Nonequilibrium physics in integrable systems and spin-flip non-invariant conserved quantities
arXiv:2002.01069 · doi:10.1088/1751-8121/ab72ae
Abstract
Recently found spin-flip non-invariant (SFNI) conserved quantities play important roles in discussing nonequilibrium physics of the XXZ model. The representative examples are the generalized Gibbs ensemble (GGE) and the ballistic transport of the spin current. In spite of big progress in understanding nonequilibrium physics of integrable systems, the general framework to determine a minimal complete set of conserved quantities which describes the long-time steady state has not yet been found. This paper shows that the GGE of the gapless XXZ model consists of functionally independent conserved quantities rather than linearly independent. At the same time, the physical meaning of SFNI conserved quantities is provided. We also discuss that there exist ballistic channels of the spin current supported by non-quasilocal conserved quantities. The saturation of the lower bound for the Drude weight by quasilocal conserved quantities reads the linear dependence of non-quasilocal conserved quantities on quasilocal ones. We show that their (generalized) linearly dependence relation is consistent with the statement that the GGE consists of functionally independent conserved quantities without containing all linearly independent conserved quantities.
arXiv comment19 pages, 1 figure
References in corpus (25)
- Thermalization and its mechanism for generic isolated quantum systems
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Time evolution of local observables after quenching to an integrable model
- Transport and conservation laws
- Complete Generalized Gibbs Ensemble in an interacting Theory
- Exact relaxation in a class of non-equilibrium quantum lattice systems
- Dephasing and the steady state in quantum many-particle systems
- Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
- Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
- Reduced Density Matrix after a Quantum Quench
- Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
- Diffusion and ballistic transport in one-dimensional quantum systems
- Families of quasi-local conservation laws and quantum spin transport
- Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
- A Shortcut to the Q-Operator
- Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
- Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
- On the finite temperature Drude weight of the anisotropic Heisenberg chain
- Exactly conserved quasilocal operators for the XXZ spin chain
- Continued fraction TBA and functional relations in XXZ model at root of unity
- Breakdown of the generalized Gibbs ensemble for current-generating quenches
- Exterior integrability: Yang-Baxter form of nonequilibrium steady state density operator
- Generalized microcanonical and Gibbs ensembles in classical and quantum integrable dynamics
- Equilibration and GGE for hard wall boundary conditions
- Singularity confinement and chaos in two-dimensional discrete systems