Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin-1/21/2J_1-J_2J1−J2 Heisenberg model on the square lattice. Focusing on neural network architectures without physics-informed input, we argue in favor of using an ansatz consisting of two decoupled real-valued networks, one for the amplitude and the other for the phase of the variational wavefunction. By introducing concrete mitigation strategies against inherent numerical instabilities in the stochastic reconfiguration algorithm we obtain a variational energy comparable to that reported recently with neural networks that incorporate knowledge about the physical system. Through a detailed analysis of the individual components of the algorithm, we conclude that the rugged nature of the energy landscape constitutes the major obstacle in finding a satisfactory approximation to the ground state wavefunction, and prevents learning the correct sign structure. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.

Extended Hořava Gravity with Physical Ground-State Wavefunction

We propose a new extended theory of Hořava gravity based on the following three conditions: (i) power-counting renormalizable, (ii) healthy IR behavior and (iii) a stable vacuum state in a quantized version of the theory. Compared with other extended theories, we stress that any realistic theory of gravity must have physical ground states when quantization is performed. To fulfill the three conditions, we softly break the detailed balance but keep its basic structure unchanged. It turns out that the new model constructed in this way can avoid the strong coupling problem and remains power-counting renormalizable, moreover, it has a stable vacuum state by an appropriate choice of parameters.

Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions

Negative signs in many-body wavefunctions play an important role in quantum mechanics because interference relies on cancellation between amplitudes of opposite signs. The ground-state wavefunction of double semion model contains negative signs that cannot be removed by any local transformation. Here we study the quantum effects of these intrinsic negative signs. By proposing a generic double semion wavefunction in tensor network representation, we show that its norm can be mapped to the partition function of a triangular lattice Ashkin-Teller model with imaginary interactions. We use numerical tensor-network methods to solve this non-Hermitian model with parity-time symmetry and determine a global phase diagram. In particular, we find a dense loop phase described by non-unitary conformal field theory and a parity-time-symmetry breaking phase characterized by the zeros of the partition function. Therefore, our work establishes a connection between the intrinsic signs in the topological wavefunction and non-unitary phases in the parity-time-symmetric non-Hermitian statistical model.

Unveiling real active site for photocatalytic H2O2 evolution: A combined experimental and DFT-TDDFT study

Photocatalyst with multiple modification sites (MSs) exhibited better performance than single site in photocatalytic H2O2 evolution, while the corresponding reaction mechanism is more complicated. However, neither experiment nor density functional theory (DFT) based on ground state wavefunction cannot precisely confirm the role of each site in photocatalyst with multiple MSs. Here, we propose a universal method that flexibly combines experiments, DFT and time-dependent DFT (TDDFT) calculations to reveal the photocatalytic mechanism and active site of nitrogen deficiency g-C3N4 (NDCN) containing two MSs (bicoordinated nitrogen vacancy and cyano group). Characterization techniques and control experiments prove that generation of H2O2 on NDCN is a two-step single electron transfer process, and NDCN exhibits enhanced charge separation efficiency and higher selectivity for two-electron oxygen reduction. DFT-TDDFT calculations further indicate that nitrogen vacancy is the real catalytic site for activating O2, which promotes O2 adsorption and continuously formation of •O2−, thus inhibiting electron-hole recombination.

Imaging the Holon string of the Hubbard model

It has been a long-sought goal of quantum simulation to find answers to outstanding questions in condensed-matter physics. A famous example is finding the ground state and the excitations of the two-dimensional (2D) Hubbard model with strong repulsion below half-filling. This system is a doped antiferromagnet and is of great interest because of its possible relation to high-Tcsuperconductors. Theoretically, the fermion excitations of this model are believed to split up into holons and spinons, and a moving holon is believed to leave behind it a string of “wrong” spins that mismatch with the antiferromagnetic background. Here, we show that the properties of the ground-state wavefunction and the holon excitation of the 2D Hubbard model can be revealed in unprecedented detail by using the imaging and the interference technique in atomic physics. They allow one to reveal the Marshall sign of the doped antiferromagnet. The region of wrong Marshall sign indicates the location of the holon string.

Effect of the Diamagnetic term in the ultra-strong coupling regime

We consider a set of two level atoms interacting with a single quantized bosonic mode governed by the Dicke model. In this model it is well known that under a critical value of the light-matter coupling a spontaneous radiation process takes place. In the present work, we investigate the dynamics of the system and we study the Wigner distribution function to visualize the effect of the minimal coupling on the ground state wavefunction from the normal phase to the superradiant one. We show also that the entanglement of Bi-partite model is limited by the presence of the diamagnetic term.

Structure of free complement wavefunction for the ground and the first excited state of helium atom

We review the fundamental ideas of free complement (FC) method through its application on both ground and first excited states of helium atom. We have found that lower energies can be obtained with fewer number of terms in the FC expansion of the ground state wavefunction. In this case, the optimization of orbital exponents was not necessary for achieving spectroscopic accuracy, especially at higher orders where the structure of the FC wavefunction converges to that of the exact one. We have discovered that permanents naturally appear in the FC expansion of the first triplet excited state wavefunction. Including permanents in the FC expansion is shown to be energetically important for the first triplet excited state of helium atom whereas it is not computationally favorable at higher orders. Finally, considering the group theoretical properties of the symmetric group [Formula: see text] and using immanants, a compact and more elegant form for the FC expansion of the first triplet excited state of the helium atom is achieved.

Neutral donor in a bilayer spherical semiconductor quantum dot

The binding energy of bilayer spherical quantum dots (BSQDs) with randomly distributed neutral donor [Formula: see text] is computationally simulated. We analyze the ground state energy by using different potentials of confinement that include changes in its height, transition region and width, considering theoretical development in which the variational procedure takes a trial function as a product of the ground state wavefunction of the uncoupled electron in the heterostructure, with a correlation function that depends only on electron–ion separation. We find that the curves of the binding energy with repulsive layer have additional peaks, whose position and height depend on the configuration of the confinement is chosen at the center of the dot. Additionally, our results include novel curves for the density of [Formula: see text] impurity states for different potentials’ shapes.