All Questions
Tagged with spin-chains quantum-mechanics
54
questions
2
votes
0
answers
33
views
Difference between boundary conditions in thermodynamic limit
Consider a model for a spin chain. I somehow am able to find a general formula for the expectation value of some observable in both periodic and open boundary conditions. ie.,
under PBC, I have
$\...
- 193
4
votes
0
answers
47
views
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
1
vote
1
answer
113
views
What is the Haldane gap?
The Haldane Phase is a topological phase of matter in which a Haldane gap opens due to the breaking of either time-reversal symmetry or inversion symmetry. Physically speaking, what is the "...
- 43
1
vote
0
answers
44
views
What is the appropriate 'Page Value' for entanglement entropy in a symmetry sector, say for example with a $U(1)$ symmetry?
Don Page derived the formula for the average entropy of a subsystem of a quantum system (assumed to be in a pure state), if the system is partitioned into two subsystems of dimensions $m$ and $n$, ...
- 43
0
votes
0
answers
45
views
Transforming spin operators into fermionic operators and finding their anticommutation relations
The Jordan-Wigner transformation (JWT) is a method used in quantum mechanics to map spin operators, which are typically associated with spin-1/2 particles, to fermionic operators, which describe ...
0
votes
1
answer
108
views
Can the hybridization of edge states in the 1D SSH model be observed numerically?
So I was reading the lecture notes by Asboth on topological insulators . In the first chapter the SSH model is discussed :
$H_{SSH} = \sum_{i = 1}^N v|i,A\rangle \langle i,B | + h.c. + \sum_{i = 1}^{N-...
- 70
1
vote
1
answer
77
views
A simple calculation in the XXX spin chain
I am currently studying the XXX Heisenberg spin chain using the Bethe ansatz. I am working in the string hypothesis and I am having troubles deriving a simple expression for Fourier transformation of ...
0
votes
0
answers
41
views
Example of first-order quantum phase transitions between two gapped phases with unique ground state in local 1d spin chain without extra symmetry
I'm trying to better understand first-order phase transitions in local, 1d quantum systems, particularly spin chains. I realized that I don't have a strong understanding of what's possible and ...
- 2,292
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
6
votes
2
answers
26k
views
Ground state energy of infinite Heisenberg XXX model with open or periodic boundary conditions equal?
I was wondering if there is anywhere a formal proof that shows that the ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with ...
- 98
2
votes
0
answers
96
views
Obtaining a Matrix Product State (MPS) using Schmidt Decomposition for a Tripartite State
I understand that one method to derive an MPS representation of a quantum state involves applying the Schmidt decomposition $ N−1$ times. While I'm familiar with the diagrammatic notation, I wanted to ...
- 1,198
0
votes
1
answer
287
views
MPS canonical form
If I express a MPS in its (left, right or anything else) canonical form, does this representation encode all Schmidt decompositions between a subsystem and its complement,rather than only the Schmidt ...
- 325
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
1
answer
56
views
Why one can say that the inner product in $\bigotimes\limits_{n=1}^{N}\mathbb{C}_n^2$ has the following form?
In the article "Quantum theory of measurement and
macroscopic observables" of Klaus Hepp it is said that for a lattice of $N$ spin $\frac{1}{2}$ systems each in $\mathbb{C}^2$, so that the ...
- 276
7
votes
1
answer
576
views
Most general form of a spin rotation invariant Hamiltonian?
I am told that the most general form of a spin rotation invariant Hamiltonian for two systems 1 and 2 both with spin $S$, i.e., the spin operators
\begin{align}
(\hat{S}_1^x)^2 +(\hat{S}_1^y)^2 + (\...
- 904