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Questions tagged [spin-models]

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What is the critical temperature for a BKT transition in the 2D quantum XY model with $S=1$ (not $S=1/2$)?

What is the critical temperature for a BKT transition in the 2D quantum XY model with $S=1$ (not $S=1/2$)? For instance, the classical XY model has KTc/J = 0.898 and the quantum XY model with S=1/2 ...
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1answer
27 views

Swap operation with the Heisenberg Hamiltonian

According to REF 1 equation 3, a SWAP operation can be achieved via the Heisenberg Hamiltonian for spins $H=J(t)\mathbf{S}_1\mathbf{S_2}$ $U^{1/2}_{SWAP}=e^{-i\frac{\pi}{8}}\exp\left(i\frac{\pi}{2}\...
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Is it possible to implement the Invaded Cluster Algorithm on a network of Ising spins rather than a lattice?

My main concern is how to know if a cluster has percolated the network. For a periodic square lattice it is easy to determine if the cluster percolates by looking at the size of the cluster (as given ...
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Troubles with Haldane Shastry Spin Chain

I'm actually reading the article of Shastry "Exact solution of an S= 1/2 Heisenberg Antiferromagnetic Chain with Long-rnaged interactions", Phys. Rev. Lett. 60, 639 (1988)" The articles ...
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Cavity method pedagogic references

I am looking for pedagogic references (textbook, review/expository articles, lecture notes, etc.) explaining the cavity method in detail. I am talking specifically about this: https://link.springer....
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1answer
152 views

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 ...
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1answer
70 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?...
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62 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 ...
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59 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 ...
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1answer
86 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=...
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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 ...
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1answer
122 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 ...
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32 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 ...
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48 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 ...
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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
86 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 ...
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1answer
76 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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74 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
75 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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20 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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25 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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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
127 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
47 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
59 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
200 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
379 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
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 ...
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1answer
36 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
135 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
59 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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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 ...
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1answer
53 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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2answers
148 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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66 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 $\...
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1answer
96 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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76 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
84 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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39 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
48 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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22 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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330 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 ...
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0answers
54 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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168 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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1answer
87 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 ...
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1answer
91 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
70 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 ...
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1answer
255 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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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 ...