Boundary effect and quantum phases in spin chains

TL;DR

This paper introduces a boundary effect function to quantify boundary influences in spin chains, revealing phase-dependent behaviors and linking boundary changes to quantum phase transitions.

Contribution

It defines and analyzes a boundary effect function in the XXZ spin-1/2 model, connecting boundary behavior to quantum phases and phase transitions.

Findings

Different quantum phases show distinct boundary effect function forms

Quantum phase transition corresponds to a nonanalytic change in the boundary effect function

Boundary effects provide a new perspective on bulk-boundary relationships in ground states

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. Here, we analyze the quantity, which we call a boundary effect function, for an XXZ spin-1/2 model using density matrix renormalization group calculations. We find that three quantum phases of the model manifest as different functional forms of the boundary effect function. 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.