All Questions
Tagged with spin-chains phase-transition
11
questions
1
vote
0
answers
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
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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
0
votes
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41
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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
2
votes
1
answer
100
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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
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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
0
votes
0
answers
380
views
Magnetization ($z$-basis) of a 1D Transverse Ising Model
I'm trying to find the magnetization $\langle\sigma_{z} \rangle$ of a 1D transverse Ising chain and plot it as a function of the transverse field $\lambda$. More specifically, I want to plot this for ...
0
votes
2
answers
191
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What is the ground state wavefunction of $\hat{H}=-J\sum\limits_{\langle i,j\rangle}\hat{S}_i^z\hat{S}_j^z,~~ (J>0)$?
The hamiltonian of a collection of noninteracting quantum spin-$1/2$ operators $\hat{S}_i$ fixed at each lattice site $i(=1,2,..., N)$ in presence of magnetic field ${\bf B}=B\hat{{\bf z}}$ $$\hat{H}=-...
- 26.8k
2
votes
2
answers
187
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Different concepts of phase transitions in spin models
I am currently revising the lecture notes in which different spin systems
are analyzed, focussing on the occurrence (or absence) of phase transitions.
Different techniques are applied to analyze the ...
- 123
3
votes
1
answer
169
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Why do matrix product states work at critical point?
Matrix product states satisfy the entanglement area law, which should be a property of gapped states.
But usually, MPS work well in 1D quantum phase transition problems.
As far as I know, ...
- 33
11
votes
1
answer
506
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Absence of phase transitions in quantum 1D systems at positive temperature
While it is generally said that there are no phase transitions in classical lattice systems in one spatial dimension, there are also exceptions to this rule. Rigorous proofs involve some fairly strong ...
- 336
7
votes
1
answer
395
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Kosterlitz-Thouless in the XXZ chain: instanton condensation?
The anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_n S^x_n S^x_{n+1} + S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$ is known to have the same physics as the two-dimensional classical XY ...
- 9,081