Questions tagged [spin-chains]
One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.
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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 ...
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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 ...
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"Entropy" of a set of correlators in a quantum system
Please forgive the ill-posedness of this question; I am hoping someone can help me formulate what I am asking more clearly.
Consider the ground state of a one-dimensional quantum spin chain on $N$ ...
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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}\...
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Calculate partition function of 1D quantum Heisenberg models?
For the 1D Quantum Heisenberg Spin Model:
$\displaystyle {\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}^z + h\...
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Emergent higher symmetry breaking without topological order?
In this paper prof. Wen states that (p.6)
a spontaneous higher symmetry broken state always corresponds to a topologically ordered state.
Are there examples of simple (or not) quantum spin models ...
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Exact ground state degeneracy for quantum spin system with non commuting terms and its quantum phase transition?
Let's say I have a 2D quantum spin model of N spin-1/2 particles, with two terms:
$$
H = -J \sum_N \prod_{i \in G} \sigma^x_i - h \sum_N \prod_{i \in G'} \sigma^z_i
$$
The first is a collection of ...
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Integrability of spin central model
I have a central model of this form $$H = \sum_{i=1}^{N} S^z_0\otimes S^z_i$$ where the $S^z_i$ acts on the $i$th element of the environment, i.e. the Hilbert space is of the following form $\mathcal{...
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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 ...
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Question about the 'reduced basis transformation'
I' ve been reading the review Ulrich Schollwöck: The density-matrix renormalization group in the age of
matrix product states (arXiv link)
and encountered with a question about the so called 'reduced ...
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Bethe ansatz and density of states for XXX spin chain
Consider the 1 dimensional Heisenberg antiferromagnet with Hamiltonian
$$ H = J\sum_{i=1}^L \vec S_i \cdot\vec S_{i+1}$$
and periodic boundary conditions.
I understand that this can be solved exactly ...
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answer
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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 ...
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Is the dot product of spins the only way to create a scalar (Hamiltonian) invariant under spin rotation?
I wanted to generalize the result for the following question for four spins 1/2: Most general form of a spin rotation invariant Hamiltonian?.
Assume that we have a Hilbert space for four spins $(\vec{...
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Connection between diffusion and non-integrable 1D spin chains
My question concerns non-integrable (à la Bethe) 1D spin chains.
Consider, for example, the 1D non-integrable Ising model
\begin{equation}
H = \sum_{i \in \mathbb{Z}}\sigma_{i}^{z} \sigma_{i+1}^{z} + ...
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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 + (\...
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