Questions tagged [lattice-model]
Lattice is a way of discretizing a quantum field theory for numerical simulations.
470 questions
0votes
1answer
53views
Confused regarding packing fraction of 2D Hexagonal closed packing
Ok so I was doing a few questions on Solid State and Lattice points, I encountered a doubt. My book says the packing efficiency in 2D hexagonal closed packing is 𝛑/2sqrt(3). When I looked up the ...
3votes
1answer
94views
How to Calculate Virasoro's Characters of Critical 3-state Pott's model without Considering $W$ algebra?
Let's consider the critical 3-state Potts model. According to conformal field theory, it corresponds to a CFT with a central charge $c=\frac{4}{5}$. However, there are 10 characters for $c=\frac{4}{5}$...
7votes
1answer
350views
Simple proof of a high temperature disordered phase for the Ising model
The original (and probably simplest) argument for the existence of an ordered phase for the Ising model at low (but non-zero) temperature was the Peirls argument, where you basically give an upper ...
1vote
1answer
54views
Do the momentum values and the winding numbers in a compactified string theory be periodic too(along with being discrete)?
I have a question. In lattice qcd, we compactify space to make it periodic. Also because of the formation of the reciprocal brilliouin zone, even momentum becomes discrete valued and periodic. Because ...
- 445
0votes
0answers
36views
Is the transfer matrix of a 1-dimensional lattice system positive definite?
For context, this question regarding the transfer matrix formalism for 1D systems as described in Kardar Mehran's book 1 (chapter 6). For the one dimensional system described by a hamiltonian of the ...
- 107
2votes
1answer
55views
Non-doubled semion model?
There exists an abelian (2+1)d unitary topological quantum field theory (TQFT), with a single non-trivial particle: the semion TQFT. However, all microscopic (lattice) models I know of realise the ...
- 800
3votes
0answers
37views
Computing heat capacity using lattice dynamic code
I've recently aquired some lattice dynamic code which will compute the frequencies for a FCC rare gas solid. The output is a set of frequencies, 1 longitudal and 2 transverse, in the 100,110 and 111 ...
- 31
1vote
0answers
52views
Literature request about lattice gas with nearest-neighbor interaction
I have a square lattice, in which each cell can be occupied by a molecule or can be empty. This should be a "lattice gas". Then I introduce a nearest-neighbor interaction of energy $h$: the ...
1vote
1answer
46views
Periodicity of momentum space creation operators
Let's say we have a tight-binding model in a lattice with more than one atom in a unit cell. For convenience I will say two sites(with site A and site B) and call the lattice vectors $\vec{a_1}, \vec{...
2votes
1answer
64views
Positivity of the determinant of the lattice Dirac operator in (2+1)D on the lattice
As shown in "Gattringer & Lang, Quantum Chromodynamics on the Lattice, sec. 5.4.3" the lattice Dirac operator $D$ for Wilson fermions satisfies the property of "$\gamma_5$-...
- 252
2votes
0answers
123views
Checking the Cardy formula for a critical Ising model
The Cardy Formula is a fundamental result in 2D conformal field theory which predicts the entropy (equivalently, density of states). I am interested in understanding how to extract conformal data from ...
- 911
4votes
0answers
86views
Ising model from the $\varphi^4$ scalar field theory
More than a year ago, I came across a paper (which I am unable to find at the moment) that mentioned the following statement: the Ising model is a discretized version of $\varphi^4$-scalar field ...
- 1,177
1vote
1answer
38views
Does fixing particle number + only evolving to lower energy states make the simulated system isolated?
I'm working on some determinant quantum Monte Carlo simulations. Specifically using the Python package ALF (lattice fermions), which is so cool to work with! It seems like the method is clearly a ...
1vote
0answers
30views
Is Gauss law constraint in gauging a global symmetry on lattice a dynamical constraint or a kinematical constraint?
Suppose a lattice system is $G$-symmetric, when we try to gauge this symmetry, we follow the following steps (for example toric code Levin Gu Xie Chen): minimal coupling: the original Hamiltonian is ...
2votes
0answers
59views
Complex integral (residue method) in lattice quantum field theory
I was studying this reference https://arxiv.org/abs/1901.00483 and i'm stucked on this passage: at page 5 it defines $\mathcal{M}_{2L}$ in a $\lambda\phi^4$ theory and then he says to perform the ...
