Tagged Questions
0
votes
0answers
44 views
Why doublons and holons are not bounded in spin-1/2 Hubbard chain?
The Hubbard model reads
$$H = -t \sum_{\langle ij \rangle, \sigma} c_{j\sigma}^\dagger c_{i\sigma} + U\sum_i n_{i\uparrow}n_{i\downarrow} $$
In the large $U$ limit and at half-filling, the Hubbard ...
2
votes
0answers
59 views
A general wavefunction in a square lattice
Suppose we have a square lattice with periodic condition in both $x$ and $y$ direction with four atoms per unit cell, the configuration of the four atoms has $C_4$ symmetry. What will be a general ...
8
votes
1answer
116 views
What're the relations and differences between slave-fermion and slave-boson formalism?
As we know, in condensed matter theory, especially in dealing with strongly correlated systems, physicists have constructed various "peculiar" slave-fermion and slave-boson theories. For example,
For ...
6
votes
0answers
107 views
Some questions about anyons?
(1) As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" ...
4
votes
1answer
72 views
Simple uncertaintly calculation of the center coordinates of a Landau Level
I am reading the following review paper on the Quantum Hall Effect. I am sorry for the extremely stupid question, but I have been stuck on this very easy equation for long.
In equation 2.39, the ...
1
vote
1answer
58 views
Calculation of the quantized Hall coefficient in the Integral Quantum Hall Effect
I have been reading about the QHE over the past couple of days. I am facing difficulty understanding a calculation in this review.
www.nimt.or.th/nimt/upload/linkfile/sys-metrology-248-434.pdf
In ...
6
votes
2answers
146 views
Why does the quantum Heisenberg model become the classical one when $S\to\infty$?
The Hamiltonian of the spin $S$ quantum Heisenberg model is
$$H = J\sum_{<i,j>}\mathbf{S}_{i}\cdot\mathbf{S}_{j}$$
I have read that when the spin quantum number $S\to\infty$, quantum fluctuation ...
5
votes
2answers
157 views
A question on the existence of Dirac points in graphene?
As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ has two degenerate points $K$ ...
0
votes
0answers
96 views
Wave function ansatz for disclinated graphene with spin
I am currently investigating spin dynamics in disclinated graphene. More information about my approach can be found in my other post. I would like to know if my approach is somewhat correct to find ...
9
votes
3answers
329 views
Introduction to Anderson localization [closed]
I find Anderson's original paper too terse. I am looking for something that introduces me gently to the subject so that I can understand Anderson's paper and other literature. What references are out ...
4
votes
1answer
202 views
Is edge state of topological insulator really robust？
I am a little confused! Some people are arguing that the gapless edge state of Topological insulator is robust as long as the time reversal symmetry is not broken，while other people say that it is ...
1
vote
2answers
99 views
Eigenfunctions in periodic potential
For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if
$$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$
and
$$\operatorname ...
0
votes
1answer
60 views
The orthogonalized plane waves
An orthogonal plane wave with wave number $k$ is written as
$$ OPW_k=e^{ ik\cdot r}-\sum_\alpha \psi_\alpha(r) \int \psi^*_\alpha (r'') e^{ik\cdot r''} d\tau'',$$
where index $\alpha$ and $k$ ...
1
vote
1answer
281 views
Why path integral approach may suffer from operator ordering problem?
In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path.
What did ...
2
votes
0answers
31 views
Why the peak of spectrum gets vague when the dimension is lower?
In a many-body system, we can know the spectrum function at a particular temperature from Green function. It means density of states. A peak of spectrum represents one mode. My question is that in the ...
1
vote
1answer
129 views
Band Structure and Carrier Recombination/Generation
So i've been a bit confused, looking at PN junction, semiconductors and the like (trying to nail down how exactly semiconductors work, transistors and such). I've read the wiki on band structure ...
1
vote
1answer
262 views
Wave functions for three identical fermions
I would like to express the wave functions for three identical particles, each with orbital angular momentum $L=1$ and spin angular momentum $S=1/2$, in terms of single-particle wave functions. In ...
3
votes
2answers
99 views
Equivilence of One Flux Quantum and Zero Flux
In Ady Stern's review of the Quantum Hall effect, he says of a quantum hall system "The spectrum at $\Phi = \Phi_0$ is the same as the spectrum at $\Phi = 0$..." Can someone explain why this is? It ...
3
votes
1answer
209 views
Does a quantum phase transition have latent heat?
As the title says, I am thinking about the question that whether a quantum phase transition has latent heat. If so, at 0 temperature, we can drive the system by some parameter from disorder phase to ...
1
vote
0answers
81 views
guage invariance in Laughlin's argument
In Laughlin's gedanken experiment which aims to explain quantization of Hall conductance, one takes the adiabatic derivative of the Hamiltonian with respect to vector potential. Now it seems that it ...
3
votes
1answer
102 views
Measurement of topological spin
How do you measure the topological spin of an anyon? So how could an experimental setup look like? Is topological spin an observable at all?
7
votes
1answer
207 views
Simulating the evolution of a wavepacket through a crystal lattice
I am interested simulating the evolution of an electronic wave packet through a crystal lattice which does not exhibit perfect translational symmetry. Specifically, in the Hamiltonian below, the ...
1
vote
0answers
77 views
Are there any good reading materials for variational approach in many-body theory? [closed]
I need something like a summary of existing results, including the treatment of BCS Hamiltonian and Hubbard model. Auerbach's book is a good one but I still hope to get more comprehensive review. My ...
5
votes
2answers
162 views
Meissner Effect for Type-II Superconductors
I was wondering whether the breakdown field strength for the Meissner effect may be attributed to the Zeeman effect? I can see the latter (along with the Stark effect) to be more analogous to electron ...
1
vote
0answers
70 views
Asking for references on the variational treatment of spin wave
My idea is the following:
We have a system with Hamiltonian $H$, and we know that there is spin wave in this system by some symmetry-breaking arguments. Now we start from the ground state ...
1
vote
1answer
97 views
About Efimov States and Halo-Nuclei
I read that
Halo nuclei could be seen as special Efimov states, depending on the subtle definitions. (The last sentence in the second to last paragraph of this Wikipedia article.)
This does ...
1
vote
1answer
180 views
What is different between resolvent and green function
I bumped into a book, where Resolvent $R^{\pm}(E)$ is defined as
$e^{\mp iHt/\hbar}=\pm\frac{i}{2\pi}\int_{-\infty}^{\infty}dER^{\pm}(E)e^{\mp iEt/\hbar}$
and
$R^{\pm}(E)=\frac{1}{\pm ...
2
votes
1answer
37 views
Variational approach to search the excitations. What will happen if start from wrong reference state?
By 'wrong reference state' I mean a state which cannot be transformed into desired ones via variational ansatz
$\left|\Psi\left[\mathbf{n}\right]\right\rangle ...
2
votes
2answers
157 views
Has BCS Cooper pair condensate been observed in experiment?
Feshbach resonance in s-wave scattering states a BCS Cooper pair condensation at B-field just above the resonance where the scattering length a <0. Just wondering if the condensation has been ...
2
votes
1answer
250 views
Feynman diagrams and Hartree-Fock
I am puzzled by some lines I read in Mattuck's book on Feynman diagrams in many-body problems ( http://www.amazon.com/Feynman-Diagrams-Many-Body-Problem-Physics/dp/0486670473 )
Page 21 (1.14) for ...
4
votes
1answer
135 views
Is it possible to make statements about bosonic/fermionic systems by taking the limit $\theta\to \pi$ or $\theta\to 0$, of an anyonic system?
One might naïvely write the (anti-)commutation relations for bosonic/fermionic ladder operators as limits
$$
\delta_{k,\ell} = \bigl[ \hat{b}_{k}, \hat{b}_{\ell}^\dagger \bigr]
= ...
0
votes
2answers
98 views
Wave function of IQH and FQH electrons
What are the wave functions of the ground state of Integer Quantum Hall (IQH) and Fractional Quantum Hall (FQH) electrons?
1
vote
0answers
39 views
Understanding Resonance States in Condensed Matter
What exactly is a resonance state?
My understanding so far is that a resonant state appears as a large spike in the DOS of a material due to an adsorbed impurity or vacancy in the lattice and that ...
3
votes
2answers
216 views
Can I use imaginary time propagation for many-body problems?
There are various ways to numerically find the ground state energy and wavefunction of a many-body Hamiltonian. You can diagonalize the Hamiltonian and pick out the lowest eigenstate, or you use ...
2
votes
1answer
174 views
Weak Anti-Localization
On Wikipedia (pretty much the only place I can find an explanation of what weak anti-localization actually is) it is explained as:
In a system with spin-orbit coupling the spin of a carrier is ...
2
votes
1answer
177 views
Is Fractional quantum Hall effect proof that leptons are composite particles?
The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values. Should this be considered ...
1
vote
1answer
219 views
Matrix element in quantum mechanics
This is about a matrix element of a second quantized operator.
Consider the operator
$$
U=\sum_{\alpha\beta}U_{\alpha\beta}c^{+}_{\alpha}c_{\beta}
$$
Something strange emerges if we calculate again ...
5
votes
1answer
326 views
Topological Order and Entanglement
I have a question about entanglement in condensed matter physics. It seems that topological order origins from long range entanglement, but what is long range entanglement? It is the same as long ...
1
vote
0answers
34 views
In heterojunction problem, how to align the energy band in presence of bias voltage
For example, SiO$_2$ barrier embeded between Fe magnet and 2-dimensional-electron-gas such as Si.
How to align the energy bands of the three materials when an electric field is perpendicular to the ...
3
votes
2answers
189 views
Boundary conditions for crystals
As students on solid state physics, we are all taught to use the periodic boundary condition, taking 1D as an example:
$\psi(x)=\psi(x+L)$
where $L$ is the length of the 1D crystal.
My question is:
...
3
votes
2answers
213 views
Very basic question about QFT at finite density
This must be the first question everyone asks when starting to study field theory at finite density and zero temperature.
To introduce a finite density one adds a Lagrange multiplier which fixes the ...
3
votes
1answer
124 views
How are quantum potential wells fabricated?
Potential wells, such as infinite and finite potential well, have been the standard examples in quantum mechanics textbooks for tens of years. They started being only theoretical toy models but as ...
3
votes
2answers
231 views
What are the applications of delta function potentials?
Are there real applications for using delta function potentials in quantum mechanics (other than using it as an exactly solvable toy model in introductory undergraduate quantum mechanics textbooks) ?
...
7
votes
1answer
564 views
Is resonating valence bond (RVB) states long-range entangled?
Quantum liquid is at the core of condensed matter theory study, examples include superfluid in Bose Hubbard model, quantum spin liquid around the RK point of a quantum dimer model, string-net ...
17
votes
10answers
1k views
What is spontaneous symmetry breaking in QUANTUM systems?
Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture.
According to the classical picture, spontaneous ...
8
votes
1answer
382 views
Interpretation of the Random Schrödinger Equation
I should preface this by admitting that my physics background is rather weak so I beg you to keep that in mind in your responses. I work in mathematics (specifically probability theory) and a paper ...
2
votes
1answer
191 views
Fractional statistics
A common way to show that anyons exhibit fractional statistics in 2D is by arguing that the paths of two anyons winding round each other cannot be continuously deformed to zero. This seems to assume ...
4
votes
3answers
405 views
Entanglement spectrum
What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
4
votes
1answer
508 views
Tight Binding Model in Graphene
I'm following a calculation done by a guy who's done it a bit different than what I've done before (used nearest neighbour vectors and a DFT instead of what I will show below), I'm not quite sure how ...
1
vote
2answers
105 views
Quantization of momentum in nanotubes
I'm reading about carbon nanotubes and how the momentum (lets call it $k_x$) is quantized along the circumferential direction and not along the cylindrical (call this $k_y$). I can follow the maths ...
