Random quantum Ising chains with competing interactions

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• Investigates criticality in quantum Ising spin chains with competing ferromagnetic and antiferromagnetic interactions.
• Introduces quantum fluctuations using random local transverse fields.
• Examines models with nearest-neighbor and next-nearest-neighbor couplings, and a quantum Viana-Bray model on a small-world random lattice.

Purpose of the Study:

• Analyze the criticality of quantum Ising spin chains with competing random couplings.
• Generalize the study to a quantum analog of the Viana-Bray model on a small-world random lattice.
• Determine the scaling of lattice topology for infinite disorder transitions.

Main Methods:

• Employs the Dasgupta-Ma decimation technique, both analytically and numerically.
• Focuses on the scaling of lattice topology.
• Investigates renormalization group flow towards infinite disorder fixed points.

Main Results:

• For a simple chain, second-neighbor couplings are irrelevant at the transition, renormalizing towards the Fisher infinite disorder fixed point.
• The infinite disorder transition in small-world models is unstable.
• Introduction of even a small density of long-range couplings destabilizes the transition.

Conclusions:

• Second-neighbor interactions do not alter the critical behavior of the quantum Ising chain at the infinite disorder fixed point.
• Long-range couplings fundamentally change the nature of the phase transition in small-world quantum Ising models.
• The lattice topology plays a crucial role in determining the stability of infinite disorder transitions.