Quantum Ising model in a period-2 modulated transverse field.

Area of Science:

• Condensed Matter Physics
• Quantum Magnetism
• Statistical Mechanics

Background:

• Investigating finite spin chains with alternating fields is crucial for understanding complex magnetic behaviors.
• The interplay between Ising interactions and transverse fields leads to rich quantum phenomena.

Purpose of the Study:

• To analyze the ground-state properties of a finite spin-1/2 Ising chain with a spatially alternating transverse field.
• To establish a method for determining the ground-state energy and energy gap between parity subspaces.
• To derive an expression for the correlation length consistent with existing literature.

Main Methods:

• Utilizing the Jordan-Wigner transformation to map the spin chain to a one-dimensional model of free fermions.
• Calculating ground-state energies within positive- and negative-parity subspaces.
• Deriving closed-form expressions for the energy gap and analyzing its behavior.

Main Results:

• The study successfully maps the spin system to free fermions, enabling exact solutions.
• Closed-form expressions for the energy gap between parity subspaces were derived.
• The behavior of the energy gap was analyzed across different field regimes and system sizes.
• A novel expression for the correlation length was proposed.

Conclusions:

• The developed methods provide a precise way to determine the ground-state energy of the studied spin chain.
• The derived correlation length expression aligns with known behaviors near critical points.
• This work contributes to the understanding of quantum phase transitions in low-dimensional magnetic systems.