非厄米矩阵高精度计算预先判定需要的计算精度(matlab)

绘制的OBC哈密顿量是文章DOI: 10.1103/PhysRevLett.125.226402的补充材料公式(7)

clear;clc;close all
N=200;
H=zeros(N,N);
for xx=1:N
    if xx+5 <=N
        H(xx+5,xx)=H(xx+5,xx)+5;

    end

    if xx+4 <=N
        H(xx+4,xx)=H(xx+4,xx)+4;

    end

    if xx+3 <=N
        H(xx+3,xx)=H(xx+3,xx)+3;

    end


    if xx+2 <=N
        H(xx+2,xx)=H(xx+2,xx)+2;

    end

    if xx+1 <=N
        H(xx+1,xx)=H(xx+1,xx)+1;

    end


    if xx+1 <=N
        H(xx,xx+1)=H(xx,xx+1)-1;

    end

end

%val=eig(vpa(H,20));%高精度
val=eig(H);
figure
scatter(real(val),imag(val),'k.')
box on

CondSto=condest(H);%矩阵条件数检查
DigitPre=ceil(log10(10*CondSto));%ceil为向上取整
title(['开边界矩阵预计计算精度为:   ',num2str(DigitPre)])

用的判定方法来自：Numerical instability of non-Hermitian Hamiltonian evolutions (arxiv，已出版在PRB)