### ‘Back to basics’ approach helps unravel new phase of matter

Researchers from the University of Cambridge used computer modelling to study potential new phases of matter known as prethermal discrete time crystals (DTCs). It was thought that the properties of prethermal DTCs were reliant on quantum physics: the strange laws ruling particles at the subatomic scale. However, the researchers found that a simpler approach, based on classical physics, can be used to understand these mysterious phenomena.

Understanding these new phases of matter is a step forward towards the control of complex many-body systems, a long-standing goal with various potential applications, such as simulations of complex quantum networks. The results are reported in two joint papers in *Physical Review Letters* and *Physical Review B*.

When we discover something new, whether it’s a planet, an animal, or a disease, we can learn more about it by looking at it more and more closely. Simpler theories are tried first, and if they don’t work, more complicated theories or methods are attempted.

“This was what we thought was the case with prethermal DTCs,” said Andrea Pizzi, a PhD candidate in Cambridge’s Cavendish Laboratory, first author on both papers. “We thought they were fundamentally quantum phenomena, but it turns out a simpler classical approach let us learn more about them.”

DTCs are highly complex physical systems, and there is still much to learn about their unusual properties. Like how a standard space crystal breaks space-translational symmetry because its structure isn’t the same everywhere in space, DTCs break a distinct time-translational symmetry because, when ‘shaken’ periodically, their structure changes at every ‘push’.

“You can think of it like a parent pushing a child on a swing on a playground,” said Pizzi. “Normally, the parent pushes the child, the child will swing back, and the parent then pushes them again. In physics, this is a rather simple system. But if multiple swings were on that same playground, and if children on them were holding hands with one another, then the system would become much more complex, and far more interesting and less obvious behaviours could emerge. A prethermal DTC is one such behaviour, in which the atoms, acting sort of like swings, only ‘come back’ every second or third push, for example.”

First predicted in 2012, DTCs have opened a new field of research, and have been studied in various types, including in experiments. Among these, prethermal DTCs are relatively simple-to-realise systems that don’t heat quickly as would normally be expected, but instead exhibit time-crystalline behaviour for a very long time: the quicker they are shaken, the longer they survive. However, it was thought that they rely on quantum phenomena.

“Developing quantum theories is complicated, and even when you manage it, your simulation capabilities are usually very limited, because the required computational power is incredibly large,” said Pizzi.

Now, Pizzi and his co-authors have found that for prethermal DTCs they can avoid using overly complicated quantum approaches and use much more affordable classical ones instead. This way, the researchers can simulate these phenomena in a much more comprehensive way. For instance, they can now simulate many more elementary constituents, getting access to the scenarios that are the most relevant to experiments, such as in two and three dimensions.

Using a computer simulation, the researchers studied many interacting spins – like the children on the swings – under the action of a periodic magnetic field – like the parent pushing the swing - using classical Hamiltonian dynamics. The resulting dynamics showed in a neat and clear way the properties of prethermal DTCs: for a long time, the magnetisation of the system oscillates with a period larger than that of the drive.

“It’s surprising how clean this method is,” said Pizzi. “Because it allows us to look at larger systems, it makes very clear what’s going on. Unlike when we’re using quantum methods, we don’t have to fight with this system to study it. We hope this research will establish classical Hamiltonian dynamics as a suitable approach to large-scale simulations of complex many-body systems and open new avenues in the study of nonequilibrium phenomena, of which prethermal DTCs are just one example.”

Pizzi’s co-authors on the two papers, who were both recently based at Cambridge, are Dr Andreas Nunnenkamp, now at the University of Vienna, and Dr Johannes Knolle, now at the Technical University of Munich.

Meanwhile, at UC Berkeley, Norman Yao’s group has also been using classical methods to study prethermal DTCs. Remarkably, the Berkeley and Cambridge teams have simultaneously addressed the same question. Yao’s group will be publishing their results shortly.

**Reference:**

Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle. ‘Classical Prethermal Phases of Matter.’ Physical Review Letters (2021).

Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle. ‘Classical approaches to prethermal discrete time crystals in one, two, and three dimensions.’ Physical Review B (2021).

A new phase of matter, thought to be understandable only using quantum physics, can be studied with far simpler classical methods.

We thought time crystals were fundamentally quantum phenomena, but it turns out a simpler classical approach let us learn more about themAndrea Pizzi Michael Dziedzic via UnsplashAbstract, distorted view of computer motherboard

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### Four Cambridge researchers recognised in the 2022 Breakthrough Prizes

Professors Shankar Balasubramanian and David Klenerman, from Cambridge’s Yusuf Hamied Department of Chemistry, have been awarded the 2022 Breakthrough Prize in Life Sciences – the world’s largest science prize – for the development of next-generation DNA sequencing. They share the award with Pascal Mayer, from the French company Alphanosos.

In addition, Professor Suchitra Sebastian, from the Cavendish Laboratory, and Professor Jack Thorne, from the Department of Pure Mathematics and Mathematical Statistics, have been recognised with the New Horizons Prize, awarded to outstanding early-career researchers.

Professor Suchitra Sebastian has been awarded the 2022 New Horizons in Physics Prize for high precision electronic and magnetic measurements that have profoundly changed our understanding of high temperature superconductors and unconventional insulators.

Professor Jack Thorne has been awarded the 2022 New Horizons in Mathematics Prize, for transformative contributions to diverse areas of algebraic number theory, and in particular for the proof, in collaboration with James Newton, of the automorphy of all symmetric powers of a holomorphic modular newform.

Professors Balasubramanian and Klenerman co-invented Solexa-Illumina Next Generation DNA Sequencing (NGS), technology that has enhanced our basic understanding of life, converting biosciences into ‘big science’ by enabling fast, accurate, low-cost and large-scale genome sequencing – the process of determining the complete DNA sequence of an organism’s make-up. They co-founded the company Solexa to make the technology available to the world.

The benefits to society of rapid genome sequencing are huge. The almost immediate identification and characterisation of the virus which causes COVID-19, rapid development of vaccines, and real-time monitoring of new genetic variants would have been impossible without the technique Balasubramanian and Klenerman developed.

The technology has had – and continues to have – a transformative impact in the fields of genomics, medicine and biology. One measure of the scale of change is that it has allowed a million-fold improvement in speed and cost when compared to the first sequencing of the human genome. In 2000, sequencing of one human genome took over 10 years and cost more than a billion dollars: today, the human genome can be sequenced in a single day at a cost of less than $1,000. More than a million human genomes are sequenced at scale each year, thanks to the technology co-invented by Professors Balasubramanian and Klenerman, meaning we can understand diseases much better and much more quickly. Earlier this year, they were awarded the Millennium Technology Prize. Balasubramanian is also based at the Cancer Research UK Cambridge Institute, and is a Fellow of Trinity College. Klenerman is a Fellow of Christ's College.

Professor Sebastian’s research seeks to discover exotic quantum phases of matter in complex materials. Her group’s experiments involve tuning the co-operative behaviour of electrons within these materials by subjecting them to extreme conditions including low temperature, high applied pressure, and intense magnetic field.

Under these conditions, her group can take materials that are quite close to behaving like a superconductor – perfect, lossless conductors of electricity – and ‘nudge’ them, transforming their behaviour.

“I like to call it quantum alchemy – like turning soot into gold,” Sebastian said. “You can start with a material that doesn’t even conduct electricity, squeeze it under pressure, and discover that it transforms into a superconductor. Going forward, we may also discover new quantum phases of matter that we haven’t even imagined.”

In addition to her physics research, Sebastian is also involved in theatre and the arts. She is Director of the Cavendish Arts-Science Project, which she founded in 2016. The programme has been conceived to question and explore material and immaterial universes through a dialogue between the arts and sciences.

“Being awarded the New Horizons Prize is incredibly encouraging, uplifting and joyous,” said Sebastian. “It recognises a discovery made by our team of electrons doing what they're not supposed to do. It's gone from the moment of elation and disbelief at the discovery, and then trying to follow it through, when no one else quite thinks it’s possible or that it could be happening. It’s been an incredible journey, and having it recognised in this way is incredibly rewarding.”

Professor Jack Thorne is a number theorist in the Department of Pure Mathematics and Mathematical Statistics. One of the most significant open problems in mathematics is the Riemann Hypothesis, which concerns Riemann’s zeta function. Today we know that the zeta function is intimately tied up with questions concerning the statistical distribution of prime numbers, such as how many prime numbers there are, how closely they can be found on the number line. A famous episode in the history of the Riemann Hypothesis is Freeman Dyson’s observation that the zeroes of the zeta function appear to obey statistical laws arising from the theory of random matrices, which had first been studied in theoretical physics.

In 1916, during his time in Cambridge, Ramanujan wrote down an analogue of the Riemann zeta function, inspired by his work on the number of ways of expressing a given number as a sum of squares (a problem with a rich classical history), and made some conjectures as to its properties, which have turned out to be related to many of the most exciting developments in number theory in the last century. Actually, there are a whole family of zeta functions, the properties of which control the statistics of the sums of squares problem. Thorne's work, recognised in the prize citation, essentially shows for Ramanujan’s zeta functions what Riemann proved for his zeta function in 1859.

Taking a broader view, Ramanujan’s zeta functions are now seen to fit into the framework of the Langlands Program. This is a series of conjectures, made by Langlands in the 1960’s, which have been described as a “grand unified theory of mathematics”, and which can be used to explain any number of phenomena in number theory. Another famous example is Wiles proof, in 1994, of Fermat’s Last Theorem. Nowadays the essential piece of Wiles’ work is seen as progress towards a small part of the Langlands program. Thorne's work establishes part of Langlands’ conjectures for a class of objects including Ramanujan’s Delta function.

"I am deeply honoured to be awarded the New Horizons Prize for my work in number theory," said Thorne. "Number theory is a subject with a rich history in Cambridge and I feel very fortunate to be able to make my own contribution to this tradition."

For the tenth year, the Breakthrough Prize recognises the world’s top scientists. Each prize is US $3 million and presented in the fields of Life Sciences, Fundamental Physics (one per year) and Mathematics (one per year). In addition, up to three New Horizons in Physics Prizes, up to three New Horizons in Mathematics Prizes and up to three Maryam Mirzakhani New Frontiers Prizes are given out to early-career researchers each year, each worth US $100,000. The Breakthrough Prizes were founded by Sergey Brin, Priscilla Chan and Mark Zuckerberg, Yuri and Julia Milner, and Anne Wojcicki.

Four University of Cambridge researchers – Professors Shankar Balasubramanian, David Klenerman, Suchitra Sebastian and Jack Thorne – have been recognised by the Breakthrough Prize Foundation in recognition of their outstanding achievements.

L-R: Millennium Technology Prize, Nick Saffell, Jack ThorneL-R: David Klenerman, Shankar Balasubramanian, Suchitra Sebastian, Jack Thorne

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