All Questions
Tagged with spin-chains ground-state
9
questions
6
votes
2
answers
26k
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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 ...
- 98
1
vote
0
answers
79
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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 ...
- 2,292
3
votes
1
answer
446
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XXZ chain exact ground state energy
I would like to know the analytical expression of the ground state energy of the XXZ model, if such formula exists (probably from a Bethe Ansatz solution) and if it is valid in all parameter regimes.
- 325
0
votes
1
answer
131
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What does it mean for a system to be in its ground state?
From the measurement postulate, we are told that every observable quantity is represented by a Hermitian operator $\textbf{A}$, where the eigenvalues of said operator gives the possible measurement ...
- 9
0
votes
1
answer
912
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Spin-1 Heisenberg model, the AKLT model, and their ground states
I am reading literature on quantum spin chains and matrix product states, and I notice similar arguments regarding the spin-1 antiferromagnetic Heisenberg model,
$H_{H} = \sum_i S_i \cdot S_{i+1}$,
...
- 197
3
votes
1
answer
510
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ground state of spin chain with $Z_i X_{i+1} Z_{i+2}$ interaction
the problem comes from transverse field Ising model, with an extra 3-spin interaction term
$$H=H_0+H_1+H_2=-h\sum_{i=1}^{N}X_i -\lambda_1 \sum_{i=1}^{N-1}Z_i Z_{i+1}-\lambda_2 \sum_{i=1}^{N-2}Z_i X_{i+...
- 1,113
10
votes
1
answer
2k
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Parent hamiltonian of AKLT state
Given a translationally invariant Matrix Product State (assuming periodic boundary condition) on $N$ sites of dimension $d$ each, which takes the form
$\sum_{i_1,i_2\ldots i_N=1}^dTr(A_{i_1}A_{i_2}\...
- 771
2
votes
1
answer
539
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Energy gap in Parent hamiltonian of MPS
Given a block injective matrix product state (MPS) with D blocks, how does the energy gap of corresponding parent hamiltonian scale with D? And is there a good reference which gives an analysis of ...
- 771
0
votes
2
answers
297
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Example of gapped spin chain with degenerate ground space
What are the examples of a one dimensional spin chain, with local interaction and degenerate ground space (degeneracy may be a function of n, such as log(n) etc, where n is the length of chain) and a ...
- 771