Dynamics of the entanglement spectrum in spin chains

G. Torlai, L. Tagliacozzo, G. De Chiara

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.

Original languageEnglish
Article numberP06001
Number of pages19
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2014
Issue number6
DOIs
Publication statusPublished - 9 Jun 2014

Keywords

  • density matrix renormalisation group calculations
  • entanglement in extended quantum systems (theory)
  • ladders and planes (theory)
  • quantum quenches
  • spin chains
  • entanglement spectrum

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