### Canonical form for very small singular values

Posted:

**06 Nov 2019, 13:12**The present algorithm to calculate the canonical form for infinite systems calculates the left and right dominant eigenvectors and takes the square root of each, which comes with a loss in precision.

It turns out that close to criticality and at large bond dimensions singular values eventually will become smaller than 1.e-8 which is about the domain where above mentioned precision loss becomes a problem and limits the effective bond dimension of the state.

Is there a method to circumvent this problem? Do you know an algorithm which is able to compute the canonical form with higher precision? I would be happy to implement it myself.

It turns out that close to criticality and at large bond dimensions singular values eventually will become smaller than 1.e-8 which is about the domain where above mentioned precision loss becomes a problem and limits the effective bond dimension of the state.

Is there a method to circumvent this problem? Do you know an algorithm which is able to compute the canonical form with higher precision? I would be happy to implement it myself.