The study of physical properties condensed phases of matter, including solids and liquids.

learn more… | top users | synonyms

0
votes
0answers
8 views

Interacting Hamiltonian

Is it always possible to write interacting Hamiltonian in a second quantized matrix form like we do it for non-interacting form $H=C_\alpha^\dagger h_{\alpha\beta} C_\beta$ where, H is many ...
0
votes
0answers
17 views

Topological S-matrix as an operator in the graphical calculus

My question comes from the following classic paper by Kitaev: Anyons in an exactly solved model and beyond (arXiv link) In Appendix E (pg 86), Kitaev introduces a diagram operator $S_z$ which acts ...
2
votes
1answer
98 views

Quasi-particle and quasi-hole excitations of Laughlin states and generalization of Laughlin states

The Laughlin wave function at filling fraction $\nu=\frac{1}{m}$ is \begin{equation} \Psi_m=\prod_{i<j}(z_i-z_j)^m e^{-\sum|z_i|^2/4l_B^2} \end{equation} It is claimed in section 7.2.3 of Wen's ...
0
votes
0answers
16 views

Effective mass of almost ideal fermi gas

I am trying to reproduce this famous result of effective mass of almost ideal fermi gas(Galitskii 1958 The energy spectrum of a non-ideal Fermi gas). There are two kinds of ways to find effective ...
2
votes
3answers
146 views

Spectral properties in Solid state physics

So assume we have a periodic 1d Schrödinger operator $$- f'' + V(x) f(x)= \lambda f(x)$$ and we want $V$ to be periodic. Now if we assume that we are on a finite interval and that we have periodic ...
0
votes
0answers
20 views

Connected diagrams in Sine-Gordon action

I consider a bosonic action of the type $$\int dx d\tau\left( \underbrace{a(\nabla\theta)^2+b(\nabla\phi)^2}_{free} +\underbrace{c\cos{4\phi}}_{interaction}\right),$$ and want to treat the cosine term ...
0
votes
1answer
45 views

Metals/Insulators and Electron Counting

I'm a little confused by the description I commonly hear about the electron counting rule in band theory. The general statement I find is that a "solid with an odd number of electrons per unit cell ...
0
votes
1answer
30 views

About characteristic lengths

I am reading about mesoscopic characteristic lengths.But I am not able to distinguish between phase coherence length $L_{phi}$ and inelastic length $L_{in}$. please tell me the difference and ...
4
votes
2answers
367 views

Quantum to classical mapping: quantum criticality and path integral Monte Carlo

I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts: (i) in path integral monte carlo, the ...
1
vote
1answer
238 views

Intro to Solid State Physics

I didn't see this listed on the books page so here it is. I'm currently in an introductory Solid State course, and we are using Kittel's book. I have been having a rough time with this book although I ...
7
votes
4answers
3k views

Books for Condensed Matter Physics

What are some good condensed matter physics books that can fill the gap between Ashcroft & Mermin and research papers? Suggestions for any specialized topics (such as superconductivity, CFT, ...
0
votes
0answers
32 views

What are “two-centre integrals”?

Reading through some condensed matter physics literature I came across the term "two-centre integrals". Could someone explain what is meant by this in general? CONTEXT: "the overlap matrix and the ...
0
votes
0answers
41 views

Mean size of a Cooper pair [on hold]

I'm having some difficulty with a the calculation of the means quadratic average distance between two electrons of a cooper's pair. I have: $$\Psi(\vec{r}) = \int d^3 \vec{k} e^{i\vec{k} \cdot ...
1
vote
2answers
246 views

Moving Between Degenerate Vacua?

In spontaneous symmetry breaking, moving round the circular valley of Mexican hat potential doesn’t cost energy. These angular excitations are called Goldstone bosons. But doesn't the angular ...
6
votes
1answer
301 views

Donors/Acceptors in Metal Oxides

Can anyone explain to me why most articles describe chromium as an acceptor in titanium dioxide? In TiO2, titanium has the charge state Ti$^{4+}$ and oxygen has the charge state O$^{2-}$. When Cr ...
4
votes
1answer
149 views

Do indirect optical transitions “cool” the material a little?

So I'm reading in Ashcroft and Mermin about indirect optical transitions: So, a photon comes in, and it only excites the electron across the indirect band gap if a phonon with the appropriate wave ...
3
votes
1answer
214 views

The relation between spectral function and band structure

I am confused by the wavevector in spectral function A(k,w). How to understand this k for a periodic structure? And how is it related to the k (in first Brillouin Zone) we use in the band structure? ...
1
vote
1answer
65 views

Wannier functions on a ring

Let's say I have a single particle hamiltonian in a periodic potential, for example a 1D lattice such that: $$H = -\frac{\partial_x^2}{2m} + V(x) $$ with $ V(x+a) = V(x)$ where $a$ is the lattice ...
8
votes
1answer
1k views

What happens to atoms inside a black hole?

Black holes have very high gravitational force that tends to crush everything. So as we know atoms in a molecule have inter-atomic spacing between them and further electrons also revolve at a certain ...
0
votes
0answers
35 views

Berry curvature and linear response functions

Let $\hat{A}^i (i = 1, . . . , n)$ be a set of hermitian observables and $F_i$ a corresponding set of external fields that are linearly coupled to $\hat{A}^i$. Starting from the ground-state at $F_i = ...
0
votes
0answers
19 views

Conductivity from Boltzmznn Equation for a metal in electric field

I'm trying to show that conductivity of a metal in uniform Electric field is: $$ \sigma=\int \frac{d\textbf{k}}{4\pi^3}\left (- \frac{\partial f}{\partial \epsilon} \right )\textbf{v(k)u(k)} $$ where ...
16
votes
4answers
3k views

A pedestrian explanation of conformal blocks

I would be very happy if someone could take a stab at conveying what conformal blocks are and how they are used in conformal field theory (CFT). I'm finally getting the glimmerings of understanding ...
0
votes
2answers
127 views

Question about Landau's phase transition theory

I have a question about Landau's theory of quantum phase transition. In his model, the free energy is assumed to be \begin{equation} F = f_0 + \alpha (T-T_c) \Delta^2 + \beta \Delta^4 ...
0
votes
0answers
39 views

Green function for single impurity

I am working on the first problem on self-consistent T-matrix approximation in Chapter 5 of Condensed Matter Field Theory by Altland and Simons. This is on page 234 of the textbook. I have some ...
1
vote
1answer
97 views

Interacting fermionic SPT phases in 2d with time-reversal symmetry

Interacting fermionic SPT phases in 1d and 3d with $\mathbb{Z}_2^T$ symmetry are classified by $\mathbb{Z}_8$ and $\mathbb{Z}_{16}$ respectively, as shown in the paper by Fidkowski and Kitaev ...
4
votes
1answer
74 views

What kind of free energy do we use for a superconductor in a magnetic field?

My reasoning is as follows (using Gaussian units): Start from the second law: $$dU=TdS+dW,$$ where $dW$ is the work done by the magnetic field. To derive $dW$, we consider a solenoid with current ...
6
votes
2answers
754 views

Can water be magnetized?

This may be a stupid question, so feel free to shoot it down. Assuming all atoms have a magnetic moment, I would assume the water molecule too would have a resultant magnetic moment; ergo, it may be ...
0
votes
0answers
15 views

Negative Capacitance in Ferroelectrics

From the Devonshire theory of ferroelectrics we can obtain Polarization vs. Electric Field curve at a given temperature. From the graph it can be seen that a portion of the curve has negative slope ...
2
votes
1answer
62 views

Ising model on lattices with (vertical side length) $\neq$ (horizontal side length)

Consider the Ising model with nearest neighbours interactions on a rectangular lattice $L\times M$. If $L=M$ (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit ...
5
votes
1answer
84 views

Has anyone experimentally shown the quantized thermal hall conductivity in Quantum Hall systems?

For background: In a $D=2+1$ state with edge modes described by a chiral $( c_L \neq c_R )$ CFT there is a predicted thermal Hall conductance associated with the gravitational anomaly at the edge. ...
4
votes
1answer
60 views

What is the Difference Between a Type-1 and a Type-2 Superconductor?

As the title says, I was wondering what the difference was between a Type-1 and a Type-2 Superconductor. Especially in terms of the Coherent Length and Penetration Depth of a Magnetic Field - and how ...
6
votes
3answers
1k 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 $K$ ...
1
vote
0answers
23 views

Why do we use the massive dirac fermion model for MoS2?

I can derive the massive Dirac fermion Hamiltonian using a tight binding model of graphene with a staggered sublattice potential, but many (including Xiao et al, PRL 2012) use this model for MoS2 as ...
0
votes
0answers
28 views

Green function for interacting system

If we can diagonalize our interacting Hamiltonian then can we write a Green's function like we do for a non-interacting system? Green's function here means Matsubara in frequency-momentum space, ...
1
vote
0answers
67 views

How to derive the critical temperature for Bose-Einstein condensation of photon?

I found in Nature magazine that photon can have Bose-Einstein condensation. But I have a question how to derive the critical temperature for photon? Because the chemical potential of photon is zero ...
1
vote
1answer
42 views

Proof of Kohn's theorem

In 1961 W. Kohn's paper ( Phys. Rev. 123, 1242 (1961) ) first stated that the electron-electron interaction does not change the cyclotron resonance frequency in a bulk three dimensional gas. I can ...
0
votes
2answers
119 views

Compute distance between planes in a crystal

I want to compute the distance between two (111) planes in a cubic crystalline structure, in order to do some computations involving Bragg reflection. I have a sketch of which the (111) planes are, ...
3
votes
1answer
66 views

Hartree-Fock correction to $e$-$e$ interaction

The corrections to the energy per electron in a jellium model (uniform distribution of positive ion charge approximation to the regulated long range order ionic array) is given by (in units of Ry) ...
0
votes
0answers
20 views

About gauge in QHE

I have a 2D geometry with 4 leads in a square lattice structure. Please tell me how should I apply gauge to such a system that hopping term is translational invariant in the laeds in both directions ...
1
vote
1answer
95 views

Projection Method in Hubbard model

This is a question from Altland and Simons book "Condensed Matter Field Theory". In the second exercise on page 64, the book claims that if we define $\hat P_s, \hat P_d$ to be the operators that ...
0
votes
0answers
17 views

AC conductivity of graphene

The optical conductivity of graphene has two terms, interband term and intraband term. The analytical expression of intraband term is drude like. ...
7
votes
1answer
85 views

What is the Difference Between BCS Theory and Ginzburg-Landau Theory?

What is the Difference Between BCS Theory and Ginzburg-Landau Theory? I have been studying Superconductivity and I know that Both of the theories (BCS Theory and Ginzburg-Landau Theory) can be used ...
1
vote
2answers
87 views

Thomas - Fermi screening

I read in Ashcroft & Mermin's Solid State text that for the Thomas-Fermi approximation to be applicable, the external potential needs to be "slowly varying," What does it mean for a function (in ...
2
votes
1answer
195 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
1
vote
1answer
58 views

Atomic physics - lattice energy

Question: Why is ionic lattice energy inversely proportional to the radius of the atom? Most heterogeneous covalent molecules are polar to some extent. The degree of polarity, or the dipole moment, ...
1
vote
1answer
41 views

What is the clear cut difference between isotropic and anisotropic spin exchanges?

When are spin exchanges said to be isotropic or anisotropic? I have read several articles on this and can not differentiate these concepts properly.
2
votes
1answer
45 views

Fast and slow modes, and the vanishing of certain diagrams during re-normalization

In the middle of pg. 452 of Atland and Simonss Condensed Matter Field Theory, they state the following: Terms of $\mathcal{O}(\phi _{\text{s}}^3\phi _{\text{f}})$ do not arise because the addition ...
0
votes
0answers
41 views

Frustrated Heisenberg XXZ Model

At the moment, I am look at the frustrated XXZ Heisenberg model, given by the Hamiltonian \begin{align} H=\sum_{i=1}^N\left(J_1S_i^Z S_{i+1}^Z+J_1'\frac{1}{2}(S_i^+S_{i+1}^-+S_i^-S_{i+1}^+)+J_2S_i^Z ...
1
vote
1answer
20 views

Exciton in semi-conductor

I don't understand why an exciton describes only the interaction between an electron hole and an electron in the conduction band? How is this interaction different from the interaction between an ...
1
vote
0answers
15 views

Validity of the static limit of a dielectric function

In general, the dielectric function $\epsilon(q,\omega)$ reflects the spatial and temporal response of a condensed matter system to an applied potential. If we put an electron into an electron sea, ...