Spontaneous $S{U}_2(\mathbb{C})$ symmetry breaking in the ground states of quantum spin chain

Abstract

In this paper, we have proved that there exists no translation invariant pure state of $\mathbb{M}={\otimes }_{k\in \mathbb{Z}}{M}_d^{(k)}(\mathbb{C})$ that is real, lattice symmetric with a certain twist and $S{U}_2(\mathbb{C})$ invariant for any even integer $d\ge 2$. In particular, this result also says that the Heisenberg iso-spin anti-ferromagnetic model with $\frac{1}{2}$-odd integer spin degrees of freedom does not admit a unique ground state.

This version is a significant revision of the last version incorporating reports that I have received on its last version

References in corpus (2)

• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• Lieb-Robinson Bounds and the Exponential Clustering Theorem