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 modeling 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 Ph.D. 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
behaviors could emerge. A prethermal DTC is one such behavior, 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-realize systems that don't heat
quickly as would normally be expected, but instead exhibit time-crystalline
behavior 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).
Journal Link
Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle. 'Classical approaches to
prethermal discrete time crystals in one, two, and three dimensions.'
Physical Review B (2021).
Journal Link
Tags:
Physics