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The fermionic t-J model has been widely recognized as a canonical model in understanding various strongly correlated phases like cuprate high-Tc superconductivity. Simulating this model with controllable quantum platforms offers new possibilities to probe high-Tc physics, yet suffering challenges. Here we propose a novel scheme to realize the t-J model in a programmable Rydberg-dressed tweezer array. By properly engineering the Rydberg-dressed dipole-dipole interaction and inter-tweezer couplings, a highly tunable fermionic t-J model with next-nearest-neighbour hopping terms is achieved. We particularly explore quantum many-body dynamics in the large J/t limit, a regime far beyond the conventional optical lattices and cuprates. Notably, we predict a nontrivial self-pinning effect enforced by local quantum entanglement that characterizes a novel type of Hilbert space fragmentation. This effect leads to the breakdown of Krylov restricted thermalization. Our prediction opens a new horizon in exploring exotic quantum many-body dynamics with t-J model in tweezer arrays, and shall also make a step towards simulating the high-Tc physics in cold atom systems., Comment: 23 pages, 11 figures, a new version with the supplemental material added

The spin and orbital are two basic degrees of freedom, which play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we propose an orbital optical Raman lattice to study exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which features a global topological chiral orbital current, and the two-dimensional spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns. The former has topological Bogoliubov excitations characterized by a uniform Chern number, while the spin-orbital supersolid phase hosts topological excitations with opposite Chern numbers which respectively protect the chiral and antichiral edge modes in the neighboring supersolid clusters. Our findings may inspire a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and shall also advance the experimental progress of novel supersolids in higher dimensions., Comment: 7+9 pages, 4+4 figures. Discussions and references are updated

Higher-order topological phases (HOTPs) host exotic topological states that go beyond the traditional bulk-boundary correspondence. Up to now, there is still a lack of experimentally measurable momentum-space topological characterization for the HOTPs, which is not conducive to revealing the essential properties of these topological states and also restricts their detection in quantum simulation systems. Here, we propose a concept of polarized topological charges to characterize chiral-symmetric HOTPs in momentum space, which further facilitates a feasible experimental scheme to detect the HOTPs in $^{87}$Rb cold atomic system. Remarkably, our characterization theory not only shows that the second-order (third-order) topological phases are determined by a quarter (negative eighth) of the total polarized topological charges, but also reveals that the higher-order topological phase transitions are identified by the creation or annihilation of polarized topological charges. Particularly, these polarized topological charges can be measured by pseudospin structures of the systems. Due to theoretical simplicity and observational intuitiveness, this work shall advance the broad studies of the HOTPs in both theory and experiment., Comment: 8+9 pages, 4+3 figures. References are updated.Typos are corrected

The Kitaev chiral spin liquid has captured widespread interest in recent decades because of its intrinsic non-Abelian excitations, yet the experimental realization is challenging. Here we propose to realize and detect Kitaev chiral spin liquid in a deformed honeycomb array of Rydberg atoms. Through a novel laser-assisted dipole-dipole interaction mechanism to generate both effective hopping and pairing terms for hard-core bosons, together with van der Waals interactions, we achieve the pure Kitaev model with high precision. The gapped non-Abelian spin liquid phase is then obtained by introducing Zeeman fields. Moreover, we propose innovative strategies to probe the chiral Majorana edge modes by light Bragg scattering and by imagining their chiral motion. Our work broadens the range of exotic quantum many-body phases that can be realized and detected in atomic systems, and makes an important step toward manipulating non-Abelian anyons.

Rydberg atom arrays offer promising platforms for quantum simulation of correlated quantum matter and raise great interests. This work proposes a novel stripe-lattice model with Raman superarray of Rydberg atoms to realize bosonic fractional quantum anomalous Hall (FQAH) phase. Two types of Rydberg states, arranged in a supperarray configuration and with Raman-assisted dipole-exchange couplings, are implemented to realize a minimal QAH model for hard-core bosons populated into a topological flat band with large bulk gap under proper tunable experimental condition. With this the bosonic FQAH phase can be further achieved and probed feasibly. In particular, a novel quench protocol is proposed to probe the fractionalized excitations by measuring the correlated quench dynamics featured by fractional charge tunneling between bulk and chiral edge modes in the open boundary., Comment: 6+5 pages, 4+1 figures, final version accepted by Adv Quantum Technol

The study of warm dense matter, widely existing in nature and laboratories, is challenging due to the interplay of quantum and classical fluctuations. We develop a variational diagrammatic Monte Carlo method and determine the exchange-correlation kernel $K_{\rm XC}(q;T)$ of a warm dense electron gas for a broad range of temperature $T$ and momentum $q$. We observe several interesting physics, including the $T$-dependent evolution of the hump structure and the large-$q$ tail and the emergence of a scaling relation. Particularly, by deriving an analytical form for $q \to \infty$, we obtain large-$q$ tails of $K_{\rm XC}$ with high precision. It is shown that the $K_{\rm XC}$ data can be reliably transformed into real space, which can be directly used in density-functional-theory calculations of real warm dense matter.

Rydberg atoms with dipole-dipole interactions provide intriguing platforms to explore exotic quantum many-body physics. Here we propose a novel scheme with laser-assisted dipole-dipole interactions to realize synthetic magnetic field for Rydberg atoms in a two-dimensional array configuration, which gives rise to the exotic bosonic topological states. In the presence of an external effective Zeeman splitting gradient, the dipole-dipole interaction between neighboring Rydberg atoms along the gradient direction is suppressed, but can be assisted when Raman lights are applied to compensate the energy difference. With this scheme we generate a controllable uniform magnetic field for the complex spin-exchange coupling model, which can be mapped to hard core bosons coupling to an external synthetic magnetic field. The highly tunable flat Chern bands of the hard core bosons are then obtained and moreover, the bosonic fractional quantum Hall states can be achieved with experimental feasibility. This work opens an avenue for the realization of the highly-sought-after bosonic topological orders using Rydberg atoms., Comment: 5 pages, 4 figures, plus Supplementary Material. Discussions are updated, Fig. 3 and Fig. 4 are updated

We simulate the two-dimensional XY model in the flow representation by a worm-type algorithm, up to linear system size $L=4096$, and study the geometric properties of the flow configurations. As the coupling strength $K$ increases, we observe that the system undergoes a percolation transition $K_{\rm perc}$ from a disordered phase consisting of small clusters into an ordered phase containing a giant percolating cluster. Namely, in the low-temperature phase, there exhibits a long-ranged order regarding the flow connectivity, in contrast to the qusi-long-range order associated with spin properties. Near $K_{\rm perc}$, the scaling behavior of geometric observables is well described by the standard finite-size scaling ansatz for a second-order phase transition. The estimated percolation threshold $K_{\rm perc}=1.105 \, 3(4)$ is close to but obviously smaller than the Berezinskii-Kosterlitz-Thouless (BKT) transition point $K_{\rm BKT} = 1.119 \, 3(10)$, which is determined from the magnetic susceptibility and the superfluid density. Various interesting questions arise from these unconventional observations, and their solutions would shed lights on a variety of classical and quantum systems of BKT phase transitions.

The sign cancellation between scattering amplitudes makes fermions different from bosons. We systematically investigate Feynman diagrams' fermionic sign structure in a representative many-fermion system---a uniform Fermi gas with Yukawa interaction. We analyze the role of the crossing symmetry and the global gauge symmetry in the fermionic sign cancellation. The symmetry arguments are then used to identify the sign-canceled groups of diagrams. Sign-structure analysis has two applications. Numerically, it leads to a cluster diagrammatic Monte Carlo algorithm for fast diagram evaluations. The new algorithm is about $10^5$ times faster than the conventional approaches in the sixth order. Furthermore, our analysis provides important hints in constructing the relevant effective field theory for many-fermion systems.

The Weyl semimetals [1-6] are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band, and host massless quasiparticles known as Weyl fermions which were theorized by Hermann Weyl in the last twenties [7]. The lattice theory constrains that Weyl cones must come in pairs, with the minimal number of cones being two. The semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM) which is the optimal platform to explore broad Weyl physics but hard to engineer in solids. Here, we report the experimental realization of the IWSM band by synthesising for the first time a 3D spin-orbit (SO) coupling for ultracold atoms. Engineering a 3D configuration-tunable optical Raman lattice [8], we realize the Weyl type SO coupling for ultracold quantum gas, with which the IWSM band is achieved with controllability. The topological Weyl points are clearly measured via the virtual slicing imaging technique [8, 9] in equilibrium, and further resolved in the quench dynamics, revealing the key information of the realized IWSM bands. The realization of the IWSM band opens an avenue to investigate various exotic phenomena based on the optimal Weyl semimetal platforms., Comment: 4 figures in main text, 6 figures and 3 tables in Methods

There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonstrate how such fundamental Weyl semimetal can be realized in a maneuverable optical Raman lattice, with which the three-dimensional (3D) spin-orbit (SO) coupling is synthesised for ultracold atoms. In addition, a new novel Weyl phase with coexisting Weyl nodal points and nodal ring is also predicted here, and is shown to be protected by nontrivial linking numbers. We further propose feasible techniques to precisely resolve 3D Weyl band topology through 2D equilibrium and dynamical measurements. This work leads to the first realization of the most fundamental Weyl semimetal band and the 3D SO coupling for ultracold quantum gases, which are respectively the significant issues in the condensed matter and ultracold atom physics., Comment: 6 pages + supplementary material

Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a fundamentally new, high-precision dynamical approach, revealing topology through the unitary evolution after a quench from a topological trivial initial state with a two-dimensional Chern band realized in an ultracold $^{87}$Rb atom gas. The emerging ring structure in the spin dynamics uniquely determines the Chern number for the post-quench band and enables probing the full phase diagram of the band topology with high precision. Besides, we also measure the topological band gap and the domain wall structure dynamically formed in the momentum space during the long-term evolution. Our dynamical approach provides a way towards observing a universal bulk-ring correspondence, and has broad applications in exploring topological quantum matter., Comment: 9 pages, 5 figures for main text and 12 pages for supplementary material

We report the realization of a robust and highly controllable two-dimensional (2D) spin-orbit (SO) coupling with topological non-trivial band structure. By applying a retro-reflected 2D optical lattice, phase tunable Raman couplings are formed into the anti-symmetric Raman lattice structure, and generate the 2D SO coupling with precise inversion and $C_4$ symmetries, leading to considerably enlarged topological regions. The life time of the 2D SO coupled Bose-Einstein condensate reaches several seconds, which enables the exploring of fine tuning interaction effects. These essential advantages of the present new realization open the door to explore exotic quantum many-body effects and non-equilibrium dynamics with novel topology., Comment: 6 pages, 4 figures

We propose a hierarchy set of minimal optical Raman lattice schemes toward the experimental realization of spin-orbit (SO) couplings of various types for ultracold atoms, including two-dimensional (2D) Dirac type of $C_4$ symmetry, 2D Rashba and 3D Weyl types. These schemes are well accessible with current cold-atom technology, and in particular, a long-lived Bose-Einstein condensation of the 2D Dirac SO coupling has been experimentally proved. The generation of 2D Rashba and 3D Weyl types has an exquisite request that two sources of laser beams have distinct frequencies of factor-two difference. Surprisingly, we find that $^{133}$Cs atoms provide an ideal candidate for the realization. A common and essential feature is the absence of any fine-tuning and phase-locking in the realization, and the resulted SO coupled ultracold atoms have a long lifetime. These schemes essentially improve over the current experimental accessibility and controllability, and open new experimental platforms to study high-dimensional SO physics and novel topological phases with ultracold atoms., Comment: 5 pages, 4 figures, plus supplementary material. Typos are corrected and discussions are updated in supplementary material

Cold atoms with laser-induced spin-orbit (SO) interactions provide intriguing new platforms to explore novel quantum physics beyond natural conditions of solids. Recent experiments demonstrated the one-dimensional (1D) SO coupling for boson and fermion gases. However, realization of 2D SO interaction, a much more important task, remains very challenging. Here we propose and experimentally realize, for the first time, 2D SO coupling and topological band with $^{87}$Rb degenerate gas through a minimal optical Raman lattice scheme, without relying on phase locking or fine tuning of optical potentials. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in the momentum space. Our realization of 2D SO coupling with advantages of small heating and topological stability opens a broad avenue in cold atoms to study exotic quantum phases, including the highly-sought-after topological superfluid phases., Comment: 27 pages, 5 figures