Questions tagged [spin-models]

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50 views

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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49 views

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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32 views

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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1answer
35 views

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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1answer
15 views

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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1answer
49 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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32 views

What are Skyrmion bubbles?

what exactly is the difference between a skyrmion and a skyrmion bubble? Thanks.
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1answer
20 views

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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1answer
52 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 ...
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2answers
57 views

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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1answer
49 views

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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38 views

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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0answers
31 views

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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3answers
306 views

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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18 views

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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18 views

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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1answer
37 views

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 ...
3
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1answer
64 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 $\{...
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31 views

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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24 views

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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0answers
16 views

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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0answers
34 views

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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0answers
31 views

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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72 views

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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1answer
106 views

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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1answer
34 views

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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1answer
66 views

$Z_2$ 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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0answers
27 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.
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1answer
50 views

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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0answers
48 views

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 ...
2
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2answers
565 views

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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0answers
35 views

Heisenberg Hamiltonian: Energy per site on the triangular lattice

I want to find the energy per site for the Heisenberg Model with 3D spin-vectors $\bf S_i$ on a 2D triangular lattice and nearest neighbor interactions. I have a Monte-Carlo Simulation (green +) and I'...
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0answers
63 views

Question about the Dyson-Schwinger equation for 4-point function of the SYK model

In studying the SYK model, I have no idea how to get the kernel $K(t_a,t_b,t_3,t_4)$ and $\Gamma_0(t_1,t_2,t_3,t_4)$ and also ladder diagrams in the Dyson-Schwinger equation for 4 point function of ...
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1answer
66 views

Mean field solution of the Ising Model

I try to compute the variational free energy in the Ising Model using the bogoliubov inequality: \begin{equation} \mathcal{F}(\lambda) = F_{0}(\lambda) \ + \ \langle\mathcal{H_{1}(\lambda)} \rangle_{...
3
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1answer
114 views

What is the Hilbert space of the SYK model?

In reading a recent preprint [1] contrasting bosonic models with local (tensor product) Hilbert spaces with SYK-like models of fermions, I realized I was confused about something. While I have a vague ...
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1answer
46 views

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^\...
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3answers
96 views

Phase transition on magnetic materials

Is ferromagnetic to paramagnetic phase transition a reversible process? If I start with a ferromagnetic material with a spontaneous magnetization below the Curie temperature, and then I start to heat ...
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0answers
60 views

$T$-duality symmetry of $SU(2)_1$ WZW model

For bosons at self-dual radius, the CFT has T-duality symmetry. My question is can we realize this symmetry on the lattice model? for example antiferromagnetic spin chain.
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59 views

Massive Thirring model as continuum limit of Heisenberg model

The massive Thirring model $S = \int d^2 x \left[ \bar{\psi} \gamma^\mu \partial_{\mu} \psi - m \bar{\psi} \psi - \frac{g}{2} \left( \bar{\psi} \gamma_\mu \psi \right) \left(\bar{\psi} \gamma^\mu \...
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0answers
53 views

Reference for Onsager’s solution of the 2D Ising model

I am interested in Onsager‘s famous paper “Crystal statistics I” where he derives the solution of the 2D Ising model. I am reading the original paper, but I search some supplementary material (blog, ...
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163 views

What is the Haldane phase?

I'm trying to look up what is the Haldane phase, but the only thing I find is examples of physical systems that "realize" the Haldane phase, such as the AKLT model, but no clear definition of what ...
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8 views

What are some good sources to learn Spin Glass theory?

I am looking for some self study and reference books or similar material to learn Random Fields and Spin Glass Theory. Would really appreciate any suggestions.
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1answer
119 views

What is breathing Kagome lattice?

I know what kagome lattice is. While reading some article I came to know the term breathing kagome lattice. Looked up the web didn't found any definitions of it. My suspicion is that when hopping ...
3
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1answer
130 views

What are $U(n)$ or $\mathbb{Z}_2$ quantum spin liquids?

Quantum spin liquid is a state of matter in which spins are correlated and fluctuate even at zero temperature. My question is about these terms in general. When we say that a state or a quasi-...
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11 views

How to obtain Hamiltonian parameters with EPR technique

I want to ask you how to obtain the parameters of the spin Hamiltonian of a system. I’m doing simulations with the EasySpin tool to obtain these parameters such as, J, the anisotropy factors D and E, ...
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0answers
82 views

Calculating expected values $\langle S_x \rangle$ and $\langle S_y \rangle$ in the Heisenberg model

Let's say, that we are considering the basic Heisenberg model with only two spin-particles. So our Hamiltonian can be written as follows: $$ H = \sum_{\langle i,i' \rangle} S^{(x)}_i S^{(x)}_{i'} + S^...
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0answers
87 views

Irrational Conformal Field Theory v.s. Non-Unitary Conformal Field Theory?

Unitary conformal field theories (CFTs) with irrational (or including the special case of rational) central charge is called irrational conformal field theory (ICFT). Irrational conformal field ...
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1answer
91 views

Calculating the local energy in neural network quantum state

given a Hamiltonian of Heisenberg 1D model as following: $$H = -J\sum_{I}\sigma_{i}^{z}\sigma_{i+1}^{z}$$ I am trying to solve it with a neural network function given by Restricted Boltzmann machine ...
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71 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 ...

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