{"work":{"id":"e3cbdff6-1438-4f54-a794-fb01b39dae30","openalex_id":null,"doi":null,"arxiv_id":"1008.3477","raw_key":null,"title":"The density-matrix renormalization group in the age of matrix product states","authors":null,"authors_text":"U","year":2010,"venue":"cond-mat.str-el","abstract":"The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.","external_url":"https://arxiv.org/abs/1008.3477","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-06-29T03:53:04.523642+00:00","pith_arxiv_id":"1008.3477","created_at":"2026-05-08T18:28:57.434919+00:00","updated_at":"2026-06-29T03:53:04.523642+00:00","title_quality_ok":true,"display_title":"The density-matrix renormalization group in the age of matrix product states","render_title":"The density-matrix renormalization group in the age of matrix product states"},"hub":{"state":{"work_id":"e3cbdff6-1438-4f54-a794-fb01b39dae30","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":16,"external_cited_by_count":null,"distinct_field_count":4,"first_pith_cited_at":"2019-06-26T09:24:44+00:00","last_pith_cited_at":"2026-06-26T15:02:02+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-06-29T16:19:05.502574+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":6},{"context_role":"method","n":1}],"polarity_counts":[{"context_polarity":"background","n":6},{"context_polarity":"use_method","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}