# Many-body physics

## Table of Contents

### Information spreading in many-body systems #

The spreading of entanglement has been a major research theme in the many-body physics community for several years now. Most recently, a lot of attention has been devoted to the entanglement phase transition that occurs in monitored quantum circuits.

We were wondering how fundamentally “quantum” this phenomenology is. To our surprise, we found that one can define classical models that exihibt very similar behaviour [1].

*Bridging the gap between classical and quantum many-body information dynamics*

Pizzi, Malz, Nunnenkamp, Knolle, PRB (2022), arXiv

### Discrete time crystals #

Time crystals are nonequilibrium phases of matter that spontaneously break time-translation symmetry. The classic example here is one of a spin chain with a pi-pulse applied every period. Two pi-pulses are equivalent to the identity, which means the systems recurs only after two periods [a].

In a generic closed system, one would expect the drive to heat up the system to a infinite temperature state, which is why it is understood that one needs to add MBL to stabilize the phase [a]. Yet, even in the absence of MBL gives a subharmonic response for time scales that are exponentially long in systems sizes, which would suggest time-crystalline order in the absence of MBL. In a numerical analysis, we have shown that a previously overlooked, subtle effect can explain why the apparent subharmonic response scaling is misleading, thus further clarifying the role of MBL in such systems [2].

In classical systems, it is less clear how time crystalline phases can arise, as also the “rules” are less clear. Previous work has suggested that in one-dimensional systems, short-range interactions are not sufficient [b], but long-range interactions may indeed stabilize DTC order [c]. In our work we take ask more questions about this classical setting, by studying the example of seasonal epidemic spreading on small-world graphs, and identify a setup where an arbitrarily small density of random (infinite-range) bonds is sufficient for a transition to a time-crystalline phase [3]. In contrast to previous models, our model includes non-Markovianity in the form of “immune sites” that are non-dynamical for a set period of time. This opens an interesting parallel between research on DTCs and models that have been in use for decades in epidemiology.

*Time crystallinity and finite-size effects in clean Floquet systems*

Pizzi, Malz, Nunnenkamp, Knolle, PRB (2020), arXiv.*Seasonal epidemic spreading on small-world networks: Biennial outbreaks and classical discrete time crystals*

Malz, Pizzi, Nunnenkamp, Knolle, PRR (2021), arXiv

### Topological magnon amplification #

This project concerns the amplification of magnons in chiral topological edge modes [4]. Such modes arise in certain (3D, but effectively 2D) magnetic insulators with Dzyaloshinskii-Moriya interaction, most notably with kagome [e] and honeycomb [f] lattices. We show that driving such systems with light can lead to edge mode instabilities and nonequilibrium steady states with large edge magnon population and further show that driving with a gradient leads to some sort of driven magnon Hall effect, two aspects that will aid their direct experimental detection. Beyond the characterisation these materials, our magnon amplification mechanism can be used to build a coherent magnon source (a magnon laser) and a travelling-wave magnon amplifier, two devices with great potential in the realm of magnon spintronics.

*Topological magnon amplification*

Malz, Knolle, Nunnenkamp, ncomms (2019), arXiv