All Questions
12
questions
4
votes
0
answers
47
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Are strong correlations of boundary spins possible in the absence of long-range order in the bulk?
Question about one-dimensional models with short range interaction of quantum spins, such as transverse Ising and Heisenberg models. Are there any examples when, in the ground state of the system, the ...
- 5,697
0
votes
0
answers
52
views
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:
...
- 23
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
155
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How to take into account finite temperature in transverse Ising chain?
A similar question has already been asked here
What I'm wondering is how to take into account finite temperature in the transverse Ising chain and see how that affects the magnetization. The reason ...
- 741
1
vote
0
answers
204
views
Parity of XYZ model ground state
I am considering the XYZ Hamiltonian (with PBC) $$\widehat{H}_{\mathrm{XYZ}}=\sum_{i=1}^{N} \left(\hat{\sigma}_{i}^{x} \hat{\sigma}_{i+1}^{x}+J_{y}\hat{\sigma}_{i}^{y} \hat{\sigma}_{i+1}^{y}+J_{z}\hat{...
4
votes
0
answers
230
views
Heisenberg equation of motion and continuum limit
Given the quite simple Hamiltonian
$$\hat{\mathcal{H}}=\sum_n\big(\hat{S}_n^+\hat{S}^-_{n+1}+\hat{S}_n^-\hat{S}^+_{n+1}\big)$$
on a 1D spin chain, it basically interchanges two spins lying next to ...
- 294
1
vote
0
answers
487
views
Commutator of Hamiltonian and the spin sum
For a 1-D Heisenberg quantum spin chain the Hamiltonian is given by:
$$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$$
where $\...
- 11
2
votes
1
answer
53
views
Why is $\sum_{i=0}^N S_i^z S_{i+1}^z |\uparrow ... \downarrow_n ... \uparrow \rangle = \frac{1}{4}(N-4)$?
I am following these (http://edu.itp.phys.ethz.ch/fs13/int/SpinChains.pdf) lecture notes and I can't understand why given the following XXX Heisenberg hamiltonian
$$
\mathcal{H}=\frac{J N}{4}-J \sum_{...
- 1,544
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:
$$H = J\sum_{<n,m>} S_nS_m = J\sum_{<n,m>}[S^{z}_n S^{z}_m + \...
- 341
0
votes
1
answer
405
views
Bose-Einstein distribution and magnons
I have some doubt about the Bose-Einstein distribution for magnons/spin-waves.
A one-dimensional ferromagnet placed in an external magnetic field $\mathbf{B} = B\, \hat{z}$ obeys the Hamiltonian
$$H ...
- 451
2
votes
0
answers
124
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. ...
- 451
1
vote
0
answers
153
views
Boundary critical exponents of the 1D quantum XY model
Critical properties of the two-dimensional Ising model in the bulk and at the boundary are characterized by different critical exponent, see Ising model: exact results and McCoy: The boundary Ising ...
- 5,697