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Dynamical Phenomena in Quantum Many-Body Systems

Periodic Reporting for period 1 - QMBDyn (Dynamical Phenomena in Quantum Many-Body Systems)

Reporting period: 2017-04-01 to 2019-03-31

Interactions between particles lead to a plethora of interesting phenomena such as magnetism or superconductivity and are a central theme of condensed matter physics. They are crucial for the process of thermalization, i.e. how a system may reach the thermodynamic equilibrium over the course of time if prepared in a nonequilibrium state. This fundamental question is increasingly attracting attention due to experimental and theoretical progress in the last decade, leading to a more detailed understanding. For isolated quantum systems, thermalization is particularly interesting since the notion of thermal equilibrium has to be generalized to local quantities, since the dynamics of the wave function in isolated systems precludes reaching a complete thermal state as described e.g. by the microcanonical ensemble.

With this generalization, thermalization can be shown to exist in generic quantum systems, admiting an effective random matrix description. Surprisingly, it was recently found that there can be exceptions to thermalization in a class of generic strongly disordered interacting quantum systems due to the phenomenon of ``many-body localization'', a new dynamical nonequilibrium phase of matter.

QMBDyn was devoted to the development of a better understanding of strongly interacting quantum many-body systems out of equilibrium and their thermalization process using numerically exact large methods and high performance computing to obtain unbiased results. The main results are: i) a computational confirmation of the analytical prediction that thermal inclusions may thermalize many-body localized systems with a large enough localization length; ii) the demonstration that generic periodically driven quantum many-body systems exhibit diffusive transport; iii) the construction of a new class of discrete time pseudo-crystals as a generic out of equilibrium state of matter; iv) the demonstration of anomalous thermalization in periodically driven disordered quantum many-body systems below critical disorder; v) the publication of a high performance open source code for the massively parallel shift-invert diagonalization of very large sparse matrices, along with a new computational record for the MBL problem; vi) the discovery of emergent locality in quantum many-body systems with long range interactions.

Our work has multiple societal implications: Firstly, it is a contribution to fundamental science, paving the way to a deeper understanding of nonequilibrium quantum systems and how thermal equilibrium is reached. Secondly, our results provide important verifications of recently discovered new stroboscopic thermodynamic ensembles in periodically driven quantum systems. Thirdly, our computational work pushes significantly the state of the art for the calculation of exact central eigenpairs of large sparse matrices as they occur in the many body problem. This is an important incentive for the further optimization and use of powerful massively parallel open source codes such as MUMPS and STRUMPACK, which will benefit both science and industry.
This project resulted in seven scientific papers and a high performance open source code for the exact calculation of central eigenpairs of many-body lattice Hamiltonians published at https://bitbucket.org/dluitz/sinvertmbl/.


We could numerically confirm the theoretical prediction that there exists a critical localization length, above which even a small ergodic inclusion can thermalize a localized chain. Our results also revealed peculiar deformations of the distributions of matrix elements of local operators in the eigenbasis of the Hamiltonian, similar to observations in weakly disordered spin chains with anomalous thermalization.
Publication: D. J. Luitz, F. Huveneers and W. de Roeck Phys. Rev. Lett 119, 150602 (2017).

The nature of transport in Floquet systems is difficult to study due to limited accessible system sizes and fast dynamics. A very large scale calculation pushed the available system sizes well beyond the previous state of the art, increasing the size of the simulated Hilbert space by more than three orders of magnitude. With these results, we showed that transport in generic Floquet systems is diffusive. We also revealed a new class of time pseudocrystals, exhibiting periodic or quasiperiodic ordering in time.

Publications:

D. J. Luitz, A. Lazarides and Y. Bar Lev Phys. Rev. B 97, 020303(R) (2018)

and

D. J. Luitz, Y. Bar Lev and A. Lazarides SciPost Phys. 3, 029 (2017).

We previously showed that thermalization in systems close to an MBL transition occurs in an anomalous way, due to subdiffusive transport, generalizing the eigenstate thermalization hypothesis. This was extended to pre-MBL Floquet systems.

Publication:

S. Roy, Y. Bar Lev and D. J. Luitz arXiv:1802.03401

We pushed system sizes for which central eigenpairs can be obtained in the quantum many-body problem to unprecedented Hilbert space dimensions of 10 Million. Furthermore, we confirmed our previous results for the mobility edge in a disordered spin chain using a shift invert matrix product state method. Our work resulted in the publication of an open source code as a contribution for the community, which we hope will significantly enhance the available range of system sizes also in related problems. It is published at https://bitbucket.org/dluitz/sinvertmbl/.

Publications:

F. Pietracaprina, N. Macé, D. J. Luitz and F. Alet arXiv:1803.05395

and

B. Villalonga, X. Yu, D. J. Luitz and B. K. Clark Phys. Rev. B 97, 104406 (2018).

We studied the spreading of quantum information in quantum systems with long range interactions using an exact method for unprecedented system sizes and long times. This revealed that despite long range interactions, there is an emergent notion of locality, which was previously not captured by analytically known bounds on information spreading, opening the door for future work and the tightening of analytical bounds.

Publication:
D. J. Luitz and Y. Bar Lev arXiv:1805.06895
Our work is focussed on fundamental science and is an important contribution to scientific progress in the domain of generic many-body quantum systems. A deep understanding of the physics of such systems is crucial for future exploitation of quantum effects in technology and is part of the foundation of quantum technologies. Furthermore, our work in computational physics explores and extends the applicability of high performance computing methods of applied mathematics, such as massively parallel exact linear solvers. We hope that our efforts will help identifying bottlenecks in open source codes, such as MUMPS and STRUMPACK, enabling further progress in science and industry.

Scientifically, our numerical results extended the state of the art in terms of system sizes and accessible times in strongly entangled nonequilibrium systems significantly by multiple orders of magnitude in terms of the dimension of the Hilbert space, enabling us for the first time to identify the nature of stroboscopic spin transport in periodically driven system as well as of information transport in long range interacting models.
Spreading of a spin density excitation in a periodically driven interacting spin chain.