Supersymmetric Valence Bond Solid States

TL;DR

This paper explores supersymmetric valence bond solid states, revealing their interpolation between different spin states, exact correlation functions, and their analogy to quantum Hall states, with potential applications in understanding superconducting liquids.

Contribution

It introduces the supersymmetric valence bond solid (SVBS) states, providing exact correlation functions, Hamiltonians, and connections to quantum Hall states, extending valence bond theories into supersymmetric frameworks.

Findings

SVBS states interpolate between integer and half-integer spin chains.

Correlation functions and lengths are exactly computable and equal at the supersymmetric point.

SVBS states are analogous to bosonic Pfaffian states in quantum Hall systems.

Abstract

In this work we investigate the supersymmetric version of the valence bond solid (SVBS) state. In one dimension, the SVBS states continuously interpolate between the valence bond states for integer and half-integer spin chains, and they generally describe superconducting valence bond liquid states. Spin and superconducting correlation functions can be computed exactly for these states, and their correlation lengths are equal at the supersymmetric point. In higher dimensions, the wave function for the SVBS states can describe resonating valence bond states (RVB). The SVBS states for the spin models are shown to be precisely analogous to the bosonic Pfaffian states of the quantum Hall effect. We also give microscopic Hamiltonians for which the SVBS state is the exact ground state.