Boundary effect and quantum phases in spin chains

Abstract

Boundary effect is a widespread idea in many-body theories. However, it is more of a conceptual notion than a rigorously defined physical quantity. One can quantify the boundary effect by comparing two ground states of the same physical model, which differ only slightly in system size. This quantity, which we call a boundary effect function, restricts the correlation and entanglement that the ground state can accommodate. Here, we analyze the boundary effect function for an XXZ spin-12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}$$\end{document} model using density matrix renormalization group calculations. We find that the three quantum phases of the model manifest as different functional forms of the boundary effect function depending on the correlation length of the bulk. As a result, the quantum phase transition of the model is associated with a nonanalytic change of the boundary effect function. This work thus provides and concretizes a novel perspective on the relationship between bulk and boundary properties of ground states.