Matrix product states as thin torus limits of conformal correlators

TL;DR

This paper constructs a family of spin chain wavefunctions from conformal field theory correlators on a torus, which interpolate between infinite and finite bond dimension matrix product states in different limits, connecting CFT and MPS descriptions.

Contribution

It introduces a parameterized family of wavefunctions from conformal correlators that smoothly transition between different MPS limits, linking CFT and spin chain ground states.

Findings

In the cylinder limit, wavefunctions reduce to infinite-dimensional MPS.

In the thin torus limit, wavefunctions become finite bond dimension MPS.

Reproduces known ground states like Majumdar-Ghosh and AKLT in the thin torus limit.

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.