All Questions
Tagged with spin-models spin-chains
66
questions
1
vote
1
answer
194
views
Valence Bond Solid order paramter
I'm confused about the valence bond solid (VBS) in condensed matter literature. The idea is a lattice is covered by spin singlets and thus spin rotational invariant. It seems that it's commonly ...
- 470
4
votes
1
answer
1k
views
Ground state magnetization of the Heisenberg XXZ chain
The Hamiltonian of the Heisenberg XXZ chain (without external field) has the form
$$
H = -J \sum_{n=1}^{N}\left(S_n^xS_{n+1}^x+ S_n^yS_{n+1}^y + \Delta S_n^zS_{n+1}^z\right).
$$
It is known that this ...
- 83
3
votes
1
answer
111
views
Invariants of spin chains
I consider modelling a particular physical phenomenon using a spin chain (Ising, XYZ, Potts, etc.). Once I establish the mapping from experimental data to the states of spins for, I get the values $\{...
- 2,921
1
vote
1
answer
167
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Anisotropy in spin chain hamiltonian
The Hamiltonian of XY Spin Chain on a lattice of N sites can be written as
$$
H = -J\sum_{i=1}^N \left(\frac{1+\gamma}{2}\sigma_i^x\sigma_{i+1}^x + \frac{1-\gamma}{2}\sigma_i^y\sigma_{i+1}^y + \lambda ...
2
votes
0
answers
88
views
Lagrangian formulation of classical spin chains
Is there a way to construct a Lagrangian formulation of the classical dynamics of a spin chain - say a Heisenberg or XY chain? The Hamiltonians here are obvious.
- 958
4
votes
2
answers
2k
views
Kagome Lattice: Spin-orbit coupling Hamiltonian in tight-binding models
Consider spin-orbit coupling (of strength $\lambda_1$) on lattice, with the below Hamiltonian
$$H = i \lambda_1 \sum_{<ij>} ~\frac{E_{ij} \times R_{ij}}{|E_{ij} \times R_{ij}|} \cdot \sigma ~...
- 359
1
vote
1
answer
227
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Existence of the Schwinger boson creation operator
Schwinger boson transformation is widely used in spin systems. It represents three Pauli matrices in the following form
$$
s^+=\frac{1}{2}\sigma^+ = a^\dagger b \, ,
$$
$$
s^-=\frac{1}{2}\sigma^- = b^\...
- 93
1
vote
0
answers
105
views
Generalised Ising models?
Are there generalised Ising models:
The underslying mesh/connectivity is completely arbitrary - non rectangular, 3D...ND, complete connectivity should be possible
The interaction potential is ...
- 273
1
vote
0
answers
165
views
Where to find a Path Integral treatment of 1D Quantum Heisenberg model or Quantum Spin Chain?
All:
Where to find a Path Integral treatment of 1D Quantum Heisenberg model or Quantum Spin Chain?
I would like to find a detailed calculation of path amplitude in such situation. I did some google ...
2
votes
2
answers
187
views
Different concepts of phase transitions in spin models
I am currently revising the lecture notes in which different spin systems
are analyzed, focussing on the occurrence (or absence) of phase transitions.
Different techniques are applied to analyze the ...
- 123
0
votes
1
answer
154
views
Troubles with Haldane Shastry Spin Chain
I'm reading the article "Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions", which shows how to solve the problem of a long range-inverse squared ...
- 162
0
votes
1
answer
405
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Bose-Einstein distribution and magnons
I have some doubt about the Bose-Einstein distribution for magnons/spin-waves.
A one-dimensional ferromagnet placed in an external magnetic field $\mathbf{B} = B\, \hat{z}$ obeys the Hamiltonian
$$H ...
- 451
2
votes
1
answer
382
views
One-dimensional $SU(3)$ Heisenberg Model, the non-linear sigma model, $\theta$-term
Let's consider a one dimensional $SU(N)$ antiferromagnetic Heisenberg Model with an irreducible representation and its conjugate on alternating sites, such that they correspond to a Young tableaux ...
- 85
1
vote
0
answers
223
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How to find groundstate energy of a simple Hamiltonian at $N/L$-filling using Jordan-Wigner (JW) transformation?
$\underline{\textbf{Model:}}$
Let we have the $t-V$ model for spinless fermions on a 1D lattice, which is defined in second quantization operators as follows:
$$H_1 = -t\sum_i \big(c_i^\dagger c_{i+...
- 1,335
0
votes
1
answer
261
views
Average entropy of a subsystem
In this paper by Don Page, https://arxiv.org/pdf/gr-qc/9305007.pdf, He conjectures average entropy of a substem of dimension m with Hilbert space dimension mn, $m \leq n$. to be :
$ S_{mn} = \sum_{n+...
- 305