Is the Ground State Energy of the Two-Dimensional XX Model Known?

  • Thread starter Thread starter Gec
  • Start date Start date
  • Tags Tags
    Model
Click For Summary
SUMMARY

The ground state energy of the two-dimensional XX model with quantum 1/2-spins is not definitively known, as current literature lacks comprehensive numerical or theoretical results. The Jordan-Wigner transformation, effective in one dimension, fails to simplify the two-dimensional case, complicating exact solutions. Numerical methods such as the Lanczos algorithm and Variational Monte Carlo (VMC) are suggested for further exploration. Historical archives from Physical Review Letters (PRL) and Physical Review B (PRB) from the 1980s may contain relevant insights.

PREREQUISITES
  • Understanding of the XX model in quantum mechanics
  • Familiarity with the Jordan-Wigner transformation
  • Knowledge of numerical methods like the Lanczos algorithm
  • Basic concepts of Variational Monte Carlo (VMC) techniques
NEXT STEPS
  • Research the historical papers in Physical Review Letters (PRL) and Physical Review B (PRB) from the 1980s regarding the XX model
  • Study the application of the Lanczos algorithm in quantum systems
  • Explore the implementation of Variational Monte Carlo (VMC) for two-dimensional spin models
  • Investigate alternative methods for solving two-dimensional quantum spin systems
USEFUL FOR

Quantum physicists, researchers in condensed matter physics, and students studying quantum spin systems will benefit from this discussion.

Gec
Messages
3
Reaction score
0
I am curious about XX model with quantum 1/2-spins in two dimensions. Is ground state energy for this model known? I was not able to find numerical or theoretical results in electronical archives.
 
Physics news on Phys.org
Jordan-wigner transformation is useful for 1/2 spin system
i don't remember the Hamiltonian of xx model, but for 2 d system, seems difficult to sovle it exactly.
some numerical methods, like lanczos algorithm ,VMC...
try some old archives in prl and prb at 1980s...
 
to yuanyuan5220, thanks for your message.
Really, Jordan-Wigner transformation in one-dimensional case reduces the XX model to free fermions model, which is exactly solvable. In two dimensions it doesn't work. Can you explain to me what is "old archives in prl and prb at 1980s", please?
 
Thread 'Unexpected irregular reflection signal from a high-finesse cavity'

Thread 'Unexpected irregular reflection signal from a high-finesse cavity'

I am observing an irregular, aperiodic noise pattern in the reflection signal of a high-finesse optical cavity (finesse ≈ 20,000). The cavity is normally operated using a standard Pound–Drever–Hall (PDH) locking configuration, where an EOM provides phase modulation. The signals shown in the attached figures were recorded with the modulation turned off. Under these conditions, when scanning the laser frequency across a cavity resonance, I expected to observe a simple reflection dip. Instead...
View full post »

Similar threads

Graduate Ground state of the one-dimensional spin-1/2 Ising model
  • · Replies 1 ·
Replies
1
Views
2K
Does H = XX+YY spontaneously break symmetry in 1D?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Total spin from atomic spectroscopy term symbols, e.g. neon's excited states
  • · Replies 0 ·
Replies
0
Views
530
Graduate Antiferromagnetic ground state due to superexchange
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Issues in understanding screening effects in the Jellium model
  • · Replies 0 ·
Replies
0
Views
3K
Undergrad Confused about spontaneous emission
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Bragg condition and Bloch states
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad How can I compute edge states in the Haldane model with varying dimensions?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Criticality, phase transitions and closing bandgap
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Green's function calculation of an infinite lattice with periodicity in 1D
  • · Replies 1 ·
Replies
1
Views
2K