Quasilocal charges in integrable lattice systems
By Enej Ilievski, M. Medenjak, Tomaz Prosen, Lenart Zadnik. 2016
266 citations recorded by the source corpus.
We review recent progress in understanding the notion of locality in integrable quantum lattice systems. The central concept concerns the so-called quasilocal conserved quantities, which go beyond the standard perception of locality. Two systematic procedures to rigorously construct families of quasilocal conserved operators based on quantum transfer matrices are outlined, specializing on anisotropic Heisenberg XXZ spin-1/2 chain. Quasilocal conserved operators stem from two distinct classes of representations of the auxiliary space algebra, comprised of unitary (compact) representations, which can be naturally linked to the fusion algebra and quasiparticle content of the model, and non-unitary (non-compact) representations giving rise to charges, manifestly orthogonal to the unitary ones. Various condensed matter applications in which quasilocal conservation laws play an essential role are presented, with special emphasis on their implications for anomalous transport properties (finite Drude weight) and relaxation to non-thermal steady states in the quantum quench scenario.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/000f1c5660b9a97a93a5bfbc661cd3c57604e145
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Emergent hydrodynamics in integrable quantum systems out of equilibrium (2016, background): “On the other hand, in integrable systems, the infinite number of conservation laws is known to lead to generalized thermalization [19–21] (there are many fundamental works on the subject; see the review [22]), and the presence of quasilocal charges has been shown to influence transport [23,24] (see ”
- Drude Weight for the Lieb-Liniger Bose Gas (2017, background): “Remark : For integrable lattice models, the conserved charges are written as sums over translates of local and quasi-local densities [46].”
- Lecture notes on Generalised Hydrodynamics (2019, background): “Here, densities are either local – supported on finite regions – or quasi-local – supported on infinite regions but with an “envelope" that decays sufficiently fast (see the review [118]).”
- Entanglement dynamics after quantum quenches in generic integrable systems (2017, background): “Remarkably, a statistical description of local properties of the steady state is possible in terms of a Generalised Gibbs Ensemble (GGE) [12, 16, 17, 39–66], which is obtained by complementing the Gibbs ensemble with all the local and quasilocal conserved quantities [56,67].”
- Conformal field theory out of equilibrium: a review (2016, background): “In these studies, an important concept is that of generalized Gibbs ensembles [10] (with a refinement based on pseudolocal charges [8, 11, 14, 15]): integrable models do not, generically, thermalize, but rather a generalized thermalization phenomenon occurs.”
- Statistical localization: From strong fragmentation to strong edge modes (2019, background): “[73] Enej Ilievski, Marko Medenjak, Tomaž Prosen, and”
- Generalized Gibbs ensemble in integrable lattice models (2016, background): “Recent studies have shed light on new families of conserved quantities in this model [10, 69, 83, 84] (see also the review by Ilievski, Medenjak, Prosen and Zadnik in this volume [85]).”
- A note on generalized hydrodynamics: inhomogeneous fields and other concepts (2016, background): “In integrable systems, this set is infinite, and the charges Qi relevant to the problem span the space of pseudolocal conserved charges [34].”