Disorder induced cross-over effects at quantum critical points

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Mechanics

Background:

• Quantum spin chains are fundamental models in condensed matter physics.
• Disorder plays a crucial role in determining the critical properties and phases of quantum systems.
• Understanding the interplay between quantum criticality and disorder is essential for predicting material behavior.

Purpose of the Study:

• To investigate the critical properties of quantum spin chains at zero temperature under varying degrees of disorder.
• To map out the phase diagram of disordered quantum spin chains.
• To analyze the nature of critical behavior in different disorder regimes.

Main Methods:

• Analytical techniques were employed to study the critical properties.
• Extensive Density Matrix Renormalization Group (DMRG) methods were utilized for numerical simulations.
• Zero-temperature analysis was performed to focus on ground-state properties.

Main Results:

• A phase diagram comprising three distinct phases was identified.
• The weak disorder regime exhibits critical behavior governed by the fixed points of the pure system.
• The strong disorder regime is characterized by an infinite randomness fixed point.
• An intermediate disorder regime was discovered with anisotropic dynamical scaling and disorder-dependent exponents.

Conclusions:

• The phase diagram of disordered quantum spin chains is complex, featuring distinct regimes.
• Disorder fundamentally alters the critical behavior, leading to new universality classes.
• The identified intermediate regime highlights unique scaling properties not present in pure systems.