Questions tagged [spin-chains]
One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.
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Lower bounds on spectral gaps of ferromagnetic spin-1/2 XXX Hamiltonians?
Question. Are there any references or techniques which can be applied to obtain energy gaps for ferromagnetic XXX spin-1/2 Hamiltonians, on general interaction graphs, or tree-graphs?
I'm interested ...
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Mermin-Wagner and Heisenberg spin chains
The Hamiltonian for the spin 1/2 ferromagnetic Heisenberg spin chain is $H=-J\sum_i \vec \sigma_i \cdot \vec\sigma_{i+1}$ with $J>0$ and $\vec\sigma_i$ the Pauli matrices acting on ith lattice site....
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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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Jordan-Wigner transformation on a circle and spin structures?
Is there an analog of the Jordan-Wigner transformation between fermion algebra on a circle and a Pauli algebra? For example, the continuum analog of bosonization of "compact boson $\...
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Kosterlitz-Thouless in the XXZ chain: instanton condensation?
The anisotropic spin-$\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 ...
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1D transverse-field Ising model - what is the difference between its classical and quantum treatment?
The 1D transverse field Ising model:
$$ H(\sigma)=-J\sum_{i\in Z} \sigma^x_i \sigma^x_{i+1} -h \sum_{i \in Z} \sigma^z_i$$
is usually solved in quantum way, but we can also solve it classically - ...
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Is the only difference between tDMRG and TEBD the way the central sites are shifted?
I have been reading up on time evolution methods using matrix product states. Reading from Schollwoeck's notes on the density matrix renormalization group, (https://arxiv.org/abs/1008.3477), I looked ...
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Density Matrix Renormalization Group (DMRG) and Bethe ansatz for 1D Hubbard model
Has Density Matrix Renormalization Group (DMRG) been benchmarked against the exact Bethe ansatz result for the one dimensional Hubbard chain? If yes, then what are the relevant references?
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Are strong correlations of boundary spins possible in the absence of long-range order in the bulk?
Question about one-dimensional models with short range interaction of quantum spins, such as transverse Ising and Heisenberg models. Are there any examples when, in the ground state of the system, the ...
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Is it possible to diagonalize a Hamiltonian with both quadratic and linear terms in the fermi operators?
A quadratic Hamiltonian in the fermi operators is exactly diagonalizable. The most convenient way of describing these Hamiltonians is of the form:
$$\mathcal{H}=\displaystyle \sum_{j,k}(\alpha_{jk}a_{...
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Heisenberg equation of motion and continuum limit
Given the quite simple Hamiltonian
$$\hat{\mathcal{H}}=\sum_n\big(\hat{S}_n^+\hat{S}^-_{n+1}+\hat{S}_n^-\hat{S}^+_{n+1}\big)$$
on a 1D spin chain, it basically interchanges two spins lying next to ...
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Do magnons exist in 1D?
I'm confused about the state of a system described by the quantum Heisenberg model
$$ H = -J\sum_i \vec{S}_i \cdot \vec{S}_{i+1} $$
in 1 spacial dimension (1D spin chain). We can find the low energy ...
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Partial Transpose in Gapped Time-reversal Symmetric Spin Chains
Suppose you have a one-dimensional quantum spin system with on-site Hilbert spaces $\mathcal{S}$. Suppose there is an anti-unitary, anti-linear operator $C$ on $\mathcal{S}$ inducing an anti-linear, ...
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What is the relation between the Holstein-Primakoff Transformation and Bethe's Ansatz for the Heisenberg Ferromagnet?
Bethe's Ansatz is a method to find the eigenenergies and eigenstates of the Heisenberg ferromagnet (see also spin waves). For a general n-excitation state it involves solving rather complicated ...
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Bethe ansatz and density of states for XXX spin chain
Consider the 1 dimensional Heisenberg antiferromagnet with Hamiltonian
$$ 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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