A scaling hypothesis for matrix product states

Understand

We revisit the question of describing critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of field theories.

• Critical exponents and central charge are determined by optimizing the exponents such as to obtain a data collapse.
• We benchmark this method by studying critical Ising and Potts models, where we also obtain a scaling ansatz for the correlation length and entanglement entropy.
• The formulation of those scaling functions turns out to be crucial for studying critical quantum field theories on the lattice.