Questions tagged [spin-chains]
One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.
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How does the proof for the area law for 1D systems work?
I am currently reading this paper in order to understand the proof of the area law for one dimensional, low energy systems such as 1D spin chains. The main area law theorem is given on page 13 and is ...
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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 ...
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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 ...
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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 ...
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How do boundary conditions change during a spin transformation?
I am currently reading the following review paper:
(1) Two Dimensional Model as a Soluble Problem for Many Fermions by Schultz et. al.
Equation (3.2), which is reproduced below, introduces the Jordan-...
user261609
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Ground state of sums of commuting, translated projectors
I have in mind a spin chain of length $L$ with local Hilbert space dimension $d$ and projectors $\{ P_i \}$ that act on $r$ sites $i, i+1, ..., i+r-1$. The projectors are identical besides which sites ...
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Can bond dimension vary from bond to bond?
Consider a bipartite system composed of subsystems $A$ and $B$, with corresponding Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$, spanned by $\{\chi_1,...,\chi_n\}$ and $\{\phi_1,...,\phi_m\}$, ...
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Jordan-Wigner Transformations on fermionic system
I've been trying to use Jordan-Wigner Transformations on a given fermionic Hamiltonian. The given Hamiltonian is: $$ \hat{H}= -\sum_{m=1}^{N}(J_z \hat{S}_{m}^{z} \hat{S}_{m+1}^{z} + \frac{J_{\perp}}{2}...
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Long-range correlations in transverse field Ising model
The transverse field Ising model in 1+1d has two phases: a symmetric "disordered" phase and a symmetry-breaking "ordered" phase. Both of these phases have a finite excitation gap. ...
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What is the $XXX_s$ Hamiltonian in terms of $\vec{S}_i \cdot \vec{S}_{i+1}$?
Faddeev, Takhtajan, and others united and discovered many integrable models through the Algebraic Bethe Ansatz. For example, the integrable spin-1/2 Heisenberg model
$$H_{1/2} = \sum_{i=1}^L \vec{S}_i ...
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How to add two Matrix Product States of different bond dimensions?
If I have the MPS representation of two quantum states, how do I add them? Note that the bond -dimensions need not be the same for the two MPSs.
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Parity of XYZ model ground state
I am considering the XYZ Hamiltonian (with PBC) $$\widehat{H}_{\mathrm{XYZ}}=\sum_{i=1}^{N} \left(\hat{\sigma}_{i}^{x} \hat{\sigma}_{i+1}^{x}+J_{y}\hat{\sigma}_{i}^{y} \hat{\sigma}_{i+1}^{y}+J_{z}\hat{...
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Dispersion Relation in Spin Chains in Terms of Quantum Speed Limits
Going off the dispersion relation derived by He and Guo
$$E_k = \sqrt{\left(\frac{J}{2}\right)^2 + h^2 + Jh\cos k}$$
Where $J$ is the nearest neighbour interaction strength and $h$ is the external ...
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Basis state of non-interacting fermions
I am trying to calculate the periodic dynamics of many-body systems (spin-$1/2$ $XY$) Hamiltonian, where,
\begin{equation}
H_1 = \sum_{i=1}^{N-1}(\sigma^{x}_{i}\sigma^{x}_{i+1}+\sigma^{y}_{i}\sigma^{...
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Relationship between Hartley entropy and local dimension
I am recently reading a paper about entanglement entropy. It mentions that if we consider a 1D spin chain and write a pure state in the matrix product state:
\begin{align}
|\psi\rangle = A^{\sigma_1}A^...
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