Below are my code and .mat data. The green circles represent the correct eigenvalue range for the non-Hermitian matrix (derived using a complex mathematical method; since the method is too complicated, I’m directly using the results obtained from it). The black points represent the eigenvalues computed using the vpa function, but they do not coincide with the green circles. (Indeed, the number of green circles and black points is different, but if the black points were correct, their upper and lower bounds should overlap.) This means that I didn’t obtain the correct eigenvalues. I know that non-Hermitian matrices cannot be exactly diagonalized, but I’ve heard from others that using the high-precision vpa function can help, but it doesn’t seem to work in my case.
load list_beta0.mat
load GBZband.mat

N=90;
t1=0.5;
t2=0.5;

t3=1/5;
gamma1=5/3;
gamma2=1/3;

HH=Hobc(t1,t2,t3,gamma1,gamma2,N);
[~,val]=eig(vpa(HH,34));
tval=diag(val);
[~,index]=sort(real(tval));

sort_valR=tval(index);

figure
hold on
scatter(t1.*ones(size(GBZband)), abs(GBZband),10,’go’)
plot(t1.*ones(size(sort_valR)),abs(sort_valR),’k.’,’MarkerSize’,8)
ggg=legend(‘GBZ-eigenval’,’OBC-eigenval’);
set(ggg,’box’,’off’)
hold off

function [op]=Hobc(t1,t2,t3,gamma1,gamma2,N)
a=[1;0];
b=[0;1];
H=zeros(2*N,2*N);
n1=zeros(N,1);
n2=zeros(N,1);

for n=1:N
n1(n)=1;
n2(n+1)=1;

H=H+(t1+gamma1/2).*kron(n1,a)*kron(n1′,b’)+(t1-gamma1/2).*kron(n1,b)*kron(n1′,a’);

if n~=N
H=H+(t2+gamma2/2).*kron(n1,b)*kron(n2′,a’)+(t2-gamma2/2).*kron(n2,a)*kron(n1′,b’)+…
t3.*(kron(n1,a)*kron(n2′,b’)+kron(n2,b)*kron(n1′,a’));
end

n1=zeros(N,1);
n2=zeros(N,1);

end

op=H;
end

Does anyone have any insights on this issue? I look forward to any responses. If the question is unclear, please let me know.Below are my code and .mat data. The green circles represent the correct eigenvalue range for the non-Hermitian matrix (derived using a complex mathematical method; since the method is too complicated, I’m directly using the results obtained from it). The black points represent the eigenvalues computed using the vpa function, but they do not coincide with the green circles. (Indeed, the number of green circles and black points is different, but if the black points were correct, their upper and lower bounds should overlap.) This means that I didn’t obtain the correct eigenvalues. I know that non-Hermitian matrices cannot be exactly diagonalized, but I’ve heard from others that using the high-precision vpa function can help, but it doesn’t seem to work in my case.
load list_beta0.mat
load GBZband.mat

N=90;
t1=0.5;
t2=0.5;

t3=1/5;
gamma1=5/3;
gamma2=1/3;

HH=Hobc(t1,t2,t3,gamma1,gamma2,N);
[~,val]=eig(vpa(HH,34));
tval=diag(val);
[~,index]=sort(real(tval));

sort_valR=tval(index);

figure
hold on
scatter(t1.*ones(size(GBZband)), abs(GBZband),10,’go’)
plot(t1.*ones(size(sort_valR)),abs(sort_valR),’k.’,’MarkerSize’,8)
ggg=legend(‘GBZ-eigenval’,’OBC-eigenval’);
set(ggg,’box’,’off’)
hold off

function [op]=Hobc(t1,t2,t3,gamma1,gamma2,N)
a=[1;0];
b=[0;1];
H=zeros(2*N,2*N);
n1=zeros(N,1);
n2=zeros(N,1);

for n=1:N
n1(n)=1;
n2(n+1)=1;

H=H+(t1+gamma1/2).*kron(n1,a)*kron(n1′,b’)+(t1-gamma1/2).*kron(n1,b)*kron(n1′,a’);

if n~=N
H=H+(t2+gamma2/2).*kron(n1,b)*kron(n2′,a’)+(t2-gamma2/2).*kron(n2,a)*kron(n1′,b’)+…
t3.*(kron(n1,a)*kron(n2′,b’)+kron(n2,b)*kron(n1′,a’));
end

n1=zeros(N,1);
n2=zeros(N,1);

end

op=H;
end

Does anyone have any insights on this issue? I look forward to any responses. If the question is unclear, please let me know. Below are my code and .mat data. The green circles represent the correct eigenvalue range for the non-Hermitian matrix (derived using a complex mathematical method; since the method is too complicated, I’m directly using the results obtained from it). The black points represent the eigenvalues computed using the vpa function, but they do not coincide with the green circles. (Indeed, the number of green circles and black points is different, but if the black points were correct, their upper and lower bounds should overlap.) This means that I didn’t obtain the correct eigenvalues. I know that non-Hermitian matrices cannot be exactly diagonalized, but I’ve heard from others that using the high-precision vpa function can help, but it doesn’t seem to work in my case.
load list_beta0.mat
load GBZband.mat

N=90;
t1=0.5;
t2=0.5;

t3=1/5;
gamma1=5/3;
gamma2=1/3;

HH=Hobc(t1,t2,t3,gamma1,gamma2,N);
[~,val]=eig(vpa(HH,34));
tval=diag(val);
[~,index]=sort(real(tval));

sort_valR=tval(index);

figure
hold on
scatter(t1.*ones(size(GBZband)), abs(GBZband),10,’go’)
plot(t1.*ones(size(sort_valR)),abs(sort_valR),’k.’,’MarkerSize’,8)
ggg=legend(‘GBZ-eigenval’,’OBC-eigenval’);
set(ggg,’box’,’off’)
hold off

function [op]=Hobc(t1,t2,t3,gamma1,gamma2,N)
a=[1;0];
b=[0;1];
H=zeros(2*N,2*N);
n1=zeros(N,1);
n2=zeros(N,1);

for n=1:N
n1(n)=1;
n2(n+1)=1;

H=H+(t1+gamma1/2).*kron(n1,a)*kron(n1′,b’)+(t1-gamma1/2).*kron(n1,b)*kron(n1′,a’);

if n~=N
H=H+(t2+gamma2/2).*kron(n1,b)*kron(n2′,a’)+(t2-gamma2/2).*kron(n2,a)*kron(n1′,b’)+…
t3.*(kron(n1,a)*kron(n2′,b’)+kron(n2,b)*kron(n1′,a’));
end

n1=zeros(N,1);
n2=zeros(N,1);

end

op=H;
end

Does anyone have any insights on this issue? I look forward to any responses. If the question is unclear, please let me know. non-hermitian matrix, high-precision computation, eigenvalues MATLAB Answers — New Questions

​