All Questions
Tagged with spin-models lattice-model
16
questions with no upvoted or accepted answers
4
votes
0
answers
88
views
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
2
votes
0
answers
91
views
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
2
votes
0
answers
123
views
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
2
votes
0
answers
170
views
$T$-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
1
vote
0
answers
77
views
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
vote
0
answers
59
views
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
1
vote
0
answers
206
views
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
1
vote
1
answer
48
views
From spins to fields
In statistical field theory, one usually considers the so-called Landau Hamiltonian:
$$\beta H = \int d^{d}x\bigg{[}\frac{t}{2}m^{2}(x) + \alpha m^{4}(x)+\frac{\beta}{2}(\nabla m)^{2}+\cdots+ \vec{h}\...
- 585
1
vote
0
answers
135
views
Massive Thirring model as continuum limit of Heisenberg model
The massive Thirring model
$S = \int d^2 x \left[ \bar{\psi} \gamma^\mu \partial_{\mu} \psi - m \bar{\psi} \psi - \frac{g}{2} \left( \bar{\psi} \gamma_\mu \psi \right) \left(\bar{\psi} \gamma^\mu \...
- 4,251
1
vote
0
answers
223
views
How to find groundstate energy of a simple Hamiltonian at $N/L$-filling using Jordan-Wigner (JW) transformation?
$\underline{\textbf{Model:}}$
Let we have the $t-V$ model for spinless fermions on a 1D lattice, which is defined in second quantization operators as follows:
$$H_1 = -t\sum_i \big(c_i^\dagger c_{i+...
- 1,335
1
vote
0
answers
133
views
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
0
votes
0
answers
60
views
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
0
votes
0
answers
27
views
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:
\...
0
votes
1
answer
144
views
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 ...
- 197
0
votes
0
answers
120
views
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