Questions tagged [spin-models]

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In what sense is a magnon a particle with momentum $p$ moving in the groundstate?

(I realize this might be a more general question completely unrelated to magnons) To illustrate my question, consider the XXX Heisenberg model, $$ \mathcal{H}=\frac{J N}{4}-J \sum_{i} \left( \frac{1}{...
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Why is $\sum_{i=0}^N S_i^z S_{i+1}^z |\uparrow … \downarrow_n … \uparrow \rangle = \frac{1}{4}(N-4)$?

I am following these (http://edu.itp.phys.ethz.ch/fs13/int/SpinChains.pdf) lecture notes and I can't understand why given the following XXX Heisenberg hamiltonian $$ \mathcal{H}=\frac{J N}{4}-J \sum_{...
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Clebsch-Gordan coefficients, spin networks and intertwiners

After spending some time with LQG books and articles i have still some problems regarding concepts of this theory. Spin network is built from lines labeled by spin label $j$ and since angular momentum ...
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Monte Carlo sampling libraries for many-body Hamiltonians

This is possibly a very broad resource request question. I would like to know about the various Monte-Carlo libraries/codes that are used by researchers for sampling from the ground states or thermal ...
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Different sectors of the Ising gauge theory

The Hamiltonian of Quantum 2D Ising gauge theory is given by: $$ H=-\sum_p \prod_{i\in \square}\sigma^z_i -g \sum_{i\in \text{links}} \sigma^x_i$$ This $H$ is invariant under the local symmetries: $$ ...
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Antiferromagnetic chain from Altland/Simons book (p.81)

In Condensed Matter Field Theory (2nd edition) by Altland/Simons there considered antiferromagnetic chain with Hamiltonian: $$H = J\sum_{<n,m>} S_nS_m = J\sum_{<n,m>}[S^{z}_n S^{z}_m + \...
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Why can't I diagonalize the antiferromagnetic Heisenberg Hamiltonian? [closed]

So I started with the antiferromagnetic Heisenberg Hamiltonian with $J =-1 $: $H = -(-1) \sum_{NN}\sigma_i\cdot\sigma_j$. I wrote the Pauli-matrices as their matrix-representation and got for eg. the ...
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Is there any study about using DMRG to simulate two spin chains coupled at only several sites on each chain?

Is there any study about the DMRG simulation of such kind of systems? or Each blue site is a spin, for example. Only one or several spins on each chain are coupled.
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103 views

Why is the sequence of limits $\lim\limits_{V\to\infty}\lim\limits_{B\to 0}m(B,V)$ when reversed does not give the same result?

For spontaneous magnetization $m$ in a sample of volume $V$, what do the limiting operations $$ \lim\limits_{V\to\infty}\lim\limits_{B\to 0}m(B,V)=0,\\ \lim\limits_{B\to 0}\lim\limits_{V\to\infty}m(B,...
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Is it possible a state be a Quantum Spin Liquid and has long range order at the same time?

Quantum spin liquid ([QSL])1 is usually defined as a kind of phase that (1) no long-range order, (2) has long-range entanglement and (3) hosts emergent gauge structures or fractionalized excitations. ...
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Linear spin wave theory applied to 2D Heisenberg antiferromagnet

I have recently studied the Holstein-Primakoff transformation, and saw how it can be used to diagonalize the Heisenberg Hamiltonian and find the magnon dispersion relation. For the antiferromagnetic ...
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Can you have “ferromagnetic” order that preserves time-reversal symmetry?

Usually in systems with ferromagnetic order, the spin $\mathrm{O}(3) = \mathrm{SO}(3) \times Z_2^t$ (where $Z_2^t$ represents time-reversal) symmetry is broken down to $\mathrm{SO}(2)$. Is it possible ...
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2D Ising model on curved surface

What will be the sensible extension of the 2D Ising to some curved surface - for instance, for a sphere or even something non-orientable? For the flat space energy is given by well-known expression: $$...
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Is there existing research suggesting that critical systems' power spectra are correlated with their eigenspectra?

I am interested in how the spatial and temporal spectral exponents – in other words the exponents of the power spectrum and eigenspectrum – of a high dimensional system at criticality are related. It ...
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Rate of deformation and spin tensors

I am studying a set of notes by Ellen Kuhl of Stanford university on continuum mechanics, where I encountered the rate of deformation and spin tensors, as discussed in this set of notes. This set of ...
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What is the connection between vertex/spin models and gauge theory?

In the usual formulation of lattice gauge theories, one considers gauge variables on the links of a lattice (often hypercubic) taking value in some representation of a gauge group, $U_{ij} \in G$. The ...
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Are all gapless acoustic magnon modes essentially Goldstone modes?

We know gapless Goldstone mode appears when the system exhibits spontaneously symmetry broken. Does this means whenever we observe gapless acoustic modes it is Goldstone mode i.e. spontaneous symmetry ...
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Is the fully connected Potts model exactly solvable?

Suppose that we have "spins" $\sigma_1,\dots,\sigma_N$, with $\sigma_i\in\{1,\dots,q\}$, for $i=1,\dots,N$, and that our Hamiltonian is $$ H = -\frac{J}{N} \sum_\stackrel{i,j=1}{i\ne j}^N \...
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What if we used “Schwinger Fermions” to study spin waves?

When studying spin waves excitations in the Heisenberg Hamiltonian people often use Schwinger Bosons representation or Holstein-Primakoff which is a specific case of Schwinger Bosons. This leads you ...
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Is the Aubry-André-Harper (AAH) model renormalizable?

We know the Aubry-André-Harper (AAH) model can have a local/delocal phase transition at $\Delta/J=2$, but can this phase transition point be obtained by RG procedure? Or can this local/delocal phase ...
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Partition function for 4 spins

I was reading some notes by John Chalker on order by disorder and encountered a classical spins partition function calculation. I could not follow the integration, i.e. obtaining eqn. (1.7) from (1.5) ...
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From spins to fields

In statistical field theory, one usually considers the so-called Landau Hamiltonian: $$\beta H = \int d^{d}x\bigg{[}\frac{t}{2}m^{2}(x) + \alpha m^{4}(x)+\frac{\beta}{2}(\nabla m)^{2}+\cdots+ \vec{h}\...
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Symmetry action on spin liquid ansatz

In mean-field parton theory of Heisenberg model, the hamiltonian can be written as $$H_{MF} = \sum_{\langle i j \rangle} Tr(\psi_i^\dagger U_{ij} \psi_j) + \sum_i Tr(\psi_i^\dagger (\vec{a}_i\cdot \...
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Meaning of elastic energy formulation

In Chaikin's Principles of Condensed Matter Physics, in chapter 6 ("Generalized Elasticity"), on pg. 290, there is a formulation of what he refers to as an elastic energy associated with gradients of ...
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57 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 ...
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What are Skyrmion bubbles?

what exactly is the difference between a skyrmion and a skyrmion bubble? Thanks.
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Macroscopic properties of individual spins in a material (magnet) - and their behavior under rotations

I am wondering (A) about the influence of individual spins on the behavior of a macroscopic object (B) and about the influence of rotating the macroscopic object on the internal spins To approach ...
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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 ...
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Doping and inter plane coupling for cuprates

I'm not very familiar with high-Tc and I have naive questions on cuprates materials (CuO2). It seems common that everyone treats it as a 2D material for good reasons: in undoped system, there are two ...
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Difference between thermal hall and phonon hall effect

I know of thermal hall effect which refers to a charge-neutral excitations exhibit hall effect that transport heat: for example, a heat current along x-direction generates a temperature gradient along ...
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How to prove identity $\langle \mathbf{S} \rangle^2 + \langle \mathbf{Q} \rangle^2 = 4/3$ for any spin-1 wavefunction?

Is there an easy way to prove that for an arbitrary wavefunction of spin-one $$\langle \mathbf{S} \rangle^2 + \langle \mathbf{Q} \rangle^2 = 4/3$$ where $\mathbf{S} = (S_x, S_y, S_z)$ for spin-1, ...
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Product over integral representations and steepest descents

Suppose we have a product of Dirac or Heaviside functions in the context of a spin model and we use an integral representation to express these in order to do some manipulations, more specifically ...
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What do physicists mean by solving the Ising model?

To me, an Ising model is a setting of discrete objects, that have attributes (spins) that contribute to energy based on interactions with nearby objects. With the energy function (Hamiltonian) written ...
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Spin pumping: interface between a Ferromagnetic and a normal metal

We know that at the interface $(y=0^+)$ of a ferromagnetic material (FM) with excited magnons, and a normal metal (NM), there is an injection of spin current (or spin pumping) arising from the magnons ...
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How to get algebraic PSG solutions once we got the constraints?

The question is more technical than conceptual. I've been trying to understand the classification of spin liquids as done by Prof.Wen. I have got the constraints on IGG(Invariant gauge group) elements ...
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Is the definition of gap of a Hamiltonian, i.e. difference between two distinct eigenvalues, restrictive?

The spectral gap of a quantum model or a Hamiltonian, in the context of whether it is a gapped or gapless model, is often defined as the difference between the two lowest distinct eigenvalues of the ...
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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 $\{...
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What are differences among chiral, helical and spiral in quantum spin context?

For chiral, as far as I know, there are vector chirality $\kappa_{ij}=\mathbf{S}_{i}\times \mathbf{S}_{j}$ which characterizes non-collinear spin arrangement and scalar chirality $\chi_{ijk}=\mathbf{S}...
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Ferromagnetic/Paramagnetic Phase Transition in a Non-Zero External Magnetic Field

I'm new to condensed matter theory, especially spin-glass systems. I understand that the Ising model exhibits a Phase Transition when there is no external magnetic field (h=0). And that at the ...
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How to understand spin-phonon coupling in any material? Differs from electron-phonon coupling?

Spin-phonon coupling is an interesting phenomena, especially, in the case of multiferroic materials. Its origin is said to be the exchange interaction of magnetic ions. In that case, any magnetic ...
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Temperature of spin-glass transition

In the literature on spin glasses I see a lot of theoretical phase diagrams and experimental plots with a definite spin-glass transition temperature $T_\mathrm{G}$. For example, in this figure from J....
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De Almeida-Thouless line and spin glass in the Hopfield network

From the SK model, the Almeida-Thouless line appears to divide the stable paramagnetic phase and unstable spin-glass phase in the presence of an external magnetic field. However, in the case of a ...
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Physical argument that the Ising model has no phase transition for nonzero external field

I have seen rigorous proofs on why the Ising model does not have a phase transition for $h\ne 0$ (via the Lee-Yang theorem or GHS inequality). However, these proofs don't shed much physical intuition ...
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Implementation of neural network quantum states of the anti-ferromagnetic Heisenberg model

I'm studying this Science paper "Solving the quantum many-body problem with artificial neural networks" and looking into the implementation of the Anti-ferromagnetic Heisenberg model. The Hamiltonian ...
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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 ...
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$Z_2$ symmetry breaking in XXZ model

I have a question about an statement that is said in the paper Entanglement and spontaneous symmetry breaking in quantum spin models (Phys. Rev. A 68, 060301(R), (2013)). It is related to the XXZ ...
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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.
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Mermin-Wagner in Second Quantization

The following link provides a detailed proof of the Mermin-Wagner Theorem for the quantum spin model. However, one thing that I don't quite understand is why the underlying Hilbert space $H_\Lambda$ ...
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Order parameter fluctuations in the mean field model for ferromagnetism (mathematical approach)

I'm a math student taking first steps into statistical mechanics and... I need help! Consider the Curie-Weiss model (i.e. the classical mean field model for ferromagnetism). If $N$ is the number of ...
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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 ~...

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