Open spin chains with dynamic lattice supersymmetry

TL;DR

This paper explores the lattice supersymmetry of open spin chains, constructs compatible boundary interactions, computes supercharge cohomology, and applies findings to quantum fidelity calculations.

Contribution

It introduces a family of boundary interactions compatible with lattice supersymmetry and analyzes their cohomology and ground states.

Findings

Cohomology of supercharges is explicitly computed.

Ground states are shown to be supersymmetry singlets at specific parameters.

Exact scalar products and bipartite fidelity are determined.

Abstract

The quantum spin $1/2$ XXZ chain with anisotropy parameter $\Delta=-1/2$ possesses a dynamic supersymmetry on the lattice. This supersymmetry and a generalisation to higher spin are investigated in the case of open spin chains. A family of non-diagonal boundary interactions that are compatible with the lattice supersymmetry and depend on several parameters is constructed. The cohomology of the corresponding supercharges is explicitly computed as a function of the parameters and the length of the chain. For certain specific values of the parameters, this cohomology is shown to be non-trivial. This implies that the spin-chain ground states are supersymmetry singlets. Special scalar products involving an arbitrary number of these supersymmetry singlets for chains of different lengths are exactly computed. As a physical application, the logarithmic bipartite fidelity of the open quantum spin $1/2$ XXZ chain with $\Delta=-1/2$ and special diagonal boundary interactions is determined.