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Dynamics of the transverse Ising model with next-nearest-neighbor interactions
P R C Guimarães1, J A Plascak2, O F de Alcantara Bonfim3
1Departamento de Física, Universidade Federal de Viçosa, 36571-000 Viçosa, Minas Gerais, Brazil.
Next-nearest-neighbor interactions slow dynamics in the spin-1/2 transverse Ising model. Sufficiently large couplings cause a crossover from collective to central mode behavior, even with strong fields.
Area of Science:
- Condensed matter physics
- Quantum magnetism
- Statistical mechanics
Background:
- The one-dimensional spin-1/2 transverse Ising model is a fundamental model in condensed matter physics.
- Understanding the influence of interactions beyond nearest neighbors is crucial for realistic physical systems.
- Previous studies often focused on nearest-neighbor interactions, leaving the role of longer-range couplings less explored.
Purpose of the Study:
- To investigate the impact of next-nearest-neighbor (NNN) interactions on the dynamics of the spin-1/2 transverse Ising model.
- To analyze the behavior of the time-dependent transverse correlation function and spectral density.
- To determine how NNN coupling affects the transition between collective and central mode dynamics.
Main Methods:
- Exact diagonalization was employed to study chains of 13 spins.
- Periodic boundary conditions were used to approximate infinite-size behavior.
- The time-dependent transverse correlation function and spectral density were calculated for a tagged spin.
Main Results:
- Next-nearest-neighbor (NNN) coupling generally leads to slower dynamics.
- An enhancement of central mode behavior was observed with increasing NNN coupling.
- A crossover from collective to central mode behavior occurs with sufficiently large NNN coupling, even under a strong transverse field.
Conclusions:
- NNN interactions significantly alter the dynamics of the spin-1/2 transverse Ising model.
- The interplay between NNN coupling and transverse field strength dictates the emergence of central mode behavior.
- The findings provide insights into the role of longer-range interactions in quantum magnetic systems.
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