Hidden order in quantum world uncovered through deconfined quantum critical points
The quantum world is full of strange phenomena. What may seem simple and natural in our everyday world becomes mysterious and puzzling at the quantum scale.
For instance, we see matter change state around us, like water freezing or boiling. Scientists explain these changes or phase transitions using the laws of thermodynamics. However, in the quantum world, things work differently.
Even without any thermal energy, at absolute zero temperature, materials can still shift from one state to another. Such peculiar phase transitions occur because of “quantum fluctuations — tiny, unpredictable movements of particles at the smallest scales, known as quantum critical points,” physicists at the University of Hong Kong (HKU) note in a press release.
For decades, scientists have been debating over a special type of quantum critical point called DQCP (deconfined quantum critical points). They couldn’t figure out “whether DQCPs represent continuous phase transitions (which are smooth and gradual) or first-order transitions (which are sudden and abrupt).”
However, a new study reveals the answer to this question. This breakthrough can shed light on novel ways in which particles interact and help physicists decode the formation of rare states of matter.
Understanding DQCP in depth
In regular quantum critical points (QCPs), a material changes from one phase to another because the order in the material slowly disappears. The system becomes more and more disordered until a new phase appears. It’s like one phase fading away into another.
In contrast, at a deconfined quantum critical point (DQCP), two completely different ordered phases transform directly into each other, without the system becoming disordered first. So instead of fading out, one order smoothly morphs into a totally different kind of order, due to strange quantum behaviors that don’t happen in normal cases.
“Instead of a sharp boundary separating an ordered phase from a disordered phase, DQCPs lie between two different ordered phases, each with its own unique symmetry-breaking pattern,” the HKU team added.
This is where it becomes difficult to identify whether the phase transition happening is smooth or abrupt. To find out what kind of phase transition DQCP actually represents, the study authors conducted some simulations and developed theoretical models.
Finding the phase-transition type
Before one dives into the results of the simulations and theoretical analysis, one needs to understand two key concepts.
The first is entanglement entropy, a way to measure that to what extent two parts of a quantum system are connected when they are entangled. It helps scientists understand how entanglement works at a deep level. The second is the square-lattice SU(N) spin models, theoretical tools used to study quantum systems.
The square lattice refers to a grid of points, and SU(N) is a mathematical framework that describes how particles, like spins, behave in such a system. The N here is a parameter that controls the symmetry of the system, influencing how particles interact with each other.
The researchers used entanglement entropy to study DQCPs in square-lattice SU(N) spin models through simulations.
They observed that at small values of N, DQCPs did not behave as expected for smooth phase transitions. Instead, the system showed a pattern that grows more slowly over time, following a logarithmic curve. This is different from the usual, more straightforward continuous transitions seen in other quantum systems.
However, “one of the most striking revelations of the study was the identification of a critical threshold value of N. When N exceeds this threshold, DQCPs exhibit behaviors consistent with conformal fixed points — a mathematical framework that describes smooth, continuous phase transitions,” the HKU team said.
The researchers hope these insights will advance our understanding of the quantum world and help scientists study exotic matter states in great detail. The findings can also influence the design of new materials and various quantum applications.
Source: Interesting Engineering
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Hidden order in quantum world uncovered through deconfined quantum critical points