Shuoyi Hu | Search arXiv

arXiv2026

Leg-Tied Tensor Network States: Entanglement Beyond Virtual Bonds

We introduce a class of tensor-network states in which physical legs are shared among local tensors, termed leg-tied tensor ansätze (LETTA). Physical leg ties encode long-range correlations directly, while a virtual matrix product state (MPS) backbone retains short-range multipartite entanglement. The linear virtual backbone allows us to develop a deterministic density matrix renormalization group-like variational optimization algorithm using exact contractions over the active tie-boundary sets and local minimization. We demonstrate the advantages of LETTA for the two-dimensional frustrated $J_1$--$J_2$ Heisenberg model and the three-dimensional transverse-field Ising model. Our results show that LETTA is substantially more accurate than same-bond-dimension MPS calculations and can typically reach the accuracy of much larger MPS calculations using one order of magnitude fewer variational parameters. LETTA thus opens the door for explicitly correlated tensor-network states that can encode long-range correlation beyond virtual bonds.

quant-ph↗

arXiv2026

Constrained Optimization Algorithms for Orbital Optimization in Quantum Chemistry

We present a modular constrained-orbital-optimization framework for quantum chemistry. The formulation separates the correlated electronic-structure solver from the orbital optimizer: the solver supplies one- and two-particle reduced density matrices, while the molecular orbitals are updated on the orthonormality-constrained Stiefel manifold with an implicit steepest-descent algorithm. Because the orbital optimizer only requires reduced density matrices, MP2, CASCI, and DMRG can be treated within the same interface. For CASCI solvers, the approach is closely related to optimal-orbital full configuration interaction and CASSCF\cite{helgaker_MulticonfigurationalSelfConsistentField_2000a}, but uses a solver-independent constrained-optimization update rather than CAS-specific orbital-rotation equations. When conventional CASSCF orbital-rotation iterations converge to higher-energy local solutions, CO-CAS can recover lower-energy stationary solutions. We also introduce a modified direct inversion in the iterative subspace procedure to accelerate macro-iteration convergence and a dynamical-weighting scheme to improve state-averaged excited-state calculations. Applications to LiF, H$_2$O, and pyrazine show that orbital optimization lowers energies relative to fixed-orbital MP2, CASCI, and DMRG references while improving convergence and potential-energy-curve smoothness.

physics.chem-ph↗