Questions tagged [spin-models]
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143 questions
3
votes
0answers
42 views
Renormalization Group Decimation
I'm trying to understand how the renormalization group theory works.
In the image shown on the bottom we coarse grain by decimation in the 2D Ising model. We split the lattice in two sets, $s^{\sim}$ ...
2
votes
0answers
79 views
+50
Symmetry transformations that are self-inverse and global symmetries of the Hamiltonian
I have the simplified Ising model. The Hamiltonian is given by
$$
\mathcal{H} = -\mathrm{J}\sum_{<ij,i' j'>} \sigma_{ij} \sigma_{i'j'}.
$$
Where the sum over $<ij,i'j'>$ means just the ...
5
votes
1answer
56 views
Integrability of a non-integrable quantum spin model at critical point
Is it right, that non-integrable quantum spin models in one dimension become integrable at their critical points? Or do they stay nonintegrable at the critical point also? Are there any examples known?...
0
votes
1answer
49 views
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
$$H ...
0
votes
0answers
51 views
Why the correlation function of 2D classical XY model is written so?
2D classical XY model $$H = -J\cos(\theta_{i}-\theta_{j})%$$ is famous for Berezinskii-Kosterlitz-Thouless phase transition. This is because of the difference of correlation function between hot and ...
1
vote
1answer
58 views
Two spin-1 system and the projector onto total spin 2 subspace [closed]
I am having trouble grasping the projection operators in the context of composite spins system, e.g. with two spin-1. First off, a projector $P$ is said to be an operator that squares to itself, $P^2=...
1
vote
0answers
15 views
In spin systems, a mean field with nonzero Chern number after Gutzwiller projection changed into trivial state?
The mean field is nontrivial because of nonzero Chern number. The gauge symmetry is Z2. Under Gutzwiller projection, I calculate the ground state degeneracy(GSD) and find that the GSD is one(trivial ...
0
votes
1answer
64 views
What is the Kitaev Model and why it became so popular? [closed]
I am seeing Kitaev Model everywhere. It feels like the spin-glass model of our time. How the Kitaev model differ from spin-glass and why it can be used everywhere? Looking at equation 1 here suggests ...
1
vote
0answers
30 views
How can I compute the spin texture for a $SU(2)$ gauge model?
I am trying to determine the helicity of 4 Dirac cones in my model, and one way I want to approach it is by plotting the spin-texture. However, I am unsure of how one would calculate the spin-texture ...
0
votes
0answers
28 views
spinless and time reversal symmetry breaking of p-wave pairing in topological superconductors
In the context of Majorana zero modes, I often hear that the p-wave pairing is effectively 'spinless' and time reversal symmetry broken.
I understand that s-wave and p-wave refer to the spin portion ...
2
votes
0answers
27 views
How to quantify frustration for spin models with long range interactions?
Consider the following Hamiltonian:
$$
H=-\sum_{i\neq j}J_{ij}S_iS_j-\sum_i H_iS_i
$$
where $S_i\in\{-1,1\}$, and the summed pair $i,j$ can be any two distinct indices (not necessary adjacent spins)....
1
vote
1answer
70 views
One-dimensional $SU(3)$ Heisenberg Model, the non-linear sigma model, $\theta$-term
Let's consider a one dimensional $SU(N)$ antiferromagnetic Heisenberg Model with an irreducible representation and its conjugate on alternating sites, such that they correspond to a Young tableaux ...
1
vote
1answer
54 views
What is the order parameter of 2D generalized $XY$ model?
I'm now studying the phase transition of 2D generalized XY model. This model considered here has a mixture with ferromagnetic and nematic-like interactions,
$$\mathcal{H}=-\sum_{\langle i j\rangle}\...
1
vote
0answers
72 views
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:
$$H_1 = -t\sum_i \big(c_i^\dagger c_{i+...
0
votes
1answer
74 views
What are exactly “norms” in spin networks? Are there any non-quantum spin networks?
Roger Penrose proposed a series of networks from which, fundamentally, space-time would emerge, called spin networks
(https://en.wikipedia.org/wiki/Spin_network)
In this article, it is said:
...
0
votes
0answers
17 views
Exchange stiffness for HCP
I am studying the exchange interaction, which can be described with the Heisenberg Hamiltonian:
$\hat{H} = -\sum_{i,j}J_{ij}\hat{\mathbf{S_i}}\cdot \hat{\mathbf{S_j}}$
In the framework of constant ...
1
vote
0answers
21 views
$p$-spin spherical spin glass
Consider the $p$-spin spherical spin glass model with Hamiltonian $$H_{N,p}(\sigma)=\frac{1}{{N}^{\frac{(p-1)}{2}}} \sum \limits_{i_1,...i_p} J_{i_1,...i_p} \sigma_{i_1} \sigma_{i_2} .. \sigma_{i_p} $$...
0
votes
0answers
41 views
Which phenomenon is related to the spin of photons? [duplicate]
The phenomenon of the deflection of a moving electron in a magnetic field is related to the electrons spin. From which phenomenon it is concluded, that photons have a spin?
0
votes
1answer
83 views
Relation between spin and polarization of photon? [duplicate]
What is the possible spin configuration of photon?
And does spin has any relation with polarization?
1
vote
1answer
39 views
A dreidel on a spinning table
In the spirit of the holidays.
Let's assume that a dreidel is spinning counter-clockwise at frequency $f$ on a table.
From external point of view, what will I see if I rotate the table clockwise at ...
0
votes
1answer
50 views
Average entropy of a subsystem
In this paper by Don Page, https://arxiv.org/pdf/gr-qc/9305007.pdf, He conjectures average entropy of a substem of dimension m with Hilbert space dimension mn, $m \leq n$. to be :
$ S_{mn} = \sum_{n+...
0
votes
2answers
142 views
Pauli matrices as measurement operators versus spin probability
Pauli matrices tell us what the spin of a particle is along a certain axis.
Let's say I want to measure the spin along the z-axis then the pauli operator
$$\sigma_z = \begin{bmatrix}1&&0\\0&...
1
vote
2answers
276 views
Finding the Eigenvalues and Eigenvectors of the Hamiltonian for three spin-1/2 particles coupled antiferromagnetically
Problem
Given three spin-1/2 particles with the total spin operator $\vec{S}=\sum\limits_{i=1}^3 \vec{S}_i$ and its $z$ projection $S_z=\sum\limits_{i=1}^3 S_{z,i}$, and the Hamiltonian
$$H = J\sum\...
1
vote
0answers
25 views
Discrepancy regarding Husimi Probability distribution calculation
I am trying to simulate a system of j qubits and for visualization of the dynamics considering the Husimi distribution of the state.
To carry out the projection onto coherent states I have proceeded ...
1
vote
1answer
35 views
Constructing PEPS representation of an arbitrary quantum state
Given a quantum state we can construct its MPS (Matrix Product State) representation by doing a series of singular value decompositions. Given the freedom to choose arbitrary bond dimensions the MPS ...
2
votes
1answer
130 views
Integrability of generalized Richardson-Hubbard model
Recently I got a bit interested in the possibility of finding spectrum of few interesting class of lattice quantum mechanical hamiltonians like Richardson's pairing hamiltonian, 1D Hubbard hamiltonian,...
1
vote
1answer
53 views
Microscopic and macroscopic description of spin waves
Hamiltonian
Consider the one-dimensional Heisenberg ferromagnet specified by the Hamiltonian
$$H = -\frac{|J|}{2}\sum_{i,\delta} \mathbf{S}_i\cdot \mathbf{S}_{i+\delta}.$$
Here $i$ labels the spin ...
1
vote
0answers
56 views
Self-modifying Hamiltonians (Lagrangians) and emerging intelligence? [closed]
Are there dynamical physical systems that are governed by self-modifying Hamiltonians (Lagrangians), i.e. Hamiltonians (Lagrangians) determine not only the next point in phase space, but also the form ...
1
vote
1answer
50 views
Reduced density matrix of the edge spin-1/2 in AKLT spin chain
I am trying to understand the paper titled, "Entanglement in a Valence-Bond-Solid State" by Fan, Korepin, and Roychowdhury (https://arxiv.org/abs/quant-ph/0406067).
I was able to understand the ...
3
votes
2answers
141 views
How can I say whether a Hamiltonian is integrable or not?
The transverse field Ising Hamiltonian $$ H = J\sum_{i=0}^{N}\sigma_{i}^{z}\sigma_{i+1}^{z}+h_{x}\sum_{i=0}^{N}\sigma_{i}^{x} $$ is integrable because it can be exactly solved using Jordan Wigner ...
2
votes
0answers
60 views
Elitzur theorem and the Ising model
I was recently studying the Elitzur theorem and its application to the Ising model on Kogut: An introduction to lattice gauge theories and spin systems, chapter $5$C. I was wondering how he obtain $\...
2
votes
1answer
80 views
Physical Realization of Three-Level System
I have come across the Hamiltonian (where $\varepsilon,\Delta\geq0$) in one of my problem sets:
$$H=
\left(\begin{array}{c c c}
0&0&0\\
0&\varepsilon-\Delta&0\\
0&0&\...
1
vote
0answers
69 views
Practical/experimental difference between (quantum) Heisenberg and (classical) Ising model
I have read a few discussions about the difference between the Heisenberg model (using quantum spin operators) and Ising model (with spins $\pm 1$), notably this one or this Quora post.
All the ...
1
vote
1answer
77 views
About spin chain string order
We know that the string order of a spin chain is defined as
$$\mathcal{O}^\alpha=\lim_{i-j\to\infty}\left\langle S_i^\alpha\prod_{k=i+1}^{j-1}\exp(i\pi S_k^\alpha)\ S_j^\alpha \right\rangle$$
now ...
2
votes
0answers
38 views
Translation Holonomy
I'm trying to get a mental image of translation holonomy.
I start with rotational holonomy, which corresponds to intrinsic curvature. This is the quantitative failure of a continuous process of ...
0
votes
0answers
47 views
Classical statistical model based on group multiplication
For a (finite) group $G$, consider the following classical statistical model on a 2 dimensional lattice with oriented edges:
Each edge carries a classical degree of freedom that can take values in ...
0
votes
0answers
17 views
What is Four-spin susceptibility
I was reading a paper about the charge electronic nematicity in iron-based superconductors. And there is one sentence saying that 'while NMR and neutron scattering can give crucial information on the ...
0
votes
0answers
63 views
Correlation length
I am working with the spin-1/2 quantum antiferromagnet Heisenberg model. I have found literature about the correlation length of this model for 2D. However, what would it be in 1D?
I have the ...
0
votes
0answers
271 views
Transfer matrix of 1D Ising model
I'm sorry if this is trivial, I've been stuck on a definition in Yeomans, Statistical mechanics of phase transitions. In chapter five she describes the transfer matrix of the 1D Ising model with ...
2
votes
0answers
53 views
Can we have a spin glass in the one-dimensional Heisenberg hamiltonian with nearest neighbours only?
Consider the one dimensional Heisenberg Hamiltonian of the form
\begin{equation}
H = - \sum_{<i,j>} J_{ij} \mathbf{S}_i \cdot \mathbf{S}_j
\end{equation}
with nearest neighbour interactions. ...
1
vote
0answers
152 views
Transverse field Ising model with open boundary conditions
what is the energy dispersion of the transverse field Ising model looks like in the case of open boundary conditions?
In the case of periodic boundary, the energy takes the form of
and the ground ...
0
votes
0answers
34 views
Meaning of $\left< (S_{\vec r}^{x})^2 \right>$ etc for spin-waves?
In the context of spin-waves does the ground state expectation value of:
$$\left< (S_{\vec r}^x)^{n}\right>$$
have any physical significance (and likewise for the $y$ and $z$ components - but ...
2
votes
1answer
83 views
Why is a spin network a spinfoam's boundary?
i read in Wikipedia that spinfoams boudaries are spin networks, but nothing is said about what is a boundary in this case.
i know that a spin foam is a spin network where other colours and ...
3
votes
1answer
82 views
Magnetism - Large Spin Limit
In class we were computing the partition function given the following Hamiltonian:
$$H = - g\mu_B \sum_{i} \vec{h}.\vec{S_i}$$
where $\vec{h}$ is the external magnetic field, and $\vec{S_i}$ is the ...
0
votes
0answers
24 views
Analytic methods for studying thin films (approximately 2D spin systems)
I am working on a project involving thin films of a magnetic material represented by essentially an Ising model on a 3 dimensional lattice. The bulk case is relatively straight forward, the ...
1
vote
1answer
55 views
Acoustic, optical, ferromagnetic and antiferromagnetic spin-waves?
In the context of spin-waves I have seen the following words as descriptors*:
Acoustic
Optical
Ferromagnetic
Antiferromagnetic
which I have seen used together e.g. "acoustic ferromagnetic spin ...
3
votes
1answer
222 views
R-matrix for spin chains
In algebraic Bethe ansatz procedure, one of the central objects is the R-matrix satisfying the Yang-Baxter equation, but all the papers/books give directly its expression without deriving it, so my ...
1
vote
0answers
38 views
Force caused by the magnetic field on the electron spin
I have read there are two ways to express the force caused by a variable magnetic field over a magnetic moment depending on the source of the magnetic moment since it can come from a dipole or a loop ...
0
votes
1answer
153 views
Information from four point correlation functions in Ising model
For a one-dimensional classical Ising model with the Hamiltonian $$H=-J \sum_{i}\sigma_{i} \, \sigma_{i+1}$$ where $\sigma=\left\{+1,-1\right\}$ one can calculate two point correlation for the spins $$...
1
vote
0answers
69 views
Correlation between spins using delta function in Potts model
In reading about the Potts model, I found this correlation:
$$\langle s_{i}s_{j} \rangle = \frac{q}{q-1}\frac{1}{N_{p}} \sum_{s_{i},s_{j}} (\delta(s_{i} - s_{j})-\frac{1}{q})$$
with the following text:...
