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Dynamics of Correlated Quantum Matter: From Dynamical Probes to Novel Phases of Matter

Periodic Reporting for period 2 - DYNACQM (Dynamics of Correlated Quantum Matter: From Dynamical Probes to Novel Phases of Matter

Reporting period: 2019-12-01 to 2021-05-31

While the foundations of quantum mechanics have been established about a century ago, many of the rich physical phenomena that emerge due to the interplay of quantum fluctuations and correlation effects are not yet understood—recently discovered exotic quantum phases of matter represent a prominent example. Understanding these challenging quantum-many body systems is a problem of central importance in theoretical physics and the basis for the development of new materials for future quantum technologies. Dynamical properties can provide characteristic fingerprints that allow to identify such novel phases in newly synthesized materials and optical lattice systems. Moreover, when brought out of equilibrium, correlated quantum matter can exhibit dynamical phases that cannot occur in equilibrium settings.

The project DYNACQM develops new theoretical and numerical frameworks to study dynamical properties of correlated quantum matter. We address three main objectives:

(a) Predict dynamical fingerprints of emergent quantum phases. We derive universal signatures and perform numerical simulations of microscopic model Hamiltonians to understand the dynamics of exotic quantum orders. These allow for direct comparisons with experiments, e.g. the dynamical spin structure factor that can be measured in neutron scattering experiments, and help to identify new topological materials. We mainly focus on topologically ordered phases with non-abelian anyons, symmetry protected topological phases, dynamics on the edge of chiral phases, and gapless spin liquids.

(b) Investigate dynamical phases in quantum many body systems and their robustness. We study systems far out of equilibrium and explore the stability of dynamical quantum phases. The focus will lie on the many-body localization transitions in one- and two-dimensional systems, stability of quantum orders in many-body Floquet systems, and dynamical signatures of such.

(c) Understand the dynamics of many-body entanglement and quantum thermalization in systems out of equilibrium. We focus on the fundamental understanding of the spreading of entanglement in many-body systems. A particular focus lies on the study of how a quantum system thermalizes. This allows us on the one hand to obtain a fundamental understanding of quantum dynamics. On the other hand, it will help us to design new algorithms for the efficient simulations of the dynamics in quantum many-body problems.
Our research in the past reporting period has focussed on the three central objectives and we made important progress on all of them.

One of our central objectives is the study of dynamical correlations in frustrated quantum spin systems in order to predict experimentally accessible fingerprints of emergent quantum phases. This entails for example the numerical calculation of spectral functions which can be compared to neutron scattering experiments. Here we made an important methodological breakthrough by developing an efficient algorithm that allows to obtain the dynamical response functions for two-dimensional lattice systems. Using this algorithm, we obtained the dynamic spin structure factor of the paradigmatic Heisenberg model on the square lattice and reproduced a puzzling feature which had been observed in experiment. We also considered the Heisenberg model on the triangular lattice. Due to its severe geometric frustration, previous analytic works had predicted that even though the ground state is a magnet, its magnon excitations would be short-lived. Our novel algorithm made the dynamic spin structure factor in this highly-quantum model accessible for the first time with an unbiased method. Remarkably, we found that the emergent quasiparticle excitations are long-lived —in contradiction with the common belief— and developed a simple microscopic theory to explain this phenomenon.

We also made substantial progress on the investigation of quantum phases that emerge when a many-body system is brought out of equilibrium. Here we discovered the concept of Stark many-body localization (MBL) and showed that several existing experimental probes, designed specifically to differentiate between these scenarios, work similarly in the Stark many-body localization (MBL) setting. Moreover, we found several new dynamical phases of matter in quantum many body systems and were able to prove their robustness in different settings. In this context, we investigated the stability of a many-body localized phase that can be realized in a central spin system. In a series of works, we discovered a new phenomenon dubbed “Hilbert space fragmentation”. In particular, we showed that the combination of charge and dipole conservation leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead to a breakdown of thermalization. Excitingly, this new phase of matter can protect symmetry protected topological order in highly excited states in certain settings. This might be highly relevant to build robust quantum memories.

In order to efficiently simulate complex quantum many-body systems, we developed novel tensor-network based tools and quantum algorithms for using noisy intermediate-scale quantum (NISQ) devices. Tensor network algorithms are efficient classical algorithms for simulating quantum many-body systems. In our project, we developed a number of new matrix-product state based methods to simulate out of equilibrium dynamics of one-dimensional quantum many body systems. To go beyond the one-dimensional limit, we introduced the class of isometric tensor network states, which enables novel algorithms for the simulation of two-dimensional quantum lattice models. In addition to developing algorithm for the use on classical computers, we have also been investigating the possibility of using quantum computers for simulating condensed matter physics. Our first work considered Trotterized evolution of non-equilibrium quantum dynamics and was able to see signatures of non-trivial many-body physics in small scale systems.
The project DYNACQM has already led to several results which go beyond the state of the art and we will continue to work on our main objectives. One main focus lies now on making concrete proposals to realize and detect the predicted physical phenomena in experiments.

First, we have significantly extended the numerical and analytical toolbox to obtain dynamical response functions of two-dimensional lattice systems. Using this toolbox, we found that quasi-particle excitations are surprisingly long-lived. This novel mechanism deserves further study; one route we plan to explore is by numerically studying a model where the avoided decay can be tuned with a parameter in experiment. As a concrete model, we will explore models where our numerical results can be compared to recent theoretical predictions. Second, we identified novel dynamical phases in quantum many body systems, including Stark many body localization and Hilbert space fragmentation. We are currently discussing with experimental groups and made concrete proposals for realizing these phases in cold atom systems. Third, using the framework of random-unitary circuits, we made substantial contribution towards the understanding of the spreading of entanglement. We are now using this knowledge to develop new numerical tools to extract emergent hydrodynamics from microscopic Hamiltonians.
Strong quantum interactions prevent quasiparticle decay [Nat. Phys. 15, 750].