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Phase Transitions

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...

Phase Transitions

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...

Phase Diagrams of Ternary Systems

Phase Diagrams of Ternary Systems

Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...

Phase Transitions: Vaporization and Condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...

Phase Transitions: Melting and Freezing

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

Phase Transitions: Sublimation and Deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Published on: August 2, 2019

Quantum phase transitions in the Hubbard model on a triangular lattice.

Takuya Yoshioka¹, Akihisa Koga, Norio Kawakami

¹Department of Applied Physics, Osaka University, Suita, Osaka, 565-0871, Japan.

Physical Review Letters

|August 8, 2009

Summary

We studied quantum phase transitions in the Hubbard model on a triangular lattice. A paramagnetic metal transitions to a nonmagnetic insulator, then to a 120° Néel ordered state as interaction strength increases.

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Area of Science:

Condensed Matter Physics
Quantum Materials Science

Background:

The Hubbard model is crucial for understanding strongly correlated electron systems.
Triangular lattices exhibit unique magnetic and electronic properties.

Purpose of the Study:

Investigate quantum phase transitions in the half-filled Hubbard model on a triangular lattice.
Clarify the nature of transitions and the existence of intermediate phases.

Main Methods:

Employed the path-integral renormalization group (PIRG) method.
Utilized a novel iteration and truncation scheme for enhanced accuracy.
Simulated a 36-site cluster to analyze system behavior.

Main Results:

Identified two first-order quantum phase transitions as Hubbard interaction (U) increases.
Paramagnetic metallic state transitions to a nonmagnetic insulating (NMI) state at Uc1 ≈ 7.4t.
NMI state transitions to a 120° Néel ordered state at Uc2 ≈ 9.2t.

Conclusions:

Confirmed the existence of an intermediate nonmagnetic insulating phase.
Resolved long-standing controversies regarding quantum phase transitions in this model.
Results provide insights into correlated electron behavior on frustrated lattices.