All Questions
Tagged with spin-chains symmetry
14
questions
1
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0
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23
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Can the edge degeneracy in spin-$2$ AKLT go away on an arbitrarily small $SO(3)$-symmetric bulk perturbation?
I am learning about SPTs, or symmetry-protected-topological phases. There is a rich structure in antiferromagnetic spin chains. The Heisenberg point is gapless in half-integer-spin antiferromagnets ...
- 2,292
2
votes
1
answer
134
views
Phase transitions in the XXZ model
Consider the one-dimensional quantum XXZ model defined by the Hamiltonian:
$$
H = J \sum_{i} \left (X_i X_{i+1} + Y_i Y_{i+1} + \Delta Z_i Z_{i+1} \right).
$$
First, let us focus at zero ...
- 31
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
2
votes
1
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573
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$G$-injective MPS and symmetry-broken phases
First, a little bit of motivation. I was reading the paper "Matrix Product States and Projected Entangled Pair States" to try to learn more about MPS representations of symmetry broken ...
- 2,292
1
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0
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70
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CFT description of polynomially degenerate, critical spin-chain
For length $L$ spin chains described by conformal field theories, there's a nice a way to extract the central charge via fitting the following ansatz for the entanglement entropy of the ground state:
$...
- 2,292
3
votes
2
answers
350
views
Is there a zero correlation length spin-$1$ chain in the Haldane phase?
The ground state of the spin-$1$ AKLT model gives an example of a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-protected topological (SPT) phase, the Haldane phase. This state is a nice example of the ...
- 2,292
2
votes
1
answer
387
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How can I actually get to the AKLT state from a product state in finite depth?
I'm currently learning about symmetry-protected topological phases in one dimension. The ground state of the AKLT model provides one such example. In particular, the AKLT state for any length $L$ ...
- 2,292
2
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0
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89
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How to stack two Haldane chains?
This questions is a follow up to a pervious question of mine:
Inverse of Haldane phase?
Now that I know that Haldane phase is it's own inverse, I am having trouble is visualizing how could we stack ...
- 513
2
votes
1
answer
98
views
Inverse of Haldane phase?
Based on what I have learned so far, Haldane phases are a nontrivial SPT for 1D spin-1 chains. The trivial phase acts as an "identity" under the group of SPT phases ( with stacking as the ...
- 513
1
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0
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178
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Bosonization of critical theories without $U(1)$ symmetry?
When studying lattice models using bosonization, we expect the total charge is conserved so that the elementary excitation is particle-hole-like bosonic degrees of freedom. How about models without $U(...
- 356
3
votes
2
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652
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Jordan-Wigner transformation for lattice models without $U(1)$ symmetry
The Jordan-Wigner transformation is a powerful approach to studying one-dimensional spin models. The following dictionary between spin operators and creation/annihilation operators for fermions allows ...
- 759
3
votes
1
answer
477
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What are the differences between Haldane phase, non-interacting topological insulator/superconductor, and SPT order?
Haldane phase, and non-interacting topological insulator/superconductor are often regarded as examples of symmetry protected topological (SPT) orders.
- 13.2k
0
votes
1
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241
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The most general $SU(2)$ invariant spin-$1/2$ Hamiltonian on 5 sites
I have periodic chain of spins $s=1/2$. I want to know what is the most general $SU(2)$ invariant and translation-invariant Hamiltonian. My guess is:
$$\sum_i (j_1 S_i \cdot S_{i+1}+j_2 S_i \cdot S_{i+...
- 1
3
votes
1
answer
111
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Invariants of spin chains
I consider modelling a particular physical phenomenon using a spin chain (Ising, XYZ, Potts, etc.). Once I establish the mapping from experimental data to the states of spins for, I get the values $\{...
- 2,921