Questions tagged [spin-chains]
One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.
221
questions
1
vote
0
answers
37
views
Parity of a 1d Ising model, and with higher order terms
I don't know if this should be asked here or in a math stack exchange, but I'll try here first.
Consider the classical 1d Ising model with periodic boundary condition:
\begin{equation}
H_2 (\vec{\...
- 368
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
0
votes
1
answer
72
views
Is there a name for a Heisenberg-like model, but instead of the ZZ operator, we have one that favor only spin-up-spin-up configurations?
I understand that the Quantum Heisenberg XXZ model in 1D has the form:
$$\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}...
- 700
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
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
1
vote
0
answers
43
views
Limit of solving the 1D Heisenberg chain to find the dynamics numerically
I am trying to simulate the dynamics of a 1D Heisenberg chain using Python.
I am going step-by-step.
There is an external magnetic field along +Z direction.
At first we consider a single classical ...
3
votes
1
answer
100
views
Time reversal symmetry and Bosonization
Bosonization of Spin 1/2s to fields $\phi(x)$, $\theta(x)$ is defined as (Ref: 'Quantum Physics in 1-D' by Giamarchi):
$S^z(x)=\frac{-1}{\pi}\nabla\phi(x)+\frac{(-1)^x}{\pi a}\cos 2\phi(x)$,
$S^x(x)=\...
- 358
2
votes
0
answers
88
views
How non-local can the interactions be for Density Matrix Renormalization Group (DMRG) to still work?
I know that Density Matrix Renormalization Group (DMRG) / Tensor Networks (TN) work well for local Hamiltonians, where on each site I have a fermion or boson, which only have nearest-neighbor ...
- 2,921
2
votes
1
answer
100
views
Coupling two Ising chains via an energy-energy interaction
Consider the transverse-field Ising model on a chain with periodic boundary conditions:
$$ H = -\sum_{i=1}^{L} \sigma_{i}^z \sigma_{i+1}^z + h \sigma_{i}^x$$
There's a phase transition at $h=1$, which ...
- 2,292
1
vote
2
answers
169
views
Mapping a 1D quantum Ising chain to a 2-dimensional classical Ising system
Going through Ref. 1 (I'll stick with the book's equation numbering), I'm learning about the mapping of quantum systems into classical systems. First of all let me briefly recap notation and some ...
- 1,989
1
vote
1
answer
200
views
Symmetry Protected Topology and Edge Modes
I have a spin 1/2 chain with open boundary conditions described by Hamiltonian $H=\sum_i \sigma_{2i}^z \sigma_{2i+1}^z$. From $H$ it's clear that boundary sites are decoupled from the rest of the ...
- 358
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
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