Questions tagged [spin-chains]
One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.
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Verification of an algebra involving Pauli Matrices and Jordan-Wigner Transformation
I was working out the Review article Geometry and non-adiabatic response in quantum and classical systems, Kolodrubetz, Polkovnikov et al. . Due to a context from ...
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Coupling three Ising chains via an energy-energy-energy interaction
I want to note that this question is related to another one I asked involving just two chains coupled by an energy-energy interaction. I'm choosing to ask them separately because I suspect they may ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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Recipe for finding out the effective spin chain model/hamiltonian for the low dimesional spin chain materials
I am interested in modeling or finding an effective Hamiltonian (quantum spin chain model) for low-dimensional magnetic materials. Let's consider the case in 1D only for simplicity.
As we know in ...
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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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$G$-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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iTEBD real time evolution for 3-body time evolution operator
I am trying to implement the iTEBD algorithm for real-time evolution of the PXP model. Here, $P$ is the projector onto the ground state, and $X$ is the Pauli spin matrices.
I know for the 2-body case, ...
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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:
$...
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What is $v$ in conformal field theory?
In reading about conformal field theory applied to spin chains of length $N$, I've seen the following expression several times, describing how the central charge $c$ can be extracted from the ground ...
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Normalization in tensor networks [closed]
I am trying to implement the iTEBD algorithm for the $PXP$ model, i.e, the hamiltonian is
$$H = \sum_iP_{i-1}X_iP_{i+1}.$$
Here $P$ is the projector onto the ground state and $X$ is the usual pauli x ...
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How do you calculate the entanglement entropy of a tensor network?
I found that the entanglement entropy can be calculated using the Schmidt coefficients of the state, using
$S = -\sum_i|\alpha_i|^2\log(|\alpha_i|^2)$
In the case of tensor networks, does this simply ...
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Why the ground-state energy of S-1/2 Anti-Ferromagnetic Heisenberg Chain is not$-\frac{N}{4}J$
The Hamiltonian of traditional Heisenberg model is
$$\hat H = J\sum_{<i,j>}\vec{S_i}\cdot\vec{S_j}=J\sum_{<i,j>}\left(S_i^zS_j^z+\frac{1}{2}\left(S_i^+S_j^-+S_i^-S_j^+\right)\right)$$
if J ...
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Magnons and creation and annihilation operators
I am trying to obtain the spin waves (or magnons) arising from a 1D Heisenberg spin-chain, namely
\begin{equation}
{\cal H}=-J\sum_{i=1}^N \mathbf{S}_i\cdot \mathbf{S}_{i+1}
\end{equation}
After ...
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Transverse-field Ising model in the presence of a longitudinal field - ferromagnetic phase diagram
I am wondering what is the phase diagram of the transverse-field Ising model in the presence of a longitudinal field, in particular, a one-dimensional spin-1/2 chain with ferromagnetic interactions. ...
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How to handle Dzyaloshinkii-Moriya imaginary terms in Heisenberg chain?
The DM interaction has three coordinate-specific terms when splitting it up. Two of these, the DM-x and DM-z terms, are imaginary when we transform them into series of raising and lowering operators. ...
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How to efficiently get the largest probabilities / amplitudes of a quantum state stored as an MPS?
Let's say, that we have the following pure, superposition state
$$ |\psi \rangle = \frac{1}{\sqrt{2}}|000001 \rangle + \frac{1}{2}|101101 \rangle + \frac{1}{2}|100100 \rangle $$
stored in the MPS form....
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Is there a relationship between spin correlation and entanglement entropy?
Can someone explain whether there is a connection between spin correlation in say a 1D Heisenberg chain and its entanglement entropy? I'd say, albeit naively, that there is just from their concepts. ...
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Writing the Random Matrix model corresponding to any physical hamitonian model
I am an amateur in Random Matrix Theory (RMT). In RMT, we start with ensemble of a random matrices of a certain symmetry classes (GOE, GUE..) to find the various distribution of our interest, e.g.- ...
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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 ...
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Magnetization in the quantum Ising model
In the quantum Ising model $$\hat H=-J\sum_{j=1}^n \hat\sigma_j^z\hat\sigma_{j+1}^z-g\sum_{j=1}^n\hat\sigma_x $$ there is a quantity of interest, namely the average magnetization along the $z$-axis $\...
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Calculating entanglement negativity without constructing density matrix
There are two procedures that I know of for finding the von Neumann entanglement entropy of a bipartite system split between $A$ and $B$ - a bad way and a better way. I have in mind computationally ...
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Edited: General Form of Hamiltonian $H$ for Low dimensional Quantum Spin Models (1D/ 2D)
I was looking for a general form of a Hamiltonian describing the low dimensional spin models. I came across the following form. I want the Literature/Source Reference for following Hamiltonian for ...
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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 $L$ ...
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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-...
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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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