String-charge duality in integrable lattice models

2015/12/31 by Enej Ilievski, Eoin Quinn, Jacopo De Nardis +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Duality (order theory) #Entropy (arrow of time) #Integrable system #Lattice (music) #Physics of Superconductivity and Magnetism #Product (mathematics) #Quantum #Quantum many-body systems #Simple (philosophy) #cond-mat.stat-mech #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/1742-5468/2016/06/063101

published as J. Stat. Mech. (2016) 063101 · 18 pages + appendices, revised version as accepted by JSTAT

openalex publication_date 2016/06/02 · arxiv created 2016/06/03 · arxiv updated 2016/06/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We present an identification of the spectra of local conserved operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is derived explicitly for the Heisenberg XXZ spin chain. As an application we discuss a quantum quench scenario, in both the gapped and critical regimes. We outline an exact technique which allows for an efficient implementation on periodic matrix product states. In addition, for certain simple product states we obtain closed-form expressions for the density distributions in terms of solutions to Hirota difference equations. Remarkably, no reference to a maximal entropy principle is invoked.

Citations

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• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Quenches from bosonic Gaussian initial states to the Tonks-Girardeau limit: Stationary states and effects of a confining potential