Collective quantum dynamics: Teamwork of quantum particles

Matter appears in phases with distinct properties. Some materials become magnetic when they are cooled to low enough temperatures; others conduct power without dissipation – they turn into superconductors. Both of these phases are examples of collective quantum phenomena, arising due to the interactions between the electrons in a solid.

Focus Group Collective Quantum Dynamics

Prof. Michael Knap (TUM), Alumnus Rudolf Mößbauer Tenure Track Professor | Dr. Alvise Bastianello (TUM), Postdoctoral Researcher | Annabelle Bohrdt, Johannes Feldmeier, Wilhelm Kadow, Clemens Kuhlenkamp, Alexander Schuckert, Elisabeth Wybo, Philip ­Zechmann, (TUM), Doctoral Candidates | Host: Collective Quantum Dynamics, TUM

In condensed matter physics we have the luxury that we are able to write down the microscopic theory of any matter. The Hamiltonian describes the kinetic energy of electrons and ions and their mutual interactions. However, this microscopic theory is fundamentally insoluble because we are interested in its behavior for many quantum degrees of freedom. Instead of solving it, we should rather ask the question, “What are the emergent and universal properties of condensed matter?”

Over the recent years it became possible to create and explore non-equilibrium states of matter using novel quantum technology. These new experimental capabilities range from pump-probe spectroscopy in the solid state to quantum computers and quantum simulators. Big open questions are: What are the universal properties of quantum matter out of equilibrium? How do they manifest in experiments? How can we classify dynamical quantum phases?

Figure 1

Our Focus Group is working on collective quantum dynamics, which is a subfield of condensed matter theory. We are mainly interested in understanding the universal properties of non-equilibrium quantum states of matter (Figure 1). In order to elucidate the effects of strong interactions and emergent collective behavior, we develop both classical analytical and numerical methods, exploit artificial intelligence and machine learning, and develop algorithms for quantum computers. An important factor of our research is also its immediate relevance for experiments, which leads to a close collaboration with experimental groups all over the world.

Universality out of equilibrium: Emergent hydrodynamics

Understanding the fundamental mechanism of how non-equilibrium states relax toward thermal equilibrium has fascinated scientists for centuries. Ludwig Boltzmann derived his famous transport equation based on the statistical behavior of non-equilibrium states. Later, the term arrow of time was coined to describe the asymmetry of the flow of events that is rooted in the second law of thermodynamics. How macroscopic dynamics emerges from the microscopic, reversible physics is a long-standing question. A common anticipation is that effective classical hydrodynamics of a few conserved quantities emerges also at late times for complex, isolated quantum systems, as strong interactions effectively scramble quantum degrees of freedom. Over the past years, we have developed novel techniques to study the emergence of conventional diffusion in strongly interacting lattice bosons [1] and the emergence of fracton hydrodynamics in magnets with charge and dipole conservation [2]. (See Figure 2.)

Figure 2

Absence of equilibration: Disordered many-­body systems

Disorder has a drastic effect on transport properties. In the presence of a random potential, a system of interacting electrons can become insulating; this phenomenon is known as many-body localization. However, even beyond the vanishing transport such systems have very intriguing properties. For example, many-body localization describes an exotic phase of matter that is robust to small changes in the microscopic Hamiltonian. Moreover, fundamental concepts of statistical mechanics break down in the many-body localized phase. In a collaboration with Immanuel Bloch’s group, we analyzed properties of the many-body localization transition with a quantum simulator of cold atoms [3]. With the Google quantum computing team, we have characterized the local integrals of motion of many-body localized superconducting qubits [4]. Due to the ability to create quantum superpositions of the qubits, a detailed investigation of the fundamental constituents was possible.

Figure 3

New probes of correlated quantum states

Quantum simulators offer the opportunity to develop novel probes to study the effects of correlations in interacting many-body systems. We have pioneered the study of quantum snapshots using machine learning techniques, which has developed into an active field of research [5]. Recent developments made it possible to realize the doped Fermi-Hubbard model, which is believed to describe the essential physics of high-temperature superconductors. We have made significant steps toward gaining a deeper understanding of this model using high-end numerical techniques, semi-analytical theory, and collaborations involving cold atom experiments [6]. Our work has helped to establish a parton theory of charge carriers in the 2D Hubbard model which captures essential features in a large regime of its phase diagram. The methods we developed enable a detailed comparison of different candidate theories with experimental and numerical results.

Figure 4

A. Bohrdt, C. B. Mendl, M. Endres and M. Knap, “Scrambling and thermalization in a diffusive quantum many-body system”, New Journal of Physics, vol. 19, 063001, 2017.

J. Feldmeier, P. Sala, G. de Tomasi, F. Pollmann and M. Knap, “Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems”, Physical Review Letters, vol. 125, 245303, 2020.

P. Bordia, H. Lüschen, S. Scherg, S. Gopalakrishnan, M. Knap, U. Schneider and I. Bloch, “Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems”, Physical Review X 7, 041047, 2017.

B. Chiaro, C. Neill, A. Bohrdt, M. Filippone et al., “Growth and preservation of entanglement in a many-body localized system”, arXiv:1910.06024.

A. Bohrdt, C. S. Chiu, G. Ji, M. Xu, D. Greif, M. Greiner, E. Demler, F. Grusdt and M. Knap, “Classifying Snapshots of the Doped Hubbard Model with Machine Learning”, Nature Physics, vol. 15, 921, 2019.

C. S. Chiu, G. Ji, A. Bohrdt, M. Xu, M. Knap, E. Demler, F. Grusdt, M. Greiner and D. Greif, “String patterns in the doped Hubbard model”, Science, vol. 365, issue 6450, pp. 251-256, 2019.