Infinite Matrix Product States for long range SU(N) spin models

TL;DR

This paper constructs long-range SU(N) spin models as parent Hamiltonians from infinite matrix product states, linking them to fractional quantum Hall systems and analyzing their critical behavior through analytical and numerical methods.

Contribution

It introduces a novel class of long-range SU(N) spin models derived from infinite matrix product states, connecting them to fractional quantum Hall states and the SU(N) Haldane-Shastry model.

Findings

The uniform model is exactly solvable and equivalent to the SU(N) Haldane-Shastry model.

The uniform model is critical and described by a SU(N) level 1 WZW conformal field theory.

Numerical analysis of the alternating model indicates it is also critical, but requires numerical methods for characterization.

Abstract

We construct 1D and 2D long-range SU(N) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N) level 1 WZW model. Since the resulting groundstates are of Gutzwiller-Jastrow type, our models can be regarded as lattice discretizations of fractional quantum Hall systems. We then focus on two specific types of 1D spin chains with spins located on the unit circle, a uniform and an alternating arrangement. For an equidistant distribution of identical spins we establish an explicit connection to the SU(N) Haldane-Shastry model, thereby proving that the model is critical and described by a SU(N) level 1 WZW model. In contrast, while turning out to be critical as well, the alternating model can only be treated numerically. Our numerical results rely on a reformulation of the original problem in terms of loop models.