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

learn more… | top users | synonyms

2
votes
0answers
89 views

Some questions about the Kitaev Chain Model

In the paper,'Unpaired Majorana Fermions in Quantum Wires', Kitaev shows that unpaired Majorana Modes can be found at the end of a Quantum Wire for certain conditions. The effective Hamiltonian ...
2
votes
0answers
52 views

Tight binding Hamiltonian in the k-space

I want to find the band structure of this 2 dimensional lattice which isn't completely flat: Using a tight binding model.And take unit cells as they are shown in the figure. And assuming that each ...
2
votes
1answer
46 views

Why does Fermi Level change due to change in donor atom concentration?

Suppose I have a n-type semiconductor whose fermi-level lies (say) 0.2 eV below the conduction band. Why would this level change if I changed the doping by making the donor concentration (say) 4 times ...
0
votes
0answers
16 views

How does from the curvature of the energy surface, different phases of matter can be identified?

I have recently started reading about the topological order in condensed matter. I am trying to understand the role of topology of the energy surface in distinguishing the different phases of matter. ...
0
votes
1answer
20 views

Is a typical glass slide really amorphous or does it just have very small crystallites?

I heard today that there's not really any true amorphous materials; that the theoretical concept (no level of ordering whatsoever) exists of course, but that no materials are 100% truly random and ...
2
votes
1answer
136 views

Calculating the boundary modes in Kitaev Chain

In section 2 of the paper, 'Unpaired Majorana Fermions in Quantum Wires', equation (14), the following transformation: \begin{equation} b^{'} = \sum_{j} (\alpha_+ ^{'} x_+ ^{j} + \alpha_- ^{'} x_- ^{...
0
votes
0answers
63 views

Confused about the substitution of the fermionic operators with their Fourier transform in an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
votes
0answers
53 views

Why is there a state which is annihilated by two different operators with same absolute Fourier index?

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposed a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
votes
1answer
33 views

Reasoning behind taking the Fourier transform of the fermionic operators for a circular $1$D spin chain [closed]

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
votes
1answer
28 views

Boundary value condition used during Jordan-Wigner transformation for a $1 D$ Ising chain

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
1
vote
1answer
49 views

Reason behind choosing the invariant states for an operator which commutes with an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
4
votes
2answers
105 views

Partition function and coherent state path integral

I have been working through the derivation of the partition function expressed as a path integral in terms of coherent states, following the many-body condensed-matter field theory books of Altland &...
1
vote
0answers
30 views

Why do the singularities of the thermodynamic functions expected to be non-negative powers?

I am going through the first chapter of Exactly Solved Models in Statistical Mechanics. On page 4, at the end of section 1.1 it is said that: I would like to know the basis of this expectation. ...
2
votes
1answer
65 views

Is zero heat capacity possible without violating the third law of thermodynamics?

Suppose we have a gapped system i.e. no gapless excitation is possible. If the thermal energy is insufficient to excite atoms from ground state to excited state of any kind (of a single atom or of a ...
2
votes
1answer
74 views

Kitaev Chain Spectrum (Unpaired Majorana Fermions in quantum wires) [closed]

How does one arrive at the spectrum equation(13): $$\epsilon (q)=\pm \sqrt{(2w \cos q +\mu)^2+4\cdot \mid {\Delta} \mid^2 \sin ^{2} q}$$ from the initial Hamiltonian. Also, shouldn't (12) in the ...
1
vote
0answers
22 views

Derivation of zero temperature conductivity in Dirac materials - Einstein formula

I've come across this in multiple papers but have no idea where this comes from. For the Dirac materials the zero temperature conductivity $\sigma$ can then be expressed as $\sigma = e^2v_{F}^2D\ \...
2
votes
1answer
76 views

Why does $\prod^n_{j=1}\sigma^{(j)}_x$ commute with this adiabatic Hamiltonian? [closed]

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. The adiabatic Hamiltonian is defined as $$...
4
votes
1answer
90 views

Ground state of an adiabatic Hamiltonian as an eigenstate of the total spin

I am going through Quantum Adiabatic Evolution Algorithms with Different Paths by Farhi et al. Here, the authors propose to add a special term to the adiabatic Hamiltonian so that the path of the ...
2
votes
1answer
21 views

Experimental confirmation of the finite jump of the occupation number at the Fermi surface

It is a well-known result in Fermi-liquid theory that the occupation number has a finite jump at the Fermi surface. But, is it confirmed experimentally?
4
votes
1answer
76 views

Finding explicit unimodular transformations for Chern-Simons K-matrices

An invertible, symmetric matrix with integer entries, $K$, that encodes the braiding and statistics of an Abelian topologically ordered state, is equivalent to another such matrix, $K'$, if there ...
1
vote
1answer
36 views

Question about the Luttinger liquid

I am learning Luttinger liquid now. It is a very basic question, I think. Look at the figure. For each $k $, there is a state for the left mover and a state for the right mover, right? They have the ...
1
vote
0answers
27 views

High pressure deformation of metals

Does copper undergo elastic recovery after being exposed to high pressures (above 30 GPa in a diamond anvil) at room temperature?
1
vote
1answer
45 views

What is the Single Mode Approximation?

When Girvin and co-workers solved the excited collective modes called magneto-rotons in Fractional Quantum Hall liquids, they used something called the Single Mode Approximation (SMA). My question is: ...
2
votes
1answer
102 views

Why is Wick contraction a $c$-number?

It is mentioned in Fetter's Quantum Theory of Many-Particle Systems (in contraction part of section 8 Wick's Theorem), that: contractions are c numbers in the occupation-number Hilbert space, not ...
4
votes
1answer
77 views

Computing the density operator commutation relations (Atland & Simons)

I'm trying to work through Altland and Simons' example of interacting fermions in one dimension. It's in chapter 2, page 70 (you can find it here). They define fermionic operators $$ a_{sk}^\dagger $$...
0
votes
0answers
31 views

Questions on the Lechner-Hauke-Zoller quantum annealing architecture

The Lechner-Hauke-Zoller quantum annealing architecture was first introduced in A quantum annealing architecture with all-to-all connectivity from local interactions. While going through the paper, I ...
0
votes
0answers
44 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
votes
0answers
26 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 ...
7
votes
2answers
71 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
votes
0answers
42 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 Landau-...
0
votes
0answers
20 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 ...
6
votes
1answer
139 views

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: http://link.springer.com/book/...
1
vote
0answers
30 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
votes
0answers
28 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 ...
4
votes
1answer
58 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
84 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 ...
8
votes
3answers
126 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 $...
2
votes
1answer
46 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} + \...
15
votes
2answers
937 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
votes
3answers
88 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 ...
4
votes
1answer
63 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 ...
1
vote
0answers
58 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
votes
0answers
60 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: ...
2
votes
0answers
63 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 ...
0
votes
0answers
21 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 ...
2
votes
0answers
36 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} C^{\dagger}...
0
votes
0answers
10 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 ...
1
vote
0answers
34 views

Relationship between energy bands, DOS and magnetic ordering

I'm struggling to understand whether we can tell if a system will have magnetic ordering (e.g. antiferromagnetic) based on the aspect of an energy bands plot or/and the form of the DOS. My thought ...
0
votes
1answer
31 views

Conformational Analysis of Ethane and Butane

How does a condensed matter theorist explain conformations of Ethane and Butane using tools from Quantum field theory? If they don't how do they calculate energy differences and predict differences ...
2
votes
0answers
35 views

Why electron phonon interaction happends near fermi surface?

Usually the energy correction to electron by electron phonon interaction in metals at zero tempreture has the form(Gerald D.Mahan Many-Particle Physics, Third Edition, Sec. 7.4) $$ \sum(k,u)=\int\frac{...