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

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Eigenvalues of a nearest-neighbour tight-binding Hamiltonian in (Mahan, 2003)

In this paper by G. D. Mahan, he obtains the following electron Hamiltonian in a nearest-neighbour tight binding scheme: (page 2 of the paper, top of the right column) \begin{align} H_0 &= J_0 \...
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555 views

Can one define wavefunction for Bogoliubov quasiparticle excitation in a superconductor?

Wavefunction is essentially a single particle concept. It is easily extended to multiparticle system as follows- if one has say five electrons the wavefunction of this five electron state is any ...
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80 views

Magnetization $\ M$ of a ferromagnet as a function of temperature $T$, nearby $T=0$

Using mean-field theory, the magnetization per spin, $M$, for a ferromagnet always obeys the equation: $M=\frac{g \mu_{\mathrm{B}}}{2}\mathrm{tanh} \left( \frac{2}{g \mu_{\mathrm{B}}} \frac{T_{\...
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Grand canonical Hamiltonian

How to explain introducing "grand canonical" Hamiltonian $$ \hat{H'}= \hat{H}-\mu \hat{N} $$ when we study a quantum system with fixed chemical potential? I understand such a substitution in a ...
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53 views

Eigenvalue for interacting Hamiltonian [closed]

Consider the Hamiltonian $$H=\omega_{1} a_{1}^\dagger a_{1}+\omega_{2}a_{2}^\dagger a_{2}+\alpha a_{3}^\dagger a_{3}(a_{1}^\dagger a_{2}+a_{2}^\dagger a_{1})$$ with $$ [a_\alpha^\dagger,a_\...
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365 views

Derivation of Rashba spin-orbit coupling in tight-binding model

Rashba spin-orbit coupling Hamiltonian in free space can be written as: $H_{\text{so}}=\int d^3r \Psi^{\dagger}(\mathbf{r}) \gamma (p_{x}\sigma _{y}-p_{y}\sigma _{x})\Psi(\mathbf{r})$. I expand $\...
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118 views

In string-net condensation, what does the quantized charge means? [closed]

The electrical charge is quantized strictly for elementary particles. What kind constraints does this fact applied to string-net theory? For the this question, I want to understand why electrical ...
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141 views

Does it make sense to define the mean free path in quantum mechanics?

The mean free path defined in classical molecule dynamics has a strong classical flavor. Is it sensible to generalize the idea to quantum mechanics?
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111 views

Energy gap in Parent hamiltonian of MPS

Given a block injective matrix product state (MPS) with D blocks, how does the energy gap of corresponding parent hamiltonian scale with D? And is there a good reference which gives an analysis of ...
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23 views

Can one calculate the electric conductivity of iron?

Iron is a commonplace material. It is common knowledge that it conducts. Is it possible to accurately calculate the electric conductivity of iron? With what kind of method? Up to what precision?
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Are there any known continuous (non-lattice) quantum error correction codes?

I come from a hep-th background, but I have noticed that quantum information is becoming increasingly common in discussions of AdS/CFT and black hole information, and so I've begun thinking about it ...
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139 views

scaling theory of Anderson localization

Initially, Anderson studied the eigenstates of the tight-binding Hamiltonian $$ H = \sum_n \epsilon_n a_n^\dagger a_n + V \sum_{m,n} a_m^\dagger a_n . $$ His question was whether the eigenstates ...
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36 views

Mott's conjecture about NiO verified or not?

Mott in his 1949 paper, said: ''On the view explained above, therefore, if a substance such as NiO were subjected to very high pressure it should suddenly show metallic conduction for some value of ...
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120 views

Axiom approach for majorana fermions

This is the usual way of introducing majorana operators. First we have $N$ fermionic modes. The corresponding operators satisfy the commutation relations $$ \{c_i, c_j \}= \{c_i^\dagger, c_j^\dagger \...
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54 views

What is an off-axis peak in x-ray diffractometry?

I'm looking at a $\theta$ - 2$\theta$ pattern of my thin film which in bulk is cubic (bcc) and I see 001 and 002 peaks of the film. There is supposed to be a tetragonal distortion meaning that I need ...
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105 views

Variation over complex function in Ginzburg-Landau theory

When deriving the Ginzburg-Landau equations, we minimize the following free energy over the complex function $\psi$: $$F = \int dV \left \{\alpha |\psi|^2 + \frac{\beta}{2}|\psi|^4 + \frac{1}{2m^*} \...
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crystal momentum conservation

Electrons on 1D chain interacting with each other $$ H = \sum_{k_4,k_3, k_2, k_1} V(k_4-k_1) c_{k_4}^{\dagger}c_{k_3}^{\dagger}c_{k_2}c_{k_1}\delta_{k4+k3=k2+k1;\text{mod}~G}$$ where $G$ is ...
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95 views

Example of gapped spin chain with degenerate ground space

What are the examples of a one dimensional spin chain, with local interaction and degenerate ground space (degeneracy may be a function of n, such as log(n) etc, where n is the length of chain) and a ...
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42 views

What is the microscopic state of an electron in a charged insulator?

Assume we put an extra electron in a neutral insulator (on surface or in bulk). The insulator becomes charged. What would be the quantum state of that electron? Is it confined somewhere between the ...
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78 views

What is the physical mechanism of the topological phase transition driven by temperature?

The topological property of topological insulators (TIs) is characterized by the non-trivial topological invariants of their band structures, such as $Z_{2}$ topological invariants. While it's clearly ...
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Proof of equivalence between soundwaves and phonons in large wavelength limit (Ashcroft-Mermin, ch. 22)

In chapter 22, Ashcrof and Mermin argue that the normal modes of a harmonic crystal are not only formal but precisely equal to the large wavelength limit of acoustic phonons (which sounds, of course, ...
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686 views

Peierls substitution vs minimal coupling

In the presence of vector potential (let's assume it's uniform), a tight-binding Hamiltonian will be changed according to the Peierls substitution: $$t_{ij}c_i^{\dagger}c_j \to t_{ij}e^{iqA|i-j|}...
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224 views

Density of state vs energy

Please bear me for this naive question. In the definition of density of state in 3D we know that DOS $\rho(E)$ varies as $E^{\frac{1}{2}}$ i.e as energy increase it should increase. But when I see ...
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braiding bosons or fermions around majorana fermion

Majorana fermions are described by their topological charge. My question is whether we can see the topological charge of Majorana fermions by braiding a boson or a fermion around it ? Is the only ...
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208 views

Why does a half filled Brillouin zone result in conductivity?

As stated in the title, why does a half filled Brillouin zone result in an element being a conductor, or conversely, why does a filled Brillouin zone result in an insulator?
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153 views

Does point group symmetry also act within “spin space” for a lattice spin system?

As an example, let's consider a quantum spin system on a 2D square lattice. The lattice point group symmetries include $C_4$ rotation, parities, etc.... And let's take $C_2$ symmetry (2-fold rotation) ...
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74 views

Why use class multiplication to describe topological entangling and merging?

I'm studying some references about topological defects in ordered media like Soft matter physics: An introduction by Kleman and the Review modern physics paper The topological theory of defects in ...
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315 views

Majorana zero mode and 1D Ising model

It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two ...
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229 views

FCC lattice as a stack of triangular lattices

According to Marder, Condensed Matter Physics, Chapter 2: Within the planes normal to the vector [1,1,1], the atoms of an fcc lattice lie in a two dimensional triangular lattice However, he does ...
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314 views

Double semion model on a square lattice

We consider the double semion model proposed in Levin and Wen's paper http://arxiv.org/abs/cond-mat/0404617 http://journals.aps.org/prb/abstract/10.1103/PhysRevB.71.045110 In their paper, the ...
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243 views

Difference between adsorption and condensation

So I just stumbled across the Wikipedia article on adsorption - and I asked myself, if there is a difference between (physical) adsorption and condensation on a surface? When I look at the water ...
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Is there an intuitive reason for why the reciprocal lattice of FCC is BCC and vice versa?

This can be proved using formulae for generating reciprocal lattice vectors from direct lattice vectors. But does this result have more to it than meets the eye?
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199 views

How to prove Bloch function is periodic in reciprocal lattice?

How to prove Bloch function is periodic in reciprocal lattice? I saw in some textbooks this formula: $$ \Psi_{\mathbf{k}} (\mathbf{r}) = \sum_{\mathbf{G}} c_{\mathbf{k}+\mathbf{G}}e^{i(\mathbf{k}+\...
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310 views

How does the notion of topological order relate to the Landau-Ginzburg theory of phase transitions?

As per Landau-Ginzburg (LG) theory, we write down a theory (Hamiltonian) with all possible interactions/operators (in terms of some order parameter) that respects certain symmetries. The ground state (...
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198 views

A naive question on the “continuously” degenerate ground states of 1d phonons?

In general, the gapless Goldstone mode is related to the "continuously" degenerate ground states. The Mexican hat potential is an example (see the logo of this SE website), where the bottom circle is ...
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33 views

Cryogenic Conductivity of a Defective Semiconductor

If I have a semiconductor with a lot of defects what happens to its conductivity at at mK type temperatures? I'm expecting that defects would give rise to greater conductivity than for a perfect ...
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826 views

Why do electron and hole mobilities decrease with temperature?

From page 35 of "Microelectronics" by Millman Grabel Mobility $\mu$ decreases with temperature because more carriers are present and these carriers are more energetic at higher temperatures. ...
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428 views

Goldstone modes of spin density wave

A spin density wave (SDW) is a phase in which a material suddenly shows a periodically modulated spin density $S_{\vec{q}}(\vec{r}) $ below a certain critical tempereature $T_C$. Obviously some kind ...
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How to derive the effective Langrangian of matter field, say, fermi field and quasiparticle, say, spin wave?

In the Fermi-Hubbard model, it may lead to spin wave due to SO(3) symmetry breaking. I know how to derive the effective Lagrangian for the spin wave by integrating out the Fermi fields. However, how ...
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299 views

Questions on gapless edge excitations in symmetry-protected topological state

I am studying a one-dimensional bosonic system with $ U(1) \rtimes Z_2^T$ symmetry numerically, which might has a symmetry-proteced toplogical(SPT) phase. I have several questions about the symmetry-...
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161 views

Local phase gauge in momentum space of Bloch state

We know Bloch state has a phase undetermined, so $\Psi_k \to \Psi_k' = e^{i\theta(k)}\Psi_k$ is still the same eigenstate. My question: Are there some restriction on $\theta(k)$ except to be a real ...
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217 views

Numerical study of Hubbard Model and Spin Charge Separation effect

Hi, How can i implement the creation operator effect on the ground state(in FORTRAN)? we calculate the ground state using modified Lanczos method,and we obtain a vector(array) with lots of numbers in ...
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148 views

How to observe Floquet state?

The Schrodinger equation is $i\hbar\partial_t\psi(t)=H(t)\psi(t)$. Now given that the situation that the Hamiltonian is periodically driven, i.e., $H(t+T)=H(t)$, then the equation can be solved by ...
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82 views

How to find dispersion relation for 1 d topological insulator?

Is it correct to write the dispersion relation for following Hamiltonian where $\sigma_{x}$ act in spin space and $\tau_{x}$ acts in pseudo spin particle hole spin $H_{BdG} (k)=(\xi_{k}+B\sigma_{x}+u ...
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How to distinguish Shake-Up Satellites from Plasmons?

I am studying XPS spectra (X-ray Photoelectron Spectroscopy) at the moment. In XPS, different processes can influence the final state energy of detected electrons. One of these processes is the ...
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95 views

Eigenvalue of Hamiltonian under gauge transform of Bloch state

$H = \sum_{k} V(q) a_{k4}^{\dagger}b_{k3}^{\dagger}b_{k2}a_{k1}$ where $q$ is the transfer momentum, $a$ $b$ are two orbits or two sublattice sites. Will the eigenvalues of the above Hamiltonian ...
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239 views

How can Multiple Andreev Reflections be explained as a succession of individual Andreev reflections?

I have understood the mechanisms at work in single Andreev reflections (N(ormal)-S(uperconducter) interface) and Andreev bound states (N-S-N). For multiple Andreev reflections of order 3, the ...
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134 views

Which Symmetry class and what kind of topological invariant for $2D -p+ip$?

What kind of topological invariants are there for $2D-p+ip$ topological superconductor and to which symmetry class it belongs to?
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Is there any method to solve the many particle stationary scattering problem like the one for the single particle problem?

The stationary scattering problem by a potential barrier lies in every textbook of quantum mechanics, in which the scattering amplitudes for the single particle wave can be obtained by solving the ...