Geometric dissipation in non-Abelian quantum spin systems and beyond

• Applicant: Professor Dr. Alexander Shnirman
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 276873045

The presence of geometric phases (a.k.a. Berry phases (BPs)) affects the dynamics of a broad spectrum of systems, including nano-magnets, quantum dots close to the Stoner instability, various realizations of q-bits (elementary building blocks of quantum computing schemes), coherent superpositions of Majorana excitations and more. In certain cases BPs assume the form of topological phases, such as the statistical phase associated with the braiding of anyons (quasi-particles that possess fractional statistics, intermediate between bososns and fermions). Understanding the role of noise and a decohering environment is a crucial prerequisite for designing and controlling such systems. We have very recently understood that BPs can enter not only the deterministic dynamics of the system at hand, but also determine the nature of dissipation and stochastic noise terms, when it comes to open system dynamics.The underlying idea behind the present project is that in a broad variety of systems dissipative dynamics has geometric attributes, and the Langevin noise appearing in the equation-of-motion may be critically influenced by the Berry phase associated with the motion of the degree-of-freedom at hand. We predict that such geometric noise will give rise to new physics. Our proposal will venture beyond studying dissipation of quantum spin systems to include also systems supporting topological excitations (Majoranas and anyons). Along with reviewing the proposed directions, we briefly assess here the level of risk associated with the various tasks. Successful completion of the project (or significant parts thereof) will imply that (i) with a high probability our results will stimulate experimental effort to observe geometrical noise in a variety of setups; (ii) common wisdom concerning transport and a.c. response in the field of spintronics will need to be revised, particularly in parameter regimes marked by low temperature and high frequency; (iii) new physics concerning noise and fluctuations in certain systems supporting topological excitations will be predicted.The two principal investigators have each an established record of achievements in the general field of nanoelectronics. Important for the present project is their experience and major contributions to a range of topics that includes quantum dynamics, Berry phases in solid state systems, quantum dissipation, Abelian and non-Abelian interferometry, and decoherence. The techniques they have employed, and in some cases developed (e.g., stochastic dynamics, non-equilibrium (perturbative and sigma-model) Keldysh, non-equilibrium bosonization etc.) are ideally suitable to tackle the present challenges. They also have a proven record of close collaboration in recent years. This strong collaboration, including mutual visits by the PIs and younger members of their groups, will continue in earnest within the present project.

• DFG Programme: Research Grants
• International Connection: Israel
• International Co-Applicant: Professor Dr. Yuval Gefen