`Back to basics' approach helps unravel new phase of matter

Date:
September 27, 2021
Source:
University of Cambridge
Summary:
A new phase of matter, thought to be understandable only using
quantum physics, can be studied with far simpler classical methods.



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


========================================================================== 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.

========================================================================== Story Source: Materials provided by University_of_Cambridge. The original
text of this story is licensed under a Creative_Commons_License. Note:
Content may be edited for style and length.


========================================================================== Journal References:
1. Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle. Classical
Prethermal
Phases of Matter. Physical Review Letters, 2021 DOI: 10.1103/
PhysRevLett.127.140602
2. Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle. Classical
approaches
to prethermal discrete time crystals in one, two, and three
dimensions.

Physical Review B, 2021 DOI: 10.1103/PhysRevB.104.094308 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2021/09/210927082239.htm

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