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Identifying local and quasilocal conserved quantities in integrable systems
Marcin Mierzejewski1, Peter Prelovšek2,3, Tomaž Prosen2
1Institute of Physics, University of Silesia, 40-007 Katowice, Poland.
Physical Review Letters
|April 25, 2015
Summary
Researchers developed a new method to find conserved operators in integrable lattice systems. This technique systematically generates quasilocal conserved quantities, revealing new ones in Heisenberg models and impacting the study of quenched systems.
Area of Science:
- Condensed Matter Physics
- Quantum Integrable Systems
- Statistical Mechanics
Background:
- Integrable lattice systems possess numerous conserved quantities crucial for understanding their dynamics.
- Identifying these conserved operators, especially quasilocal ones, is essential but challenging.
Purpose of the Study:
- To introduce a systematic procedure for counting and identifying all local and quasilocal conserved operators in integrable lattice systems.
- To explore the properties and abundance of these operators, particularly in Heisenberg models.
Main Methods:
- Developed a method to generate independent, conserved quasilocal operators based on the time average of local operators.
- Analyzed operators with support on up to M consecutive sites.
- Applied the procedure to the anisotropic and isotropic Heisenberg spin-1/2 chains.
Main Results:
- The method systematically generates all independent conserved quasilocal operators.
- For the anisotropic Heisenberg chain, the number of operators scales linearly with M.
- Discovered novel quasilocal conserved quantities across all parity sectors for both anisotropic and isotropic models.
Conclusions:
- The developed procedure provides a complete set of conserved operators for integrable lattice systems.
- The existence of abundant quasilocal conserved operators has implications for understanding anomalous relaxation in quenched systems.
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