Questions tagged [spin-models]

A mathematical model used in physics primarily to explain magnetism.

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Time for ferromagnet to align with magnetic field

A ferromagnet is inside a solenoid. When the current in the solenoid flips its direction, the solenoid magnetic field flips. As a consequence, the ferromagnet magnetization flips. What determines the ...
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Spin-squeezing scaling with the number of particles in one-axis twisting hamiltonian

I am exploring the one axis twisting (OAT) hamiltonian $\hat{H}=\chi S_z^2$ with $S_z=\sum_{i=1}^N\frac{\sigma_z^i}{2}$ and considering the initial state to be $\left|\psi(0) \right>=\left|+x\right&...
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Diagonalizing the all-to-all quantum spin model (quantum Curie-Weiss) with uniform couplings

I am interested in diagonalizing the all-to-all quantum spin model \begin{align} \hat{H} = \frac{1}{2}\sum_{i,j \neq i} \hat{S}_i \cdot \hat{S}_j \end{align} or, if possible, a more general form ...
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Clarification of Dynamic, Static, and Equal-Time Spin Susceptibilities

I am trying to better understand the meaning of various spin susceptibility functions used in condensed matter physics especially in neutron scattering experiments. In the following definitions, $\...
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Generating Matrix Product States from a (random) vector

I try to decomposite an arbitrary quantum state into a matrix product state. For this i follow this paper by U. Schollwöck where especially section 4.1.3 is relevant. So far I did the following: ...
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Determining a gapped Hamiltonian from correlation function [closed]

Consider a spin Hamiltonian. I am interested in understanding how the spin-spin correlation function $C(r_{ij}) = \langle \boldsymbol{S}_i \cdot \boldsymbol{S}_j \rangle - \langle \boldsymbol{S}_i \...
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2 votes
1 answer
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Product of Majorana operators after a orthogonal transformation

The question I want to ask is the following: There are $N$ Majorana fermion modes: $\gamma_1, \gamma_2, \dots, \gamma_N$, and they satisfy the anti-commutation relation: $\{ \gamma_i, \gamma_j \} = 2\...
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Spinfoams and LQG

I know up to some degree how spinfoam models and LQG work, but there are some details that i still miss since i have still a naif knowledge. In the literature it as often said that an open problem is ...
LolloBoldo's user avatar
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3 votes
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Hamiltonians with collective quantum spins and their ground states

This feels like it could be a undergrad/grad-school quantum mechanics course level problem, or potentially something pretty interesting. I'd be happy with either answer, but I don't know which one is ...
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Phase space of the $n$-vector model

The classical Heisenberg model is described in terms of the three-component unit vector $S_a(x)$, which is a function of position, $$H=\int d^dx\frac{1}{2}\sum_{a,i}\left(\partial_i S_a(x)\right)^2.$$ ...
octonion's user avatar
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5 votes
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Mathematical meaning for Algebraic Bethe Ansatz

I'm a mathematician who's trying to understand the meaning of Algebraic Bethe Ansatz. What I understood is that when dealing with quantum integrable models (like XXZ Heisenberg spin chain), one is ...
BlueCharlie's user avatar
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Trying to understand Kitaev's calculation of relative Majorana number in two dimension

In appendix C.4.3 of "Anyons in an exactly solved model and beyond", Kitaev provides a proof of the fact that when the Chern number is odd, a vortex in the gauge field accompanies an ...
fdsfsd sd's user avatar
2 votes
1 answer
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Magnetization Plateau and Entanglement

In some low dimensional quantum spin systems, magnetization plateau is observed before the saturation in magnetization curve. . I have couple of questions related to this effect- It seems, ...
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Breaking a classical ground state degeneracy by a quantum term and order-by-disorder

Let’s assume we have a Hamiltonian for spin-1/2 particles with two terms, a classical interaction term and a “quantum” (non-diagonal) term. For simplicity, let’s assume that the quantum term is a ...
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Isotropic classical model with a different phase transition than its anisotropic quantum limit

I have often heard that the isotropic ferromagnetically-coupled 2d classical Ising model and the quantum 1d transverse field Ising model have similar phases and the same universality class of their ...
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Integrability of long range Heisenberg chain

Is the long range heisenberg spin 1/2 chain integrable? More generally, is the long range version of famous spin chain models integrable?
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Why is my Ising Gauge Theory calculation showing magnetization?

I wrote a Mathematica code to test out the 2d Ising Gauge Theory (by computing the exact partition fucntion) on a $3\times 3$ lattice (so that there are ($4\times 3$ spins on the horizontal bonds and $...
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1 vote
1 answer
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Ising model and the axiomatics of Statistical Mechanics

I am revisiting Statistical Mechanics to better understand models of spin glass and was wondering to what extent axiomatics of Stat.Mech. applies to an ensamble of spin configurations. In particular, ...
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Equivalent definitions of (dis)continuous phase transitions at criticality

Consider a classical lattice model on $\mathbb{Z}^d$ and suppose that the system undergoes a phase transition as you lower the temperature, i.e., increase $\beta$. The most general definition of a ...
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Two-dimensional Ising model for square lattices

Consider Onsager's exact solution of two-dimensional Ising model for square lattices with nearest neighbour interaction energy ‘J ‘being equal in the horizontal and vertical directions. At the ...
sangara's user avatar
1 vote
1 answer
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Obtaining the Ising and XY model from the XYZ $O(3)$ model

I have the classical XYZ model Hamiltonian $\mathcal{H}$ with a magnetic field $\vec{H}$ given as \begin{equation} \mathcal{H} = -\sum_{i< j} J^x_{ij}S_i^xS_{j}^x + J^y_{ij}i^yS_{j}^y+ J^z_{ij}S_z^...
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Tunneling lowers the energy of a ground state superposition of spins up and down in the quantum Ising model

Considering an Ising model in the quantum scenario in quantum spatial dimension d=1 (that corresponds to classical D=2=d+1 dimension). Starting with the Ising model hamiltonian under the approximation ...
Cuntista's user avatar
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2 answers
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What is a parent Hamiltonian? [closed]

The term is used throughout the literature but I was not able to find a definition or even a paper properly introducing the term. What does a Hamiltonian have to satisfy to be a parent Hamiltonian? An ...
Suppenkasper's user avatar
2 votes
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How to show random cluster models with non-integer $q$ have no local description?

It is known that the random cluster model with $q = 1$ corresponds to bond percolation, and $q = 2, 3, ... $ corresponds to the $q$-state Potts model. Both of these have a local description. What ...
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Spin lattice model fitting particular spin correlations and spectra

I want to write down a spin hamiltonian for $N$ sites (let's say for starters each site is spin = 1/2) that yields particular spin correlation functions, $$C_{ij} = \langle \hat{\vec{S}}_{i} \cdot \...
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Ground state of the Heisenberg XXX model with a coupling?

I have a one-dimensional Heisenberg chain with a Magnetic field with $N$ sites with $J>0$ \begin{equation} \mathcal{H} = -J \sum_{i = 1}^{N-1} \vec{S_i}\cdot \vec{S_{i+1}}- \sum_{i = 1}^N \vec{H}\...
QFTheorist's user avatar
2 votes
1 answer
104 views

Potts model 1st order transitions and the sensitivity of $q_c=4$ to microscopic details

The ferromagnetic $q$-state Potts model describes a lattice of classical spins $\sigma=\{1,2,...,q\}$ and has Hamiltonian with nearest-neighbor interactions $$ H = -\sum_{<ij>} \delta_{\sigma_i, ...
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Do particles with higher spins have shorter wavelengths?

When they say that a half-spin particle 'spins' through 720° before returning to its original state, does that mean it has travelled twice as far as an otherwise identical particle possessing the same ...
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3 votes
1 answer
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Necessity and Sufficiency of Yang-Baxter Equation for Integrability

Yang-Baxter Equation (YBE) seems to be a sufficient condition for integrability, i.e. if you have an $R$-matrix satisfying YBE, then the model is integrable. But how about the reverse? More ...
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Non-degeneracy of the ground states of quantum spin models

It is known that the ground state of some quantum spin models is non-degenerate. For example, the ground states of the quantum Ising model and the ferromagnetic Heisenberg model on the subspace of a ...
Gec's user avatar
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Hubbard-Stratonovich transformation for pairwise interactions

Consider a (classical) Potts-like model in which $N$ 'spins' can take on $Q$ distinct states; let $x_i$ be the state of the $i$th spin. The energy of a particular configuration is, $$ H = -\sum_{i<...
Emmy B's user avatar
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Higher-spin ising model optimization problem

Ising model is used as an Ising machine for solving the combinatorial optimization problems. The spin of the Ising machine for this application is normally 1/2. But I wonder if there is any ...
Alex's user avatar
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Lattice symmetry operations in strongly spin-orbit coupled systems

I think this is a FAQ when we are studying the rotation operations of lattice spin systems, but I can't find much references. Background Considering a Hamiltonian defined on a triangular lattice: \...
Seira Asakawa's user avatar
2 votes
0 answers
28 views

Integrable many-body system and complete set of conserved charges

In an integrable quantum system (say XXZ model), where there is an extensive number of conserved charges, does the set of local conserved charges obtained from expanding the log of the transfer matrix ...
symanzik138's user avatar
1 vote
1 answer
121 views

$p$-state Potts Model and symmetry [closed]

Consider a lattice spin system where the spin variable is the $i$th site can have $p$ values, 0, 1, . . . , p − 1, and the nearest-neighbor Hamiltonian describes the system This is called a $p$-state ...
Santanu Singh's user avatar
-1 votes
1 answer
208 views

Calculate partition function of 1D quantum Heisenberg models?

For the 1D Quantum Heisenberg Spin Model: $\displaystyle {\hat H = -\frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z + h\...
david's user avatar
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6 votes
2 answers
492 views

Is there Difference Between 1D and 2D in Spin model?

The Motivation is That:In the Tensor Network method, they say 'time evolution MPS(Matrix Product State) work quite well in 1 Dimension'. but as I think any 2D could be expressed by 1D for example in ...
Cha's user avatar
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1 answer
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Sublattice Magnetization of Heisenberg Model on triangular lattice

I'm trying to rederive the expressions for the square of the sublattice magnetization of the $120^\circ$ Neel antiferromagnetic (NAFM) and the stripe phase on the triangular lattice as shown in ...
WikawTirso's user avatar
2 votes
0 answers
72 views

Current Operators on Lattice

Peierls substitution method by taking the functional derivative of Hamiltonian can be used to determine the form of current-operator in continuum model (See Bruus-Flensberg) as well as lattice model. ...
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Total spin for the ground state of the Kitaev honeycomb model is 0?

We consider the Kitaev honeycomb model: \begin{align} H=\sum_{\langle ij\rangle_{\mu}}J_{\mu}S^{\mu}_iS^{\mu}_j. \end{align} If $J \equiv J_x=J_y=J_z$, the Hamiltonian can be written in \begin{align} ...
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0 answers
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Dimension of the eigenspace at de Almeida-Thouless calculation

I'm now reading the paper Stability of the Sherrington-Kirkpatrick solution. In the appendix, the eigenvalue problem $G \mu = \lambda \mu$ is being solved. At (A.5), the following form of the ...
movinggk's user avatar
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1 answer
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Plaquette operator in Kitaev honeycomb model

In his honeycomb model, Kitaev defines link operators \begin{equation} K_{jk} = \begin{cases} \sigma_j^x \sigma_k^x & \text{if }(j, k)\text{ is an }x\text{-link;}\newline \sigma_j^x \sigma_k^y &...
xzd209's user avatar
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1 vote
1 answer
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Simplification through the replica symmetry Ansatz

I'm going through some lecture notes dealing with the replica method and I feel like that I did not fully understand the concept of the replica symmetry (RS) Ansatz. At some point in the notes we come ...
SphericalApproximator's user avatar
2 votes
1 answer
74 views

Measuring vortices in numerical $XY$-like models

I am simulating an $XY$ model, meaning that I have a $L\times L$ lattice with a unit vector $\vec s_i$ associated with each site. Each $\vec s_i$ is univocally specified by its angle $\theta \in [0,2\...
sonarventu's user avatar
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Magnetization derivation for non-Ising systems

Can anyone help get me started on deriving a more general magnetization for non-Ising systems? I cannot find any information on a general derivation of the magnetization of 1D, 2D, or 3D systems of ...
AspiringPhysicist's user avatar
3 votes
2 answers
233 views

Explanation of massive Goldstone modes

I'm solving this exercise with a Heisenberg Hamiltonean in linear spin-wave theory and at some point we are asked to compute the dispersion relation at $k=0$, which leads me to finding two different ...
Rye's user avatar
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1 vote
0 answers
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Emergent higher symmetry breaking without topological order?

In this paper prof. Wen states that (p.6) a spontaneous higher symmetry broken state always corresponds to a topologically ordered state. Are there examples of simple (or not) quantum spin models ...
Kostas's user avatar
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1 vote
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Exact ground state degeneracy for quantum spin system with non commuting terms and its quantum phase transition?

Let's say I have a 2D quantum spin model of N spin-1/2 particles, with two terms: $$ H = -J \sum_N \prod_{i \in G} \sigma^x_i - h \sum_N \prod_{i \in G'} \sigma^z_i $$ The first is a collection of ...
Kostas's user avatar
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0 votes
1 answer
99 views

Integrability of spin central model

I have a central model of this form $$H = \sum_{i=1}^{N} S^z_0\otimes S^z_i$$ where the $S^z_i$ acts on the $i$th element of the environment, i.e. the Hilbert space is of the following form $\mathcal{...
raskolnikov's user avatar
2 votes
3 answers
531 views

Is there angular momentum conservation in models like the Ising model?

In Quantum Mechanics conservation laws are fundamental, I was thinking about spin altering models of interaction such as the Ising Model and realized that it isn't at all clear how angular momentum ...
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