Boundary-driven steady states of the Hubbard model
Theoretical Condensed Matter Physics
Final Report Abstract
To achieve full control of quantum systems underlies the active field of research of building quantum devices used for quantum technology and quantum information. Over a long time a coupling of a quantum system to an environment has been seen as a nuisance which destroys the coherence of the system and thereby the quantumness. Only in recent years, the environment has been seen as an asset which can be tailored in order to stabilize and manipulate quantum states. Our project considers quantum many body systems which are coupled at their boundary to environments. We investigate how a tailored coupling can stabilize interesting quantum states, transport properties and even topological properties. The realization and control of topologically non-trivial quantum phases is currently of great interest after discovery of the topological insulators. An exciting (and surprising) finding is the existence of “spin-helix” states in spin chains dissipatively projected boundary spins and where the anisotropy of the bulk spin-spin interaction takes specific values which are from a discrete set. These states are pure states in which the spin vector winds along the chain with a winding number that can be regarded as a topological characteristic of the state. They support a spin current that is ballistic for winding numbers of the order of the length of the chain, irrespective of their integrability. As the anisotropic interaction is varied, the current peaks at these special values to a strength that has been computed exactly, while the entanglement entropy dips to zero. In a similar setting, in the Zeno limit of strong dissipation, helical states of rank two were identified in the boundary-driven anisotropic Heisenberg chain which are superpositions of states with opposite winding numbers. It was shown that the transition between topological states with different winding numbers passes through mixed states and that the topological states themselves are not protected by a gap in the relaxation spectrum of the evolution operator, which is in contrast to the more familiar previously studied topological states. Moreover, we could show that in the Zeno limit the time evolution of the reduced density matrix of a general quantum chain involves a renormalized effective Hamiltonian with weak effective dissipation. Remarkably, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. A deep link of general quantum dynamics to classical large-scale hydrodynamics was uncovered by proving rigorously that charge-current correlation identities are valid under conditions more general than thought previously (viz. also in the absence of translation invariance) and give rise to a fundamental current symmetry also in dissipative quantum systems and classical Markovian dynamics in any space dimension.
Publications
- (2019) Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state. SciPost Phys. (SciPost Physics) 6 (6) 074
Medenjak, Marko; Popkov, Vladislav; Prosen, Tomaz; Ragoucy, Eric; Vanicat, Matthieu
(See online at https://doi.org/10.21468/SciPostPhys.6.6.074) - Transition between dissipatively stabilized helical states
Simon Essink, Stefan Wolff, Gunter M. Schütz, Corinna Kollath, Vladislav Popkov
(See online at https://doi.org/10.1103/PhysRevResearch.2.022007) - Matrix Product Ansatz for Nonequilibrium Quantum Steady States, In: Gonçalves P., Soares A. (eds) From Particle Systems to Partial Differential Equations, Springer Proceedings in Mathematics & Statistics, 209, pp 221– 245 (Springer, Cham, 2017)
Dragi Karevski, Vladislav Popkov, Gunter M. Schütz
(See online at https://doi.org/10.1007/978-3-319-66839-0_11) - Solution of the Lindblad equation for spin helix states, Phys. Rev. E 95, 042128 (2017)
Vladislav Popkov, Gunter M. Schütz
(See online at https://doi.org/10.1103/PhysRevE.95.042128) - Spin-helix states in the XXZ spin chain with strong dissipation, J. Phys. A: Math. Theor. 50 435302 (2017)
Vladislav Popkov, Johannes Schmidt, Carlo Presilla
(See online at https://doi.org/10.1088/1751-8121/aa86cb) - Effective quantum Zeno dynamics in dissipative quantum systems, Phys. Rev. A 98, 052110 (2018)
Vladislav Popkov, Simon Essink, Carlo Presilla, Gunter M. Schütz
(See online at https://doi.org/10.1103/PhysRevA.98.052110) - Charge-current correlation equalities for quantum systems far from equilibrium, SciPost Phys. 6, 068 (2019)
Dragi Karevski and Gunter M. Schütz
(See online at https://doi.org/10.21468/SciPostPhys.6.6.068) - Exact results for the entanglement in 1D Hubbard models with spatial constraints, J. Stat. Mech. 063102 (2019)
Ioannis Kleftogiannis, Ilias Amanatidis, Vladislav Popkov
(See online at https://doi.org/10.1088/1742-5468/ab1dd5) - Exact results for the isotropic spin-1/2 Heisenberg chain with dissipative boundary driving, Theoret. and Math. Phys. 198, 296–315 (2019)
Dragi Karevski, Vladislav Popkov, Gunter M. Schütz
(See online at https://doi.org/10.1134/S0040577919020107)
