Symmetry-protected local minima in infinite DMRG

Robert N C Pfeifer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The infinite density matrix renormalization group (iDMRG) algorithm is a highly successful numerical algorithm for the study of low-dimensional quantum systems, and is also frequently used to initialize the more popular finite DMRG algorithm. Implementations of both finite and infinite DMRG frequently incorporate support for the protection and exploitation of symmetries of the Hamiltonian. In common with other variational tensor network algorithms, convergence of iDMRG to the ground state is not guaranteed, with the risk that the algorithm may become stuck in a local minimum. In this paper, I demonstrate the existence of a particularly harmful class of physically irrelevant local minima affecting both iDMRG and to a lesser extent also infinite time-evolving block decimation (iTEBD), for which the ground state is compatible with the protected symmetries of the Hamiltonian but cannot be reached using the conventional iDMRG or iTEBD algorithms. I describe a modified iDMRG algorithm which evades these local minima, and which also admits a natural interpretation on topologically ordered systems with a boundary.

Original languageEnglish
Article number205127
Pages (from-to)1-13
Number of pages13
JournalPhysical Review B: Condensed Matter and Materials Physics
Issue number20
Publication statusPublished - 23 Nov 2015


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