Saturday 15 March 2025
For decades, physicists have been studying the behavior of particles in one dimension, known as Tomonaga-Luttinger liquids (LLs). These systems are fascinating because they exhibit unique properties that don’t occur in higher-dimensional systems. Now, researchers have made a significant breakthrough in understanding the nature of LLs near phase separation points.
Phase separation is a phenomenon where particles or atoms cluster together to form distinct domains. This happens when the interactions between particles become strong enough to overcome their kinetic energy. In one-dimensional systems, phase separation can lead to the formation of domain walls that separate these clusters.
The research team used a spinless fermionic system as an analogue to study LLs near phase separation points. They found that at this critical point, the system exhibits a new type of symmetry called Carrollian symmetry. This is different from the more well-known Poincaré symmetry, which describes the behavior of particles in high-energy physics.
The team’s findings suggest that Carrollian symmetry plays a crucial role in understanding the behavior of LLs near phase separation points. They were able to demonstrate this by analyzing the density-density correlations of the system and found that they are consistent with Carrollian symmetry.
One of the key implications of this research is that it provides new insights into the nature of phase transitions in one-dimensional systems. Phase transitions occur when a system undergoes a sudden change from one state to another, such as from a liquid to a solid. In LLs, phase transitions can be influenced by the interactions between particles.
The researchers used a lattice model to simulate the behavior of their system and found that at high energies, the system exhibits a flat state, which is a superposition of all possible configurations of particles on the lattice. This state has zero entropy, meaning it’s highly ordered.
However, as the energy decreases, the system undergoes a phase transition, and the flat state becomes degenerate with other states. This means that there are multiple configurations that have the same minimum energy. The researchers found that these degenerate states form a subspace of the ground state Hilbert space, which is a mathematical framework used to describe quantum systems.
The implications of this research are significant for our understanding of one-dimensional systems and their behavior near phase separation points. It opens up new avenues for studying phase transitions in LLs and could have important applications in fields such as condensed matter physics and quantum computing.
Cite this article: “Unveiling Carrollian Symmetry in Tomonaga-Luttinger Liquids Near Phase Separation Points”, The Science Archive, 2025.
Tomonaga-Luttinger Liquids, Phase Separation, Carrollian Symmetry, Poincaré Symmetry, One-Dimensional Systems, Phase Transitions, Condensed Matter Physics, Quantum Computing, Lattice Model, Entropy.
