Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice t-J Model.

The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t_{2}>0) but a dominant charge density wave (CDW) order on the hole-doped side (t_{2}<0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ=1/16-1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1/8 doping, demonstrating the winning of SC over CDW by increasing the system width. Our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.

Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators.

The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. In this Letter, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice t-J model on the six- and eight-leg cylinders, we identify a d+id-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number C=2 and quasi-long-range superconducting order. We map out the quantum phase diagram with by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into d-wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a d-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition.

Search for Spin-Dependent Gravitational Interactions at Earth Range.

Among the four fundamental forces, only gravity does not couple to particle spins according to the general theory of relativity. We test this principle by searching for an anomalous scalar coupling between the neutron spin and the Earth's gravity on the ground. We develop an atomic gas comagnetometer to measure the ratio of nuclear spin-precession frequencies between ^{129}Xe and ^{131}Xe, and search for a change of this ratio to the precision of 10^{-9} as the sensor is flipped in Earth's gravitational field. The null results of this search set an upper limit on the coupling energy between the neutron spin and the gravity on the ground at 5.3×10^{-22} eV (95% confidence level), resulting in a 17-fold improvement over the previous limit. The results can also be used to constrain several other anomalous interactions. In particular, the limit on the coupling strength of axion-mediated monopole-dipole interactions at the range of Earth's radius is improved by a factor of 17.

Intermolecular Non-Bonded Interactions from Machine Learning Datasets.

Accurate determination of intermolecular non-covalent-bonded or non-bonded interactions is the key to potentially useful molecular dynamics simulations of polymer systems. However, it is challenging to balance both the accuracy and computational cost in force field modelling. One of the main difficulties is properly representing the calculated energy data as a continuous force function. In this paper, we employ well-developed machine learning techniques to construct a general purpose intermolecular non-bonded interaction force field for organic polymers. The original ab initio dataset SOFG-31 was calculated by us and has been well documented, and here we use it as our training set. The CLIFF kernel type machine learning scheme is used for predicting the interaction energies of heterodimers selected from the SOFG-31 dataset. Our test results show that the overall errors are well below the chemical accuracy of about 1 kcal/mol, thus demonstrating the promising feasibility of machine learning techniques in force field modelling.

Quantum Phases of Transition Metal Dichalcogenide Moiré Systems.

Moiré systems provide a rich platform for studies of strong correlation physics. Recent experiments on heterobilayer transition metal dichalcogenide Moiré systems are exciting in that they manifest a relatively simple model system of an extended Hubbard model on a triangular lattice. Inspired by the prospect of the hetero-transition metal dichalcogenide Moiré system's potential as a solid-state-based quantum simulator, we explore the extended Hubbard model on the triangular lattice using the density matrix renormalization group. Specifically, we explore the two-dimensional phase space spanned by the key tuning parameters in the extended Hubbard model, namely, the kinetic energy strength and the further-range Coulomb interaction strengths. We find competition between Fermi fluid, chiral spin liquid, spin density wave, and charge order. In particular, our finding of the optimal further-range interaction for the chiral correlation presents a tantalizing possibility.

Search for Monopole-Dipole Interactions at the Submillimeter Range with a

Monopole-dipole interactions involving scalar couplings between a spin and a massive particle violate both P and T symmetry, and can be mediated by axions. We use a ^{129}Xe-^{131}Xe-Rb atomic cell comagnetometer to measure the ratio of precession frequencies between the two xenon isotopes, and search for changes of the ratio correlated with the distance between the atomic cell and a nonmagnetic bismuth germanate crystal. A modulated Rb polarization scheme is used to suppress systematic effects by 2 orders of magnitude. The null results of this search improve the upper limit on the coupling strength g_{s}^{N}g_{p}^{n} over the interaction range 0.11-0.55 mm, and by a maximum improvement factor of 30 at 0.24 mm. The corresponding propagator mass range of this new excluded region covers 0.36-1.80 meV.

Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice.

A spin-[Formula: see text] lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the [Formula: see text] point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.

Robust d-Wave Superconductivity in the Square-Lattice t-J Model.

Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.

SU(4) Chiral Spin Liquid, Exciton Supersolid, and Electric Detection in Moiré Bilayers.

We propose a moiré bilayer as a platform where exotic quantum phases can be stabilized and electrically detected. Moiré bilayers consist of two separate moiré superlattice layers coupled through the interlayer Coulomb repulsion. In the small distance limit, an SU(4) spin can be formed by combining layer pseudospin and the real spin. As a concrete example, we study an SU(4) spin model on triangular lattice in the fundamental representation. By tuning a three-site ring exchange term K∼(t^{3}/U^{2}), we find the SU(4) symmetric crystallized phase and an SU(4)_{1} chiral spin liquid at the balanced filling. We also predict two different exciton supersolid phases with interlayer coherence at imbalanced filling under displacement field. Especially, the system can simulate an SU(2) Bose-Einstein condensation by injecting interlayer excitons into the magnetically ordered Mott insulator at the layer polarized limit. Smoking gun evidences of these phases can be obtained by measuring the pseudospin transport in the counterflow channel.

Orbital Chern Insulator and Quantum Phase Diagram of a Kagome Electron System with Half-Filled Flat Bands.

We study the quantum phase diagram of electrons on kagome lattice with half-filled lowest flat bands by considering the antiferromagnetic Heisenberg interaction J, and short-range Coulomb interaction V. In the weak J regime, we identify a fully spin-polarized phase. The presence of finite V drives a spontaneous chiral current, which makes the system an orbital Chern insulator by contributing an orbital magnetization. Such an out-of-plane orbital magnetization allows the presence of a Chern insulating phase independent of the spin orientation in contrast to the spin-orbit coupling induced Chern insulator that disappears with in-plane ferromagnetism constrained by symmetry. Such a symmetry difference provides a criterion to distinguish the physical origin of topological responses in kagome systems. The orbital Chern insulator is robust against small coupling J. By further increasing J, we find that the ferromagnetic topological phase is suppressed, which first becomes partially polarized and then enters a nonmagnetic phase with spin and charge nematicity. The frustrated flat band allows the spin and Coulomb interaction to play an essential role in determining the quantum phases.

Topological Interface between Pfaffian and Anti-Pfaffian Order in ν=5/2 Quantum Hall Effect.

A recent thermal Hall experiment triggered renewed interest in the problem of ν=5/2 quantum Hall effect, which motivated novel interpretations based on the formation of mesoscopic puddles made of Pfaffian and anti-Pfaffian topological orders. Here, we study an interface between the Pfaffian and anti-Pfaffian states, which may play crucial roles in thermal transport, by means of state-of-the-art, density-matrix renormalization group simulations. We demonstrate that an intrinsic electric dipole moment emerges at the interface, similar to the "p-n" junction sandwiched between N-type and P-type semiconductor. Importantly, we elucidate the topological origin of this dipole moment, whose formation is to counterbalance the mismatch of guiding-center Hall viscosity of bulk Pfaffian and anti-Pfaffian states. In addition, these results imply that the formation of a dipole moment could be helpful to stabilize the puddles made of Pfaffian and anti-Pfaffian states in experimental conditions.

Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene.

We develop a proposal to realize a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings ν=±3+1/2 and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band structure of bilayer graphene and includes the fluctuations between the n=0 and n=1 cyclotron orbitals of its zeroth Landau level to delineate the most favorable region of parameters to experimentally access this unconventional critical point. We also find evidence for a new anisotropic gapless phase stabilized near the level crossing of n=0/1 orbits.

A minimum quantum chemistry CCSD(T)/CBS dataset of dimeric interaction energies for small organic functional groups.

We have performed a quantum chemistry study on the bonding patterns and interaction energies for 31 dimers of small organic functional groups (dubbed the SOFG-31 dataset), including the alkane-alkene-alkyne (6 + 4 + 4 = 14, AAA) groups, alcohol-aldehyde-ketone (4 + 4 + 3 = 11, AAK) groups, and carboxylic acid-amide (3 + 3 = 6, CAA) groups. The basis set superposition error corrected super-molecule approach using the second order Møller-Plesset perturbation theory (MP2) with the Dunning's aug-cc-pVXZ (X = D, T, Q) basis sets has been employed in the geometry optimization and energy calculations. To calibrate the MP2 calculated interaction energies for these dimeric complexes, we perform single-point calculations with the coupled cluster with single, double, and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS] using the well-tested extrapolation methods. In order to gain more physical insights, we also perform a parallel series of energy decomposition calculations based on the symmetry adapted perturbation theory (SAPT). The collection of these CCSD(T)/CBS interaction energy values can serve as a minimum quantum chemistry dataset for testing or training less accurate but more efficient calculation methods. As an application, we further propose a segmental SAPT model based on chemically recognizable segments in a specific functional group. These model interactions can be used to construct coarse-grained force fields for larger molecular systems.

Disorder-Driven Transition in the ν=5/2 Fractional Quantum Hall Effect.

The fractional quantum Hall (FQH) effect at the filling number ν=5/2 is a primary candidate for non-Abelian topological order, while the fate of such a state in the presence of random disorder has not been resolved. We address this open question by implementing an unbiased diagnosis based on numerical exact diagonalization. We calculate the disorder averaged Hall conductance and the associated statistical distribution of the topological invariant Chern number, which unambiguously characterize the disorder-driven collapse of the FQH state. As the disorder strength increases towards a critical value, a continuous phase transition is detected based on the disorder configuration averaged wave function fidelity and the entanglement entropy. In the strong disorder regime, we identify a composite Fermi liquid phase with fluctuating Chern numbers, in striking contrast to the well-known ν=1/3 case where an Anderson insulator appears. Interestingly, the lowest Landau level projected a local density profile, the wave function overlap, and the entanglement entropy as a function of disorder strength simultaneously signal an intermediate phase, which may be relevant to the recent proposal of a particle-hole Pfaffian state or Pfaffian-anti-Pfaffian puddle state.

Spin-Orbital Density Wave and a Mott Insulator in a Two-Orbital Hubbard Model on a Honeycomb Lattice.

Inspired by the recent discovery of correlated insulating states in twisted bilayer graphene, we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group simulation, we identify a metal-insulator transition around U_{c}/t=2.5-3. In the vicinity of U_{c}, we find strong spin-orbital density wave fluctuations at commensurate wave vectors, accompanied by weaker incommensurate charge density wave fluctuations. The spin-orbital density wave fluctuations are enhanced with increasing system sizes, suggesting the possible emergence of long-range order in the two-dimensional limit. At larger U, our calculations indicate a possible nonmagnetic Mott insulator phase without spin or orbital polarization. Our findings offer new insight into correlated electron phenomena in twisted bilayer graphene and other multiorbital honeycomb materials.

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons.

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit 'strange metal' behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal--the 'd-wave metal'. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian--the usual t-J model with electron kinetic energy t and two-spin exchange J supplemented with a frustrated electron 'ring-exchange' term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.

Numerical Study of Quantum Hall Bilayers at Total Filling ν_{T}=1: A New Phase at Intermediate Layer Distances.

We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1

Two Universality Classes for the Many-Body Localization Transition.

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

Kinetic energy partition method applied to ground state helium-like atoms.

We have used the recently developed kinetic energy partition (KEP) method to solve the quantum eigenvalue problems for helium-like atoms and obtain precise ground state energies and wave-functions. The key to treating properly the electron-electron (repulsive) Coulomb potential energies for the KEP method to be applied is to introduce a "negative mass" term into the partitioned kinetic energy. A Hartree-like product wave-function from the subsystem wave-functions is used to form the initial trial function, and the variational search for the optimized adiabatic parameters leads to a precise ground state energy. This new approach sheds new light on the all-important problem of solving many-electron Schrödinger equations and hopefully opens a new way to predictive quantum chemistry. The results presented here give very promising evidence that an effective one-electron model can be used to represent a many-electron system, in the spirit of density functional theory.