Investigating prethermal discrete time crystals with novel computer modelling method

Researchers at the University of Cambridge have utilised computer modelling to examine possible new phases of matter known as prethermal discrete time crystals.

It has been widely theorised that the properties of prethermal discrete time crystals (DTCs) are contingent on quantum physics, which is the laws determining particles at the subatomic scale. However, now, a team the University of Cambridge has discovered a more straightforward methodology – based on classical physics – that can be applied to greater comprehend this mysterious phenomenon.

Attaining a thorough comprehension of prethermal DTCs will be a significant step towards the control of complex many-body systems, which is a long-standing goal with numerous possible applications, including simulations of complex quantum networks.

The researchers’ findings have been published in two joint papers in Physical Review Letters and Physical Review B.

New discoveries

When something new is discovered, scientists learn more about it by studying it at greater detail. First, more straightforward methods are used, and if we still do not understand the discovery, then more complex techniques are tried.

“This was what we thought was the case with prethermal DTCs,” explained 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 incredibly intricate physical systems with unusual properties that are not yet fully understood. While standard space crystal break space-translational symmetry since its structure is not the same everywhere in space, DTCs break a distinct time-translational symmetry as, 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,” explained 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.”

Difficulty with quantum theories

Discrete time crystals were first predicted in 2012 and have since facilitated the opening of a novel area of research. DTCs have been examined in various types, such as in experiments. Among these, prethermal discrete time crystals are comparatively simple-to-realise systems that do not heat quickly – as would typically be anticipated – but instead exhibit time-crystalline behaviour for a very long time: the quicker they are shaken, the longer they survive. However, it was hypothesised that they are dependent 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,” added Pizzi.

A classical approach to prethermal discrete time crystals

A novel study conducted by Pizzi and his co-authors has discovered that complex quantum techniques can be avoided and that classical methods can be utilised. Through these methods, the researchers can stimulate these phenomena far more comprehensively.

For example, 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.

With the application of a computer simulation, the team were able to study many interacting spins under the action of a periodic magnetic field by utilising classical Hamiltonian dynamics. The resultant dynamics clearly exhibited 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,” concluded 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.”

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