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
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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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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
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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 ...
- 2,123
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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
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1
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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, ...
- 2,292
6
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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 ...
- 8,343
2
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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
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257
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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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206
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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
652
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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
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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
answer
48
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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
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1
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Is the definition of gap of a Hamiltonian, i.e. difference between two distinct eigenvalues, restrictive?
The spectral gap of a quantum model or a Hamiltonian, in the context of whether it is a gapped or gapless model, is often defined as the difference between the two lowest distinct eigenvalues of the ...
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2
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2k
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Kagome Lattice: Spin-orbit coupling Hamiltonian in tight-binding models
Consider spin-orbit coupling (of strength $\lambda_1$) on lattice, with the below Hamiltonian
$$H = i \lambda_1 \sum_{<ij>} ~\frac{E_{ij} \times R_{ij}}{|E_{ij} \times R_{ij}|} \cdot \sigma ~...
- 359
2
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0
answers
170
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$T$-duality symmetry of $SU(2)_1$ WZW model
For bosons at self-dual radius, the CFT has T-duality symmetry. My question is can we realize this symmetry on the lattice model? for example antiferromagnetic spin chain.
- 21
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135
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Massive Thirring model as continuum limit of Heisenberg model
The massive Thirring model
$S = \int d^2 x \left[ \bar{\psi} \gamma^\mu \partial_{\mu} \psi - m \bar{\psi} \psi - \frac{g}{2} \left( \bar{\psi} \gamma_\mu \psi \right) \left(\bar{\psi} \gamma^\mu \...
- 4,251
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1
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What is breathing Kagome lattice?
I know what kagome lattice is. While reading some article I came to know the term breathing kagome lattice. Looked up the web didn't found any definitions of it.
My suspicion is that when hopping ...
- 988
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120
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Quantum Monte Carlo Loop Algorithm for quantum spin: why is the freezing graph present in ferromagnetic Ising model?
I study the loop algorithm (Evertz et al).
I cannot understand, why the freezing graph type where we have to flip all 4 spins together is not present for the quantum-XY model and the anti-/...
- 115
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223
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How to find groundstate energy of a simple Hamiltonian at $N/L$-filling using Jordan-Wigner (JW) transformation?
$\underline{\textbf{Model:}}$
Let we have the $t-V$ model for spinless fermions on a 1D lattice, which is defined in second quantization operators as follows:
$$H_1 = -t\sum_i \big(c_i^\dagger c_{i+...
- 1,335
1
vote
1
answer
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Constructing PEPS representation of an arbitrary quantum state
Given a quantum state we can construct its MPS (Matrix Product State) representation by doing a series of singular value decompositions. Given the freedom to choose arbitrary bond dimensions the MPS ...
- 1,285
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0
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133
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Correlation between spins using delta function in Potts model
In reading about the Potts model, I found this correlation:
$$\langle s_{i}s_{j} \rangle = \frac{q}{q-1}\frac{1}{N_{p}} \sum_{s_{i},s_{j}} (\delta(s_{i} - s_{j})-\frac{1}{q})$$
with the following text:...
- 11
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0
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117
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References or resource recommendation for mapping of 1D spinless Hubbard model into XXZ Heisenberg model
I read from somewhere that 1D spinless Hubbard model can be mapped onto XXZ Heisenberg model but I don't remember from where did I read this sentence. I tried googling it but couldn't find any thing ...
- 1,335
6
votes
1
answer
10k
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Bogoliubov-de-Gennes (BdG) formalism of Hamiltonians
The Bogoliubov-de-Gennes (BdG) formalism of a Hamiltonian reduces the dimension of the Hilbert space we work on. For example, in 1D superconducting Hamiltonians with $N$ lattice sites, the actual ...
- 107
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2
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420
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How to understand a Hamiltonian of the form $c^\dagger \sigma^x c$?
In a 2-dimensional lattice Dirac model (a discretized Hamiltonian on a lattice, the model could be found in this dissertation, equation (2.19)), I found a Hamiltonian with terms like:
$$ H = \sum_{m,n}...
- 706
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3
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297
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What is spin on a lattice site is it electrons or atom as a whole?
Hi I wanted to know what is spin half in lattice site means? Is it electron or atom or total spins half of electrons in a atomic 1d chain or 2d?
- 13
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Can someone explain to me the Rokhsar-Kivelson Hamiltonian? [closed]
The following paper shows the hamiltonian of the 2D quantum dimer gas (page 2)
http://www-thphys.physics.ox.ac.uk/people/ClaudioCastelnovo/Talks/050209_MIT.pdf
Here are some questions I have.
Why ...
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2
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233
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Lattice gauge and spin network
I see the similarity between the Lattice Gauge and Spin Network.
(For example, both theories depict the node part as quantum (the latter is explained as spin).)
Are there any other mathematical, ...
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