All Questions
Tagged with spin-models quantum-spin
86
questions
2
votes
2
answers
108
views
Expressing the spin-1/2 operators in terms of the quantum rotor variables
In this paper, a spin-1/2 Hamiltonian is introduced on a cubic lattice [Eq. (12)]:
$$
H_c = -J \sum_{\Box} (S_1^+ S_2^-S_3^+S_4^- + \text{H.c.}),
$$
where the sum runs over all plaquettes of the cubic ...
- 49
3
votes
0
answers
44
views
What $(2+0)d$ classical model becomes the $(1+1)d$ Heisenberg model?
The $(1+1)d$ transverse-field Ising chain is closely related to the $(2+0)d$ Ising model. In particular, the $(2+0)d$ classical Ising model has a transfer matrix that can be written suggestively as $e^...
- 2,292
0
votes
1
answer
58
views
Showing that the ground state of the Heisenberg ferromagnet is an eigenstate of the Hamiltonian
The Hamiltonian of a Heisenberg ferromagnet in terms of $S^+, S^-, S^z$ is given by:
$$H = -\frac{1}{2}|J| \sum_{i,\vec{\delta}} \left[\frac{1}{2}(S_i^+S^-_{i+\vec{\delta}} + S_i^-S^+_{i+\vec{\delta}})...
- 665
7
votes
1
answer
209
views
Why is $H = J \sum_i (S^x_i S^x_{i+1} + S^y_iS^y_{i+1})$ always gapless for any spin $S$?
In the following I have in mind antiferromagnetic spin chains in periodic boundary conditions on a chain of even length $L$.
Consider the spin-$S$ spin chain
$$H = J \sum_{i=1}^L (S^x_i S^x_{i+1} + S^...
- 2,292
0
votes
0
answers
47
views
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&...
- 219
0
votes
1
answer
53
views
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 ...
- 858
2
votes
1
answer
80
views
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\...
- 1,181
3
votes
1
answer
92
views
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 ...
- 368
6
votes
1
answer
259
views
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 ...
- 113
0
votes
0
answers
60
views
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 ...
- 29
0
votes
0
answers
15
views
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 ...
- 310
0
votes
1
answer
4k
views
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}\...
- 904
0
votes
0
answers
30
views
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 ...
- 4,509
1
vote
0
answers
76
views
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 ...
- 5,697
0
votes
1
answer
112
views
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 &...
- 2,157
0
votes
0
answers
23
views
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 ...
0
votes
1
answer
102
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 $\mathcal{...
- 565
1
vote
0
answers
53
views
Ising configuration after rotation in one sub-lattice
I do not understand Eq. (5.9) in Auerbach's book Interacting electrons an quantum magnetism. Consider the general spin-$S$ Heisenberg model on a bipartite lattice with $N$ sites:
$$
H = \frac{1}{2} \...
- 660
3
votes
1
answer
237
views
Neel ordering on the square lattice vs mean-field AFM Heisenberg model
Question:
It seems like the Neel order of the AFM Heisenberg model on the square lattice is actually stronger than the (bipartite) fully-connected case. This seems counterintuitive. Am I simply wrong ...
- 321
2
votes
0
answers
98
views
Must spin glasses really have an exponential density of states close to the ground state?
I'm a complete beginner to spin glasses. I'm not even sure of the definition; I've mostly seen examples, like Sherrington-Kirkpatric with all-all pairwise normally distributed Ising interactions. ...
- 2,292
2
votes
1
answer
676
views
Transverse-field Ising model in the presence of a longitudinal field - ferromagnetic phase diagram
I am wondering what is the phase diagram of the transverse-field Ising model in the presence of a longitudinal field, in particular, a one-dimensional spin-1/2 chain with ferromagnetic interactions. ...
- 21
0
votes
1
answer
53
views
How to handle Dzyaloshinkii-Moriya imaginary terms in Heisenberg chain?
The DM interaction has three coordinate-specific terms when splitting it up. Two of these, the DM-x and DM-z terms, are imaginary when we transform them into series of raising and lowering operators. ...
- 11
0
votes
0
answers
34
views
Correlation functions of XY quantum chain
I'm trying to understand the calculation of the correlation functions in the XY quantum chain performed by Lieb, Mattis and Schultz in the paper "Two Solvable Models of an antiferromagnetic chain&...
0
votes
0
answers
61
views
Orientation of spin operators in Heisenberg model
What is meant by orientation of a spin operator (in, for example, Heisenberg model in condensed matter physics)?
For example, in Ising model we have Hamiltonian $H=\displaystyle\sum_{i,j}J_{ij}S_{i}S_{...
- 115
4
votes
0
answers
141
views
Energy gap of a Heisenberg model on bipartite lattices
Consider the antiferromagnetic Heisenberg model on some "graph" where each vertex corresponds to a spin-1/2 and the edges represent interaction between the vertices, i.e.,
\begin{equation}
\...
- 321
0
votes
0
answers
52
views
Possible (Minor) Error in Original Lieb-Robinson Bound Paper
Introduction
I was reading through Lieb and Robinson's original paper introducing their eponymous bounds, and I came upon the following statement:
The task remains of corroborating our assertions ...
3
votes
1
answer
559
views
Static spin structure factor VS equal-time spin structure factor
It looks like many papers (maybe all papers containing "static spin structure factor") use the terminology, static spin structure factor, to refer to the equal-time spin structure factor ...
- 123
4
votes
0
answers
89
views
Operator inequality between the Heisenberg Hamiltonian and the total spin
Consider a collection of $N$ spin-1/2 particles (qubits) with total spin
$$\vec{S} = \frac{1}{2}\sum_{n=1}^N \vec{\sigma}_n$$
and a Heisenberg Hamiltonian
$$H = -J \sum_{\langle n,m\rangle} \vec{\...
- 3,684
1
vote
0
answers
50
views
What is meant by spin temperature in the context of ultrafast demagnetization's three-temperature model?
Ultrafast demagnetization and associated fields often refer to the three-temperature model introduced by Beaurepaire. As the abstract says:
The relaxation processes of electrons and spins systems ...
- 46
1
vote
0
answers
109
views
Bogoliubov-Valatin transformation generalisation
Considering the following Heisenberg Hamiltonian (with spin $S$ , and $J<0$ for the case of an antiferromagnet) when we only consider interactions between first neighbors in a square lattice in the ...
- 1,124
1
vote
2
answers
218
views
How do boundary conditions change during a spin transformation?
I am currently reading the following review paper:
(1) Two Dimensional Model as a Soluble Problem for Many Fermions by Schultz et. al.
Equation (3.2), which is reproduced below, introduces the Jordan-...
user261609
1
vote
1
answer
280
views
Spin hamiltonian matrix representation
To preface, I'm an applied mathematician trying to parse the meaning of physics notation I've come across in a paper. My goal is to understand the setting in terms of matrices and vectors so that I ...
- 133
1
vote
2
answers
131
views
Why the entropy of non-zero nuclear spin is zero at $T = 0$?
When reading Concepts in Thermal Physics (second edition) by Stephen and Katherine about the concepts of the third law, I met with such a problem. The text reads as follows:
Consider a perfect ...
- 15
2
votes
2
answers
604
views
If a spin $\frac{1}{2}$ particle flips its sign after a 360° rotation, why don't theorists just say it rotated by 180°?
Usually, when a wave or wave-like object or system goes through a $180^{\circ}$ twist or turn or whatever, we say it is opposite to how it was oriented before, and if it came across its former self ...
- 4,509
2
votes
1
answer
153
views
Spin Glass Hamiltonian
Why do Edwards and Anderson use the hamiltonian
$$
H = \sum_{i,j} J_{ij} \mathbf{s}_i \cdot \mathbf{s}_j
$$
to describe the interactions in a spin glass?
Naively I would think that from the ...
- 754
0
votes
2
answers
39
views
How is two-level optical transition in a spin 1 system affected by the third level?
Suppose you have a spin-1 system. Let us resonantly drive the transition between any 2 levels (say 0 1 transition). How would the the presence of the third level (-1) state affect this transition?
We ...
- 21
3
votes
1
answer
336
views
Conserved charge in Density Matrix Renormalization Group (DMRG)
Currently I am facing a problem which relates to the conserved quantities in DMRG. I use old-fashioned DMRG (Steven White approach) to compute the ground state of certain models. However, the ground ...
- 413
0
votes
0
answers
31
views
What is helical Dirac nature?
A concept in Spintronics which can not be found on Wikipedia. The picture is from a review of Spintronics of 2016 by Fert.
- 1
0
votes
0
answers
121
views
Is it possible to construct an operator for $z$-component of spin for a 2D system?
Let's say we have an arrangement of spins in 2D space (as given in the below picture).
Assume that the $z$-axis is out of the plane and a spin (circled in red) makes an angle $\theta$ with the $x$-...
- 1,335
1
vote
1
answer
110
views
Writing down a Hamiltonian that couples spin and phonons
I am studying spin dynamics and am trying to write down a Hamiltonian that couples the spins with the phonons. I have the following interacting spin Hamiltonian
$$H_{s}=\sum h_{i}S_{i}+H_{\text{...
- 21
1
vote
0
answers
69
views
Time evolution of spin with Anti-symmetric (Dzyaloshinkii-Moriya) interaction
I am trying to simulate the time evolution of a spin in spin chain interacting via Dzyaloshinkii-Moriya interaction. The Hamiltonian is of the form
$$H_{A}=J_{A}\sum_{i}(S^{x}_{i}S_{i+1}^{y}-S^{x}_{i+...
- 21
1
vote
0
answers
487
views
Commutator of Hamiltonian and the spin sum
For a 1-D Heisenberg quantum spin chain the Hamiltonian is given by:
$$H=-\sum_{j=0}^{N-1} J_{i,i+1}\boldsymbol{\sigma}_j^i \cdot\boldsymbol{\sigma}_{j+1}^i -\sum_{j=0}^{N}h_j\sigma_j^z$$
where $\...
- 11
2
votes
1
answer
307
views
Describing a subspace of a Hilbert space of $N$ spins 1/2
Consider having $N$ spins $1/2$, so the overall state of $N$ particles can be described by the total spin value $S=0 \ldots N/2$ (let us set $N$ to be even for simplicity), and the projection of the ...
- 133
0
votes
0
answers
36
views
Finding coupling between crystal sites related by symmetry
Say I have a crystal and the coupling between sites is described by the following local, model Hamiltonian (a spin 1/2 system):
$$
\hat{H}_{i,j} = J \bf{S}_i\cdot\bf{S}_j+\bf{d}\cdot\left[\bf{S}_i\...
- 130
0
votes
1
answer
61
views
Indistinguishability in Spin-1/2-system
In terms of statistical physics I thought the microcanonical partition function can be interpreted as summing over all possible quantum numbers. Neglecting indistinguishability in the case of two ...
- 71
2
votes
1
answer
53
views
Why is $\sum_{i=0}^N S_i^z S_{i+1}^z |\uparrow ... \downarrow_n ... \uparrow \rangle = \frac{1}{4}(N-4)$?
I am following these (http://edu.itp.phys.ethz.ch/fs13/int/SpinChains.pdf) lecture notes and I can't understand why given the following XXX Heisenberg hamiltonian
$$
\mathcal{H}=\frac{J N}{4}-J \sum_{...
- 1,544
4
votes
1
answer
201
views
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 ...
0
votes
1
answer
75
views
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 + \...
- 341
3
votes
1
answer
436
views
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 ...
- 33
1
vote
1
answer
37
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 ...
user257090