A density-matrix renormalization group algorithm for non-hermitian physics

A density-matrix renormalization group (DMRG) algorithm is proposed to deal with non- hermitian many-body systems with a biorthonormal-block representation (bbDMRG), in which a structured low-rank approximation to a non-hermitian reduced density matrix is necessarily made to satisfy the prerequisite on the biorthonormality of the renormalization transformation. Sub- sequently, a redundancy assigned to those saved blocks of reduced density matrix is exploited to reduce a condition number for both left and right transform matrices, which practically ensure the numerical stability of the renormalization procedure. The bbDMRG is successfully applied to an interacting fermionic Su–Schrieffer–Heeger model with imposing non-hermitian to the kinetic energy and various boundary conditions, for which a ground-state phase diagram is obtained to show fascinating phenomenon caused by the interaction and the non-hermitian as well.