Understanding Ground State Degeneracy in the Transverse Ising Model

  • #1
thatboi
133
18
Hi all,
I was wondering if there was a reference/textbook where the degenerate perturbation calculation for the Transverse Ising model was treated fully. I want to better understand how in the weak magnetic field limit, the ground state degeneracy only lifts at N'th order in perturbation theory (for a lattice of N spins).
 

FAQ: Understanding Ground State Degeneracy in the Transverse Ising Model

What is ground state degeneracy in the transverse Ising model?

Ground state degeneracy in the transverse Ising model refers to the phenomenon where multiple distinct quantum states share the same lowest energy level, or ground state energy. This occurs due to the symmetries inherent in the system, especially at critical points where quantum phase transitions take place.

How does the transverse field affect the ground state degeneracy?

The transverse field in the Ising model introduces quantum fluctuations that can break the degeneracy of the ground state. At zero transverse field, the system may have a highly degenerate ground state due to classical spin configurations. As the transverse field increases, these quantum fluctuations lift the degeneracy by favoring certain quantum superpositions over others, leading to a unique ground state at sufficiently high fields.

What role does symmetry play in ground state degeneracy?

Symmetry plays a crucial role in determining ground state degeneracy. In the transverse Ising model, the Z2 symmetry (spin flip symmetry) can lead to degenerate ground states. At the critical point where the symmetry is spontaneously broken, the system may transition from a degenerate ground state to a non-degenerate one, or vice versa, depending on the nature of symmetry breaking and the external transverse field.

Can ground state degeneracy be experimentally observed in the transverse Ising model?

Yes, ground state degeneracy can be experimentally observed in systems that can be modeled by the transverse Ising model. Techniques such as quantum annealing, nuclear magnetic resonance (NMR) spectroscopy, and cold atom simulations in optical lattices can be used to study the ground state properties and observe degeneracy. These experiments can reveal how degeneracy changes with varying transverse field and other parameters.

Why is understanding ground state degeneracy important in quantum computing?

Understanding ground state degeneracy is important in quantum computing because degenerate ground states can be used to encode quantum information in a robust manner. Systems with degenerate ground states can serve as qubits in quantum computers, providing resilience against certain types of errors and decoherence. Additionally, studying degeneracy in models like the transverse Ising model helps in understanding quantum phase transitions and critical phenomena, which are key to developing advanced quantum algorithms and error correction techniques.

Similar threads

I Understanding No Energy Degeneracy in Sakurai's Quantum Mechanics
Replies
2
Views
1K
I Born rule in classical Ising model: Feynman -> Boltzmann ensemble?
Replies
2
Views
1K
I How are good quantum numbers related to perturbation theory?
Replies
18
Views
2K
A Fractional Quantum Hall Effect- degeneracy of ground state (Tong's notes)
Replies
1
Views
1K
I Understanding the dynamics of a perturbed quantum harmonic oscillator
Replies
3
Views
870
How to normalize the density of states in JDoS Wang-Landau?
Replies
1
Views
1K
A 1D transverse-field Ising model - classical vs quantum differences?
Replies
1
Views
2K
I Accuracy of the Density of States
Replies
3
Views
991
A Ground state of the one-dimensional spin-1/2 Ising model
Replies
1
Views
2K
I 2D Ising Model Average Number of Domain Walls
Replies
0
Views
338

Hot Threads

Recent Insights

Back
Top