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Functional tensor network solving many-body Schrodinger equation
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DOI：10.1103/PhysRevB.105.165116.png)
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Abstract
En 中文
Solving the many-body Schrodinger equation in continuous spaces with the presence of strong correlations is an extremely important and challenging issue in quantum physics. In this work, we propose the functional tensor network (FTN) approach to solve the many-body Schrodinger equation. Provided the orthonormal functional bases, we represent the coefficients of the many-body wave function as a tensor network. The observables, such as energy, can be calculated simply by tensor contractions. Simulating the ground state becomes solving a minimization problem defined by the tensor network. An efficient gradient-decent algorithm based on automatically differentiable tensors is proposed. We here take the matrix product state (MPS), whose complexity scales only linearly with the system size, as an example. We apply our approach to solve the ground state of coupled harmonic oscillators and achieve high accuracy by comparing our results with the exact solutions. Reliable results are also given in the presence of three-body interactions, where the system cannot be decoupled from isolated oscillators. Our approach is simple and, with well-controlled error, essentially different from highly nonlinear neural-network solvers. Our work extends the applications of the tensor network from quantum lattice models to systems in continuous space. The FTN can be used as a general solver of the differential equations with many variables. The MPS exemplified here can be generalized to, e.g., fermionic tensor networks to solve the electronic Schrodinger equation.
Keywords:
MATRIX PRODUCT STATES
NEURAL-NETWORK
RENORMALIZATION-GROUP
QUANTUM COMPUTATION