# Quasilocal charges in integrable lattice systems

@article{Ilievski2016QuasilocalCI, title={Quasilocal charges in integrable lattice systems}, author={Enej Ilievski and Marko Medenjak and Toma{\vz} Prosen and L Zadnik}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2016}, volume={2016} }

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…

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## References

SHOWING 1-10 OF 197 REFERENCES

### Conservation laws, integrability, and transport in one-dimensional quantum systems

- Physics
- 2011

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ…

### Quantum group approach to steady states of boundary-driven open quantum systems

- Physics
- 2014

We present a systematic approach for constructing steady state density operators of Markovian dissipative evolution for open quantum chain models with integrable bulk interaction and boundary…

### Identifying local and quasilocal conserved quantities in integrable systems.

- MathematicsPhysical review letters
- 2015

We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice systems. The method yields a systematic generation of all…

### Thermodyamic Bounds on Drude Weights in Terms of Almost-conserved Quantities

- Physics
- 2011

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature…

### Exactly conserved quasilocal operators for the XXZ spin chain

- Physics, Mathematics
- 2014

We extend T Prosen's construction of quasilocal conserved quantities for the XXZ model (2011 Phys. Rev. Lett. 106 217206) to the case of periodic boundary conditions. These quasilocal operators stem…

### Matrix product solutions of boundary driven quantum chains

- Physics
- 2015

We review recent progress on constructing non-equilibrium steady state density operators of boundary driven locally interacting quantum chains, where driving is implemented via Markovian dissipation…

### Exact solutions of open integrable quantum spin chains

- Physics
- 2014

In the thesis we present an analytic approach towards exact description for steady state density operators of nonequilibrium quantum dynamics in the framework of open systems. We employ the so-called…

### Quasi-local conserved charges and spin transport in spin-1 integrable chains

- Physics
- 2016

We consider the integrable one-dimensional spin-1 chain defined by the Zamolodchikov–Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-1/2 model, by a continuous…

### Quasilocal conservation laws in XXZ spin-1/2 chains: Open, periodic and twisted boundary conditions

- Mathematics, Physics
- 2014

### Thermalization and Pseudolocality in Extended Quantum Systems

- Physics
- 2015

Recently, it was understood that modified concepts of locality played an important role in the study of extended quantum systems out of equilibrium, in particular in so-called generalized Gibbs…