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

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+50

Wick's theorem and transverse field ising model

I am trying to understand calculation of correlation function in the ground state of the Transverse Field Ising model, from the following book, which is freely available: ...
0
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0answers
28 views

Eigenstates of 2D harmonic oscillator in a constant magnetic field

I want to find the eigenstates of the 2D harmonic oscillator in a constant magnetic field $\vec B = \vec B(x,y)$. My Hamiltonian reads $H_0 = H_{xy} + H_z$ where $H_{xy}$, is the hamiltonian of the ...
0
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0answers
14 views

Derivation of effective mass equation in carbon nanotubes

I am trying to reproduce the calculations in the paper here by Ando and Nakanishi and am already stuck on equation 1. It is stated that in the vicinity of $\epsilon=0$ the amplitude of the ...
4
votes
3answers
421 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
4
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0answers
18 views

bare Phonon and Symmetry Breaking

In condensed matter physics, the phonon is considered as a quasiparticle which is a result of the quantization of lattice vibrations. In many textbooks on solid state physics, it can be done if we ...
0
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1answer
198 views

Tight binding Hamiltonian for 2D finite dimensional lattice and nanowire

The Hamiltonian of a 1D lattice having finite $N$ atoms, (if we consider one basis per atom) is given by the following $N\times N$ matrix- Here $E$ is the onsite energy and $t$ is the hopping ...
0
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0answers
25 views

How to calculate the string order parameter (for Haldane phase) in density matrix renormalization group?

The ground state of the spin-1 chain is the Haldane phase, which is known to be a symmetry protected topological phase and cannot be detected by conventional order parameter (beyond the ...
-3
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0answers
25 views

Condensed matter physics theorem? [on hold]

I would like to summarize theorems in theoretical and experimental condensed matter physics. such as, say, Mermin-wagner theorem or LSM theorem .. etc. Plesase tell me the names of theorems what you ...
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0answers
13 views

Topological insulators and high symmetry points

I've been reading about topological insulators (topological systems in general) and one signature (or the defining signature?) is that an odd number of surface states cross the Fermi energy between ...
2
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2answers
113 views

What is $\epsilon_\infty$ in this equation and why can it be neglected in the IR?

I'm reading this paper (warning, PDF) and they mention that the complex permittivity $\epsilon$ and complex conductivity $\sigma$ are related through the equation $$\epsilon - \epsilon_\infty = (4\pi ...
5
votes
1answer
658 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 ...
1
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0answers
23 views

Temperature dependent chemical potential

Chemical potential is determined by the number of electrons in the system and coincides with the Fermi energy at zero temperature. The chemical potential can shift as temperature changes if the ...
0
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0answers
19 views

How Periodic Boundary Condition (PBC) is related to Band Structure of Quantum Dot?

I am reading about relationship between different lattices and their band structures.I have few questions about them: Q 1. Is is possible to find out band structure of a quantum dot (which is a ...
7
votes
3answers
103 views

Validity of mean-field approximation

In mean-field approximation we replace the interaction term of the Hamiltonian by a term, which is quadratic in creation and annihilation operators. For example, in the case of the BCS theory, where ...
4
votes
1answer
44 views

quantum and thermal fluctuations in 1D, 2D, 3D

Why do thermal and quantum fluctuations destroy long-range order in 1D and 2D? Why not in 3D? If the answer is quite elaborated (with many formulas) perhaps a reference would be better. Sorry if this ...
3
votes
1answer
56 views

Why thermal conductivity increases with temperature?

what is the molecular mechanism with which thermal conductivity increases by increasing temperature? at least for metals? I know that heat increases the oscillations of the atoms in the crystal. But ...
0
votes
1answer
192 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}} ...
3
votes
1answer
269 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
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1answer
25 views

Velocity matrix and non-local pseudo potentials

It is known that velocity of bloch wave functions are related to band energy derivatives: $$v(k)=\frac{1}{\hbar}\frac{\partial \epsilon}{\partial k}$$ However, in the following paper, it is given ...
1
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2answers
212 views

What is the physical significance of the Curie constant?

What is the physical significance of the Curie constant? I understand it depends on the effective moment of the ion and hence must be some measure of it, but what is it exactly? Like some average ...
6
votes
3answers
3k views

What does Fermi level in the band gap mean?

What does it mean that the Fermi level for some semiconductors lie in the band gap? Is Fermi level definition different from what is know as usual? We define the Fermi level as the highest level of ...
7
votes
1answer
277 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
1
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1answer
275 views

Tight binding in the limit of large system size

Suppose that one has a continuous Hamiltonian with spin-orbit interaction, for example $H=-\dfrac{\mathbf{p}^2}{2m} +\kappa({\boldsymbol\sigma}\times\mathbf{p}) + U(x)$ and want to approximate this ...
12
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1answer
346 views

How to understand topological order at finite temperature?

I have heard that in 2+1D, there are no topological order in finite temperature. Topological entanglement entropy $\gamma$ is zero except in zero temperature. However, we still observe some features ...
2
votes
1answer
33 views

Is Mott insulator the same as non-compressible quantum fluid?

In the field of ultracold quantum gases we study the so called Bose-Hubbard model given in second quantization: $$\hat{\mathcal{H}} = -t\sum_{\langle i,j\rangle}\hat{a}^{\dagger}_{i}\hat{a}_{j} + ...
4
votes
1answer
59 views

Is diamagnetism a static or dynamic effect?

When we put a diamagnetic material in the presence of an external magnetic field $\vec B_0$, the magnetic field inside the material decreases to $$\vec B=(1+\chi_m)\vec B_0,$$ where the magnetic ...
14
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2answers
888 views

Rest mass of phonon: is this concept definable?

Phonons are obtaied by non-relativistic quantization of the lattice vibration. The dispersion relation is given by $\omega=c_s k$ where $c_s$ is the velocity of sound. What can we say about the mass ...
2
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3answers
3k views

Why should the Fermi level of a n-doped semiconductor be below the one of a p-doped?

In a pn-junction, the difference in Fermi level between the p doped and the n doped regions causes the apparition of a built-in electric field at equilibrium. This electric field goes from the n to ...
3
votes
1answer
746 views

Phonon Momentum

I am reading Charles Kittel's solid state physics and wondering what's the mechanism that neutron waves and photons can interact with phonons and the process obey the generalized momentum-energy ...
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2answers
447 views

Momentum change in collisions (Drude model)

A particle suffers elastic collisions with scattering centres with a probability of collision per unit time $\lambda$. After a collision the particle is in a direction characterized by a solid ...
2
votes
3answers
80 views

Why identical particle states are multiplied?

In case of identical particles we multiply the individual wave functions of the particles to get the system wave funtion. But why are we not adding? Or performing any other operation to get the system ...
5
votes
1answer
143 views

How is superconducting coherence length measured in experiment?

In a superconductor, the coherence length measure the mean distance between two electrons in the Cooper pair. How is the coherence length experimentally measured?
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21 views

Does the temperature of a solution affect the mass of Aspirin in that solution?

I have a lab in chemistry and I have to find out if the temperature could affect the mass of acetylsacytic acid in a solution. Thank you!
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24 views

What many-body physics book is taught in universities of europ and USA? [duplicate]

Please suggest me a standard many-body physics book for teaching to PhD students of solid state physics. as i know "many particle physics" by mahan is a great book in this field but cant be taught in ...
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0answers
53 views

How to calculate the contour integration with branch point? [closed]

The question come from a Mutusbara Sum like this $${ \sum _{ { z=i\omega }_{ n } } { \frac { -\alpha E\pi }{ 4{ z }^{ 3 }\sqrt { -\alpha -z } } } }$$ it equal a contour integral around Imaginary ...
0
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0answers
45 views

How should I interpret the x-axis of an electronic band structure diagram ? Is it the direction an electron is moving?

Recently I've come in contact with electronic structure diagrams for my thesis and I have some difficulties getting an intuitive interpretation of reading these diagrams. What I think is happening: ...
3
votes
2answers
386 views

Schrödinger equation for many body systems

$$H_{tot}=\sum \dfrac{p_i^2}{2m}+\sum\dfrac{p_I^2}{2M_I}+\sum V_{nucl}(r_i)+\dfrac{1}{2}\sum_{i\ne j} \dfrac{e^2}{|r_i-r_j|}+\dfrac{1}{2}\sum_{I\ne J}\dfrac{z_Iz_Je^2}{|R_I-R_J|} $$ with: ...
11
votes
1answer
266 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. ...
2
votes
0answers
43 views

Anisotropic Hiesenberg model

I am reading the review article, "Quantum spin chains and Haldane gap" by I Affleck (http://iopscience.iop.org/article/10.1088/0953-8984/1/19/001/pdf). At one point of the discussion, he considers an ...
1
vote
2answers
278 views

What kinds of behavioural anomalies can a zero-field-cooled (ZFC) / field-cooled (FC) split indicate?

If a material shows a spiltting in the ZFC and FC curves, is it necessarily superparamagnetic, or could there be any other reason for the irreversibility? I have heard spin glasses also show ZFC-FC ...
1
vote
1answer
164 views

Point group symmetries and unit cell

I was wondering if the unit cell (of a given lattice) had to have every point group symmetries of the lattice it defines ? I guess there is no unique way to define a unit cell and that it may not have ...
0
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0answers
16 views

Triangular and Kagome lattice anti ferromagnet at zero temperature

The triangular lattice with anti ferromagnetically coupled nearest neighbour ising spins has a power law ordered zero temperature state at the three sublattice wavevector. Kagome lattice, with the ...
8
votes
2answers
159 views

Can anyons emerge from momentum-space other than spatial dimensions?

So far in condensed matter physics, I only know anyons(abelian or nonabelian) can emerge as quasiparticles in 2D real-space. But is there any possibility to construct anyons in momentum-space ? And ...
3
votes
2answers
372 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
2
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0answers
35 views

Is electron phonon interaction important away from fermi surface?

In weak coupling superconductor, the effective electron phonon interaction can be written as $$ H_{eff}=\frac{1}{2}\sum_{q,k_1,k_2,\sigma_1,\sigma_2} V_{k_1,q}C^{\dagger}_{k_1+q,\sigma_1} ...
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0answers
9 views

Calculating the matrix element for interband absorption

I am reading the book by Fox 'optical properties of solids'. In chapter 3, he considers the interband absorption of photons in an direct band solid. It is necessary to calculate the matrix element ...
3
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0answers
134 views

Are symmetries of a degenerate ground-state manifold always broken?

If a Hamiltonian has a global symmetry and a degenerate ground state, then in the thermodynamic limit, the ground states $| \psi \rangle$ that are eigenstates of the symmetry operator typically become ...
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1answer
32 views

Ohm's law deviation

In terms of superconductivities and diodes (I do not know anything else except these), Ohm's law deviate from a linear relation. I search many titles or tags for this but I did not understand properly ...
4
votes
1answer
296 views

effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
3
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1answer
338 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 ...