder-free quantum many-body systems with local conservation can also exhibit AL or even many-body localization transition. We show that the AL phase exists in a modified Kondo lattice without external random potential. The density of state, inverse participation ratio and temperature-dependent resistance are computed by classical Monte Carlo simulation, which uncovers an AL phase from the previously studied Fermi liquid and Mott insulator regimes. The occurrence of AL roots from quenched disorder formed by conservative localized moments. Interestingly, a many-body wavefunction is found, which captures elements in all three paramagnetic phases and is used to compute their quantum entanglement. In light of these findings, we expect that the disorder-free AL phenomena can exist in generic translation-invariant quantum many-body systems.

Superfluid-Mott-Insulator Transition in an Optical Lattice with Adjustable Ensemble-Averaged Filling Factors* *Supported by the National Natural Science Foundation of China (Grant Nos. 61703025, 91736208, 11504328, and 11920101004), the National Program on Key Basic Research Project of China (Grant Nos. 2016YFA0301501 and 2017YFA0304204).

We study the quantum phase transition from a superfluid to a Mott insulator of ultracold atoms in a three-dimensional optical lattice with adjustable filling factors. Based on the density-adjustable Bose–Einstein condensate we prepared, the excitation spectrum in the superfluid and the Mott insulator regime is measured with different ensemble-averaged filling factors. We show that for the superfluid phase, the center of the excitation spectrum is positively correlated with the ensemble-averaged filling factor, indicating a higher sound speed of the system. For the Mott insulator phase, the discrete feature of the excitation spectrum becomes less pronounced as the ensemble-averaged filling factor increases, implying that it is harder for the system to enter the Mott insulator regime with higher filling factors. The ability to manipulate the filling factor affords further potential in performing quantum simulation with cold atoms trapped in optical lattices.

Specific heat maximum as a signature of Mott physics in the two-dimensional Hubbard model

Recent experiments on cuprates show that as a function of doping, the normal-state specific heat sharply peaks at the doping $\delta^*$, where the pseudogap ends at low temperature. This finding is taken as the thermodynamic signature of a quantum critical point, whose nature has not yet been identified. Here we present calculations for the two-dimensional Hubbard model in the doped Mott insulator regime, which indicate that the specific heat anomaly can arise from the finite temperature critical endpoint of a first-order transition between a pseudogap phase with dominant singlet correlations and a metal. As a function of doping at the temperature of the endpoint, the specific heat diverges. Upon increasing temperature, the peak becomes broader. The diverging correlation length is associated with uniform density fluctuations. No broken symmetries are needed. These anomalies also occur at half-filling as a function of interaction strength, and are relevant for organic superconductors and ultracold atoms.

Real-space dynamical mean-field theory of Friedel oscillations in strongly correlated electron systems

We study Friedel oscillations and screening effects of the impurity potential in the Hubbard model. Electronic correlations are accounted for by solving the real-space dynamical mean-field theory equations using the continuous time quantum Monte-Carlo simulations at finite temperatures and using a homogeneous self-energy approximation with the numerical renormalization group at zero temperature. We find that in the Fermi liquid phase both the amplitudes of Friedel oscillations and the screening charge decrease with increasing the interaction and follow the behavior of the Fermi liquid renormalization factor. Inside the Mott insulator regime the Friedel oscillations are absent but the residual screening charge remains finite.

Resonant two-site tunneling dynamics of bosons in a tilted optical superlattice

We study the non-equilibrium dynamics of a 1D Bose-Hubbard model in a gradient potential and a superlattice, beginning from a deep Mott insulator regime with an average filling of one particle per site. Studying a quench that is near resonance to tunnelling of the particles over two lattice sites, we show how a spin model emerges consisting of two coupled Ising chains that are coupled by interaction terms in a staggered geometry. We compare and contrast the behavior in this case with that in a previously studied case where the resonant tunnelling was over a single site. Using optimized tensor network techniques to calculate finite temperature behavior of the model, as well as finite size scaling for the ground state, we conclude that the universality class of the phase transition for the coupled chains is that of a tricritical Ising point. We also investigate the out-of-equilibrium dynamics after the quench in the vicinity of the resonance and compare dynamics with recent experiments realized without the superlattice geometry. This model is directly realizable in current experiments, and reflects a new general way to realize spin models with ultracold atoms in optical lattices.