A new family of matrix product states with Dzyaloshinski-Moriya interactions

TL;DR

This paper introduces a new family of matrix product states that serve as exact ground states for specific 1D spin-1/2 Hamiltonians with Heisenberg and Dzyaloshinskii-Moriya interactions, providing explicit forms and correlation functions.

Contribution

It defines a novel class of matrix product states and corresponding Hamiltonians with exact solutions, including explicit ground state and correlation functions.

Findings

Exact ground states for Hamiltonians with Dzyaloshinskii-Moriya interactions

Closed-form expressions for one and two-point functions

Analysis of ground state degeneracy

Abstract

We define a new family of matrix product states which are exact ground states of spin 1/2 Hamiltonians on one dimensional lattices. This class of Hamiltonians contain both Heisenberg and Dzyaloshinskii-Moriya interactions but at specified and not arbitrary couplings. We also compute in closed forms the one and two-point functions and the explicit form of the ground state. The degeneracy structure of the ground state is also discussed.