Projects / Programmes
Integrability and ergodic theory of non-equilibrium quantum many-body systems
| Code |
Science |
Field |
Subfield |
| 1.02.02 |
Natural sciences and mathematics |
Physics |
Theoretical physics |
| Code |
Science |
Field |
| P190 |
Natural sciences and mathematics |
Mathematical and general theoretical physics, classical mechanics, quantum mechanics, relativity, gravitation, statistical physics, thermodynamics |
| Code |
Science |
Field |
| 1.03 |
Natural Sciences |
Physical sciences |
Nonequilibrium steady states, open quantum systems, quantum transport, exact solutions, integrability, quantum diffusion, spin chains, quantum matter, quantum phase transitions
Researchers (6)
Organisations (2)
Abstract
We shall study non-equilibrium many-body quantum systems, considering systems with local interactions in one or perhaps two dimensions, and situations where the generator of time evolution in the bulk of the system is unitary whereas the incoherent processes are limited to the system's boundaries. Such systems are important for the study of quantum phases of matter and quantum phase transitions, as well as non-equilibrium stationary phenomena, such as quantum transport, thermoelectricity and similar in the solid state theory, and at the same time represent a fundamental paradigm of mathematical statistical physics. Focus of the research project shall be, on one hand, finding exactly solvable (integrable) non-equilibrium quantum many-body models, and on the other hand, to investigate the effect of such exact solutions on the physics of generic models, which can be understood as small perturbations of integrable models.
1) In 2011 we found exact solution for the density operator of open anisotropic Heisenberg XXZ spin 1/2 chain which is incoherently coupled with the environment through the boundary spins only. We plan to generalize our method to wider classes of open non-equilibrium quantum chains, e.g. 1d open Hubbard model, open spin-1 chains, or open Lieb-Liniger quantum field theory in 1+1 dim., and perhaps spin models on 2d lattices. These solutions represent exotic quantum phases with anomalous transport and correlation properties.
2) Within the frame of boundary-driven coherent quantum chains we shall try to find exactly solvable model of quantum diffusion. We propose to focus on boundary driven XXZ chain in the Ising limit of large anisotropy where first indications hint at exact solvability of the model. If such a program worked this would be the first exactly solvable coherent model of many-body quantum diffusion.
3) For physics applications it is important to study fluctuations, e.g. of the current in the open system exchanging particles/energy/magnetization with the environment. The question is if exact solutions of nonequilibrium states can be characterized by universal current fluctuations? We propose to study fluctuations with the method of full counting statistics and possibility of extending our exact solutions to nonzero values of the counting field. We propose also to study the validity of fluctuation theorem in exact solutions of exotic quantum phases.
4) As a byproduct of exact solutions of boundary-driven nonequilibrium steady states one may obtain quasilocal almost-conserved quantity. This enables us to strictly estimate the lower bound on Drude weight proving ballistic transport. Lower bound is nonzero when such operator is quasilocal, i.e. given as exponentially converging sum of local operators. This program has been successfully implemented in XXZ chain, and we plan its extension to other exactly solvable nonequilibrium cases. Similarly we plan to estimate more general cross transport (e.g. thermoelectric) properties of integrable models.
5) Quasilocal almost-conserved quantities obtained from solving local boundary-driven master equations for translationally invariant and fully coherent interactions are typically independent from Bethe-ansatz inspired strictly local conserved quantities. Due to quasi-local nature of these new quantities we conjecture that they might be more structurally stable to perturbations as previously known local conservation laws. We plan to systematically approach the question of stability of quasilocal almost-conserved quantities to generic perturbations with the methods of C* algebraic dynamical systems. This would be the first step towards extending the famous KAM theory from nonlinear classical dynamics to quantum many-body systems.
6) In relation to 5) we plan to explore the questions of thermalization and the transition from nonergodic to ergodic dynamics with increasing the integrability breaking parameter.
Significance for science
The results of the research group contribute towards basic knowledge and understanding of elementary processes in non-equilibrium statistical quantum physics, in particular in connection to many-body physics of strong interactions.
Significance for the country
The results are particularly important for small Slovenia since they help putting it on the world map of science excellence. Our scientists are consequently invited to most prestigious scientific meetings, editorial and decision boards, etc. Important is also the role of the project in training new scientists in terms of directing PhD and master theses.
Most important scientific results
Annual report
2013,
2014,
2015,
final report
Most important socioeconomically and culturally relevant results
Annual report
2013,
2014,
2015,
final report
