The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S=1/2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result.

We investigate the critical behavior and the duality property of the ferromagnetic q-state clock model on the square lattice based on the tensor-network formalism. From the entanglement spectra of local tensors defined in the original and dual lattices, we obtain the exact self-dual points for the model with q ≤ 5 and approximate self-dual points for q ≥ 6. We calculate accurately the lower and upper critical temperatures for the six-state clock model from the fixed-point tensors determined using the higher-order tensor renormalization group method and compare with other numerical results.

The deconfined quantum critical point (DQCP) was originally proposed as a continuous transition between two spontaneous symmetry breaking phases in 2D spin-1/2 systems. While great efforts have been spent on the DQCP for 2D systems, both theoretically and numerically, ambiguities among the nature of the transition are still not completely clarified. Here we shift the focus to a recently proposed 1D incarnation of DQCP in a spin-1/2 chain. By solving it with the variational matrix product state in the thermodynamic limit, a continuous transition between a valence-bond solid phase and a ferromagnetic phase is discovered. The scaling dimensions of various operators are calculated and compared with those from field theoretical description. At the critical point, two emergent O(2) symmetries are revealed, and the associated conserved current operators with exact integer scaling dimensions are determined with scrutiny. Our findings provide the low-dimensional analog of DQCP where unbiased numerical results are in perfect agreement with the controlled field theoretical predictions and have extended the realm of the unconventional phase transition as well as its identification with the advanced numerical methodology.

The Chebyshev expansion offers a numerically efficient and easy-implement algorithm for evaluating dynamic correlation functions using matrix product states (MPS). In this approach, each recursively generated Chebyshev vector is approximately represented by an MPS. However, the recurrence relations of Chebyshev polynomials are broken by the approximation, leading to an error which is accumulated with the increase of the order of expansion. Here we propose a reorthonormalization approach to remove this error introduced in the loss of orthogonality of the Chebyshev polynomials. Our approach, as illustrated by comparison with the exact results for the one-dimensional XY and Heisenberg models, improves significantly the accuracy in the calculation of dynamical correlation functions. * navyphysics@iphy.ac.cn † txiang@iphy.ac.cn

The Mott insulator is the quintessential strongly correlated electronic state. We obtain complete insight into the physics of the two-dimensional Mott insulator by extending the slave-fermion (holondoublon) description to finite temperatures. We first benchmark its predictions against state-of-theart quantum Monte Carlo simulations, demonstrating quantitative agreement. Qualitatively, the short-ranged spin fluctuations both induce holon-doublon bound states and renormalize the charge sector to form the Hubbard bands. The Mott gap is understood as the charge gap renormalized downwards by these spin fluctuations. As temperature increases, the Mott gap closes before the charge gap, causing a pseudogap regime to appear naturally during the melting of the Mott insulator.

Exploration of superconductivity in Cr-based compounds has attracted considerable interest because only a few Cr-based superconductors (CrAs, A2Cr3As3 and ACr3As3 (A = K, Rb, Cs, Na)) have been discovered so far and they show an unconventional pairing mechanism. We report the discovery of bulk superconductivity at 5.25 K in chromium nitride in Pr3Cr10-xN11 with a cubic lattice structure. A relatively large upper critical field of Hc2(0) ∼ 12.6 T is determined, which is larger than the estimated Pauli-paramagnetic pair-breaking magnetic field. The material has a large electronic specific-heat coefficient of 170 mJ K−2 mol−1—about 10 times larger than that estimated by the electronic structure calculation, which suggests that correlations between 3d electrons are very strong in Pr3Cr10-xN11, and thus quantum fluctuations might be involved. Electronic structure calculations show that the density of states at the Fermi energy are contributed predominantly by Cr 3d electrons, implying that the superconductivity results mainly from the condensation of Cr 3d electrons. Pr3Cr10-xN11 represents a rare example of possible unconventional superconductivity emerging in a 3D system with strong electron correlations. Nevertheless, clarification of the specific pairing symmetry needs more investigation.

We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly both the accuracy and the efficiency of the tensor-network algorithm and allows the ground state to be determined accurately using TNS with very small virtual bond dimensions. This state contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.

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