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Questions tagged [spin-models]

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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)....
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1answer
53 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
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1answer
45 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}\...
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0answers
64 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+...
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1answer
71 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: ...
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14 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 ...
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16 views

$p$-spin spherical spin glass

Consider the $p$-spin spherical spin glass model with Hamiltonian $$H_{N,p}(\sigma)=\frac{1}{{N}^{\frac{(p-1)}{2}}} \sum \limits_{i_1,...i_p} J_{i_1,...i_p} \sigma_{i_1} \sigma_{i_2} .. \sigma_{i_p} $$...
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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?
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1answer
49 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?
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1answer
34 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 ...
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1answer
42 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+...
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2answers
79 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&...
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2answers
127 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\...
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0answers
21 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
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1answer
32 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 ...
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1answer
122 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,...
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1answer
44 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 ...
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0answers
51 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
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1answer
46 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 ...
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0answers
121 views

Non-Linear Sigma Model

I read C. Mudry's book (chapter 3, p. 72, eq. 3.1a (the definition) and eq. 3.2a) and have several quaestions (1) He defines NL$\sigma$M through the following partition function: $$\mathcal{Z}(N,\...
3
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2answers
123 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 ...
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0answers
55 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
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1answer
72 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&\...
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0answers
66 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 ...
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1answer
70 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 ...
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0answers
37 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 ...
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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 ...
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0answers
15 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 ...
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0answers
12 views

Ballistic FET with channel made of ferromagnetic semiconductor

How do I find the characteristics, features, and differences of a standard ballistic FET (Field Effect Transistor) if the channel is made of a ferromagnetic semiconductor. Any papers/leads on how to ...
0
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0answers
62 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 ...
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0answers
201 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
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0answers
46 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. ...
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127 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 ...
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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
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1answer
73 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
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1answer
78 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 ...
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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 ...
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1answer
49 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
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1answer
193 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 ...
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0answers
33 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
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1answer
122 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 $$...
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0answers
62 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:...
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0answers
32 views

Introductory book on Post Newtonian (PN) approximation

I was wondering if someone could suggest me a good book on PN approximation (I am aware of the review papers by Luc Blanchet and Futamase & Itoh). I specifically want to know how the spin ...
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0answers
58 views

Boundary critical exponents of the 1D quantum XY model

Critical properties of the two-dimensional Ising model in the bulk and at the boundary are characterized by different critical exponent, see Ising model: exact results and McCoy: The boundary Ising ...
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54 views

References or resource recommendation for mapping of 1D spinless Hubbard model into XXZ Heisenberg model

I read from somewhere that 1D spinless Hubbard model can be mapped onto XXZ Heisenberg model but I don't remember from where did I read this sentence. I tried googling it but couldn't find any thing ...
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0answers
62 views

Correlation functions of exactly solvable 1D quantum models

Quantum 1d spin-1/2 transverse Ising and XY models are both related to 2d classical Ising model. Are there any known simple explicit relations between correlation functions of this models? Something ...
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2answers
208 views

Why is classical spin the spin-$\infty$ representation of $SO(3)$, not the spin-$1$ representation of $SO(3)$?

Given a classical spin model, $$H=\mathbf{S}_1\cdot \mathbf{S}_2\tag{1}$$ where $\mathbf{S}_i=(\sin\theta_i \cos\phi_i,\sin\theta_i \sin\phi_i,\cos\theta_i), i=1,2$ is the classical spin. Given a ...
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1answer
798 views

What makes an electron flip to spin-up?

The normal mode of spin for an electron is spin down: with angular momentum L pointing in the opposite direction of motion V (right) but, when a free electron approaches , say, a Helium ion it must ,...
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1answer
214 views

Heisenberg ferromagnet in continuum limit

I consider the case of the simple, say 2D, Heisenberg ferromagnet with exchange interaction between the nearest neighbors. The Hamiltonian is: $$H = -J \sum_{<ij>} \mathbf S_i \mathbf S_j,$$ ...
4
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1answer
801 views

Ground state degeneracy: Spin vs Fermionic language

Let us first consider the Hamiltonian of well-known 1D periodic Ising model as $$ H = -\frac{1}{2} \sum_{j=1}^N \sigma^x_j \sigma^x_{j+1} + \frac{h}{2}\sum_{j=1}^N \sigma^z_j. $$ Now, in the ...