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arXiv · 2507.22735

Matrix product states as thin torus limits of conformal correlators

Adrián Franco-Rubio·J. Ignacio Cirac·Germán Sierra
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Abstract

We introduce one-parameter families of spin chain ansatz wavefunctions constructed from chiral conformal field theory correlators on a torus, with the modular parameter $\tau$ serving as the deformation parameter. In the cylinder limit $\tau\to\infty$, these wavefunctions reduce to infinite dimensional matrix product states. In contrast, in the thin torus limit $\tau\to0$, they become finite bond dimension matrix product states (MPS). Focusing on families derived from the SU(2)$_1$ and SU(2)$_2$ Wess-Zumino-Witten models, we show that in the thin torus limit they reproduce known MPS ground states, such as those of the Majumdar-Ghosh and AKLT spin chains.

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Adrián Franco-Rubio, J. Ignacio Cirac, Germán Sierra. 2025-07-30. Matrix product states as thin torus limits of conformal correlators. https://arxiv.org/abs/2507.22735

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