Report
Transfer-matrix functions for algebraically decaying interactions in variational infinite matrix product states
| Title: | Transfer-matrix functions for algebraically decaying interactions in variational infinite matrix product states |
|---|---|
| Authors: | Yang, Qi |
| Publication Year: | 2026 |
| Collection: | Quantum Physics |
| Subject Terms: | Strongly Correlated Electrons, Quantum Physics |
| Description: | Variational infinite matrix product state (iMPS) calculations usually make Hamiltonians with algebraically decaying interactions compatible with standard MPO algorithms by first replacing the target Hamiltonian with a finite-pole sum-of-exponentials surrogate, thereby introducing a Hamiltonian-representation residual. We formulate the fixed-$D$ variational energy without introducing such a surrogate. For a fixed finite-$D$ MPS, the algebraic tail can be summed directly through the connected transfer matrix: the tail $e^{\mathrm{i} Qr}/r^α$ is represented by the matrix function $F_{α,Q}(\widetilde{T}_A)$, with $F_{α,Q}(z)=\operatorname{Li}_α(e^{\mathrm{i} Q}\,z)/z$. We evaluate the resulting matrix-function action using a Krylov method and obtain stable gradients by combining a Fréchet adjoint with implicit fixed-point differentiation. Benchmarks on long-range free fermions and the inverse-square Heisenberg family, including the Haldane--Shastry point, validate the transfer-matrix-function formulation. A long-range Ising-chain calculation illustrates a practical consequence of avoiding a finite-pole Hamiltonian representation. At a fixed, independently known critical field, finite-pole surrogate Hamiltonians can bias a critical diagnostic away from criticality, whereas the matrix-function calculation retains the expected critical signatures of the target algebraic Hamiltonian. 9 pages, 6 figures |
| Document Type: | Working Paper |
| DOI: | 10.48550/arXiv.2606.20522 |
| Access URL: | https://arxiv.org/abs/2606.20522 |
| Accession Number: | edsarx.2606.20522 |
| Database: | arXiv |
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