All Questions
Tagged with spin-models lattice-model
30
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Breaking a classical ground state degeneracy by a quantum term and order-by-disorder
Let’s assume we have a Hamiltonian for spin-1/2 particles with two terms, a classical interaction term and a “quantum” (non-diagonal) term. For simplicity, let’s assume that the quantum term is a ...
- 29
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Lattice symmetry operations in strongly spin-orbit coupled systems
I think this is a FAQ when we are studying the rotation operations of lattice spin systems, but I can't find much references.
Background
Considering a Hamiltonian defined on a triangular lattice:
\...
6
votes
2
answers
511
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Is there Difference Between 1D and 2D in Spin model?
The Motivation is That:In the Tensor Network method, they say 'time evolution MPS(Matrix Product State) work quite well in 1 Dimension'.
but as I think any 2D could be expressed by 1D
for example in ...
- 71
2
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88
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Current Operators on Lattice
Peierls substitution method by taking the functional derivative of Hamiltonian can be used to determine the form of current-operator in continuum model (See Bruus-Flensberg) as well as lattice model. ...
- 199
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73
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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 ...
- 29
1
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0
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57
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Holley and FKG Lattice Conditions
There's an interesting exercise (page 13, Exercise 11) in Hugo Duminil-Copin's Lectures on the Ising and Potts models on the hypercubic lattice, which states that the following 2 statements are ...
- 2,113
2
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61
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(In)finite lattice in quantum statistical mechanics: validity of phase classifications and TQFT [closed]
I would like to understand the motivation for studying quantum statistical mechanics, such as spin models, on an infinite lattice, or in other word, in the operator algebraic framework. I learned that ...
- 115
1
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1
answer
48
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Energy current in a quantum chain
I have seen in (e.g. this paper) the definition of the energy current in a chain with $H = \sum_{j=1}^L h_j$
where $H_j$ has support on the $k$ sites $j,j+1,j+2,...,j+(k-1)$ as
$$J_j - J_{j+1} = i[H, ...
- 2,282
6
votes
3
answers
1k
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Why can we choose spin-1/2 degrees of freedom to commute?
Edit 2:
The previous title of this question was "Why are qubits bosonic?" Thanks to the answers that have been provided so far, I now realize I asked my question in a sloppy way. The ...
- 8,344
2
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0
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122
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Spin glass observables in Monte Carlo simulations
I am currently simulating an Edwards-Anderson spin glass using standard Metropolis Monte Carlo techniques. The spins are placed on a 3D cubic lattice with periodic boundaries and take on Ising values (...
- 21
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1
answer
255
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Is spin-1 Ising model exactly solvable (one dimension and two dimension)?
I am working on spin-1 Ising model and I am new in this field. it seems that spin-1 Ising model in one dimension can be exactly solved by transfer matrix similar with spin 1/2 Ising model, am I right ...
- 51
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200
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Is there any relation between Lieb-Robinson velocity bounds and micro-causality?
Background
So I recently asked a question about relativistic quantum mechanics and the answerer invoked micro-causality (from QFT) to show me that the assumption the information would propagate ...
- 1,389
3
votes
2
answers
650
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Jordan-Wigner transformation for lattice models without $U(1)$ symmetry
The Jordan-Wigner transformation is a powerful approach to studying one-dimensional spin models. The following dictionary between spin operators and creation/annihilation operators for fermions allows ...
- 759
4
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88
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What is the connection between vertex/spin models and gauge theory?
In the usual formulation of lattice gauge theories, one considers gauge variables on the links of a lattice (often hypercubic) taking value in some representation of a gauge group, $U_{ij} \in G$. The ...
- 3,710
1
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1
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From spins to fields
In statistical field theory, one usually considers the so-called Landau Hamiltonian:
$$\beta H = \int d^{d}x\bigg{[}\frac{t}{2}m^{2}(x) + \alpha m^{4}(x)+\frac{\beta}{2}(\nabla m)^{2}+\cdots+ \vec{h}\...
- 585