Particle number conservation and block structures in matrix product states. (English) Zbl 1490.81099
Summary: The eigenvectors of the particle number operator in second quantization are characterized by the block sparsity of their matrix product state representations. This is shown to generalize to other classes of operators. Imposing block sparsity yields a scheme for conserving the particle number that is commonly used in applications in physics. Operations on such block structures, their rank truncation, and implications for numerical algorithms are discussed. Explicit and rank-reduced matrix product operator representations of one- and two-particle operators are constructed that operate only on the non-zero blocks of matrix product states.
MSC:
| 81S08 | Canonical quantization |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
Keywords:
second quantization; particle number conservation; matrix product states; matrix product operatorsReferences:
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