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Questions tagged [condensed-matter]

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

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Quantum statistical mechanics formalism

How do we solve a Hamiltonian written in second quantization by using quantum statistical formalism? For example, the following Hamiltonian $$H = \sum_{i=1}^L c_{i+1}^\dagger c_i + h.c.$$ I have ...
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About electrode self-energy and the relation between transmission functions and Green’s functions

I am reading Electronic Transport in Mesoscopic Systems by Supriyo Datta. I got stucked when deriving some formulas. On page 147, the book says "see exercise E.3.3" when it gives the formula (3.5.18), ...
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Two-dimensional bosonic field theory

I'm struggeling with the following question: Consider a two-dimensional bosonic field theory defined by the following action $$S =\frac{k}{2} \int dx_{1}dx_2 [(∂x_1 φ(x_1, x_2))^2 + (∂x_2 φ(x_1, ...
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Why an insufficient overlap cause vanishing exchange interaction?

Why should the exchange interaction vanish if the atoms do not have sufficient overlap in their overfunctions? For exchange interaction not to vanish, the only requirement seems to be that the ...
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Does GGA have any deviations in qualitative properties of band structure not just the quantitative band gap size compared to GW?

I found out several articles that emphasize the underestimate of the band gap by GGA calculation. And the GW method gets better results to experimental values. But it's hard to get advice for the ...
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Do condensed-matter field theories with multiple fields generically have multiple speeds of sound?

It is well known that the low-energy physics of many non-relativistic condensed matter systems can be described by field theories that display emergent Lorentz symmetry. The heuristic way to figure ...
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Deriving effective interactions, e.g. phonon-mediated electron-electron interaction

Upshot of the question: how can I derive the effective electron-electron interaction brought about by the electron-phonon interaction? I've read derivations of the electron-phonon interaction and ...
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34 views

Interacting term in Jellium model

I have a question about the deduction of interacting term in Jellium model. In the text book Condensed Matter Field Theory ed.2 Alexander Altland, Ben Simons, pg.52. Author gives the expression of e-e ...
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Equation of state of Lennard-Jones spheres

One way of accounting for van der Waals interactions in fluids is to use the Lennard-Jones potential [*], which has a repulsive term that dominates at short distances which mimics the hard-core ...
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1answer
41 views

Why do purely harmonic interatomic interactions result in infinite thermal conductivity?

When interatomic interactions are purely harmonic, normal modes cannot interact, and therefore no phonon scattering occurs, thus resulting in infinite thermal conductivity. But why is anharmonicity ...
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20 views

Why are magnon/phonon/photon velocities linear response quantities?

On page 2 of this paper, Onsager reciprocal relation for linear response is introduced as $$K_{AB}(q,\omega,B)=\epsilon_A\epsilon_B K_{BA}(-q,\omega,-B)$$ where $\epsilon_A,\epsilon_B=\pm1$ specifies ...
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Density of state $g(e)$ Bose-Einstein Condensation system [closed]

Consider Bose-Einstein condensation of a hypothetical system consisting of N boson particles. The energy of single-particle states is e= eo n^2, where eo is the energy of the ground state and n = 1, ...
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52 views

reaching from $\hat{A}=A_{\alpha\beta}|\alpha\rangle\langle\beta|$ to $\hat{A}=A_{\alpha\beta}a_\alpha^\dagger a_\beta$

In quantum mechanics we learn that an operator in a basis can be represented as $$\hat{A}=\sum\limits_{\alpha,\beta}A_{\alpha\beta}|\alpha\rangle\langle\beta|.$$ But in many-body physics we suddenly ...
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Partial Transpose in Gapped Time-reversal Symmetric Spin Chains

Suppose you have a one-dimensional quantum spin system with on-site Hilbert spaces $\mathcal{S}$. Suppose there is an anti-unitary, anti-linear operator $C$ on $\mathcal{S}$ inducing an anti-linear, ...
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Fluctuation-Dissipation Theorem in the Keldysh Formalism

In Kamenev's book Field Theory of Non-Equilibrium Systems (he also has lecture notes online here, which contains the relevant statement on pg. 17), he states that the following equation $$G^K(\epsilon)...
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Are anomalous Hall effect and spin Hall effect mutually exclusive?

In many papers that cover an analysis of hall effects, the spin hall effect is often qualitatively described as being nearly the same as the anomalous hall effect except for the fact that it doesn't ...
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1answer
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Structure factor in a homogenous system

I want to calculate the structure factor for a homogenous system. The system that I am dealing with is the results of a Vicsek type model simulation. The structure factor is defined as : $$S(q) = \...
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Tight binding hopping

The definition of the tight-binding model is that the electrons are sited on certain points(the Wannier centers) and that they can hop in linear paths, when we refer to sites that belong to the ...
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Does the polarized Kagome antiferromagnet contain Dirac or Weyl points?

I've been reading about frustrated quantum magnets lately and a prominent topic is the study of antiferromagnets on the Kagome lattice. A calculation of the spectrum for the sort of model I have in ...
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42 views

Why do the $C_v$ of gapless systems have a power law behaviour?

The functional dependence of the heat capacity $C_v$ of systems with gapless excitations (e.g., lattice with acoustic phonons, Heisenberg ferromagnet with spin waves etc) is like a power law $$C_v\sim ...
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1answer
43 views

Optical and acoustic branch

Does a diatomic crystal posses both optical and acoustic branch simultaneously; Or, whether the vibration is either optical or acoustic?
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Can we define Spin-Chern number for original QAHE Haldane model?

In Haldane's original paper [5], he discusses the quantum anomalous Hall effect as being characterized by the so-called Chern number that is the surface integral of Berry curvature over the entire ...
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Peierls phase in graphene

In the introduction of the paper presented here, a derivation of the Peierls phase is presented, using a Wannier base of eigenfunctions and the Kohn-Sham Hamiltonian. After it symbolises the hopping ...
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Conductive properties of oxidation depleted metals

When oxidation occurs on the surface of a metal it is know that there has to be diffusion of metallic elements from the bulk of the metal to the surface to react with oxygen, creating a concentration ...
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Physical Interpretation of the Spectrum of MPS Transfer Matrices

Take an injective, translation invariant MPS with transfer matrix $E = \sum_\sigma \overline{A^\sigma} \otimes A^\sigma$ (i am using the terminology of https://arxiv.org/abs/quant-ph/0410227 , eq. (6))...
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Closed and open orbit of electrons

What is exactly the difference between closed and open electron orbits?. Is it that, when crossed electric and magnetic field is applied, the electron in the real space does not complete an orbit, and ...
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31 views

Topological Hall Effect vs. Anomalous Hall Effect

Is the Topological Hall Effect just another name for the Anomalous Hall Effect in a system that isn't ferromagnetic? That is, will some papers refer to this phenomena as "Topological Hall Effect" ...
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1answer
29 views

Two Dimensional Self-Reciprocal BravaisLattice

I've been reading Quantum States of Atoms Molecules and Solids by Morrison et al. for a condensed matter course. They make the claim that all 2D Bravais lattices are self-reciprocal, but I'm having ...
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rigorous definition of coherence length at mean field theory

so as far as I know, when we are doing mean field theory, in qft, we expand a action of a theory around a classical solution. so we find a classical solution, than we add quantum mechanical ...
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147 views

Matsubara Sums and Multiple Poles

In Mahan's book, equation (4.127), he claims that \begin{align} &\frac{1}{\beta}\sum_{ik_n} \frac{1}{ik_n-\xi_1}\frac{1}{ik_n-\xi_2}\frac{1}{ik_n-\xi_3} \\ =& \frac{n_F(\xi_1)}{(\xi_1-\xi_2)(\...
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1answer
49 views

Why isn't superconductivity destroyed by the Goldstone modes?

In BCS theory they break particle number conservation and show the existence of a gap, which would explain why groundstate properties stay relatively the same even for higher temperatures (until beta ...
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32 views

Derivation of the Berry Curvature and Bloch Magentic Moment in Graphene

I am attempting to derive equations 2 and 6 from Xiao et al. paper "Valley contrasting physics in graphene" (Link to paper). The Hamiltonian for graphene with a staggered sublattice potential (in ...
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1answer
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What does the curve branch for $\omega > \omega_p$ mean for surface plasmon dispersion?

Consider a half-infinite metal (the other half is vacuum with $\varepsilon=1$). By solving Maxwell's equations and using boundary conditions at the interface, we get the dispersion: $$ \frac{\...
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Can we numerically find ground-state of a 1D tight binding Hamiltonain with odd sites at half filling?

We can numerically find ground state energy and wavefunction of a 1D Hamiltonian at half-filling ($L = \#$ of sites and $N = \# $ of particles) using exact diagonalization. i.e at $L = 10$ and $N = 5$,...
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What does it mean for a wavevector to terminate?

In the question we are told that the amplitude of a wave after being diffracted through a crystal is: $$ S\propto e^{i\mathbf{k\cdot r_D}}\sum_n e^{i(\mathbf{k-k_0)\cdot r_n}} $$ where $k_0$ is the ...
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1answer
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Honeycomb lattice Brillouin zone structure and direct lattice periodic boundary conditions

One way to construct the Brillouin zone of the Honeycomb lattice is by obtaining the standard Wigner-Seitz cell by constructing the perpendicular bisectors of the reciprocal lattice vectors and ...
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What's the difference between cylindrical geometry and disk with a hole for topological chiral $p_x\!+\!i p_y$ superconductor?

We know that for a topological chiral p-wave superconductor with a cylindrical geometry, i.e. one conserved momentum $k$ and one open boundary direction, there exists edge modes with opposite ...
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Maximizing mutual information with Restricted Boltzmann Machines and Monte-Carlo sampling

So I've been reading through Koch-Janusz and Ringel's, "Mutual Information, Neural Networks, and the Renormalization Group" (check it out here). I'm currently trying to reimplement some results from ...
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How do irrational numbers give incommensurate potential (in lattice models)?

I am trying to understand Aubry-Andre model. It has the following form $$H = \sum_n c_n^\dagger c_{n+1}+H.C.+V\sum_n \cos{(2\pi\beta n)}c_n^\dagger c_n$$ This reference (at 3rd page) says that if $\...
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QM explanation (electrons and lattice structure) why aluminum does not get hot in an oven?

I have read this question: Why can I touch aluminum foil in the oven and not get burned? But the answers therein only explain on a classical level why aluminum foil being a very good conductor and ...
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Symmetry acting on a complex fermion operator

Suppose $S$ is a $\mathbb{Z}_2$ symmetry operator, i.e. $S^2=1$, acting on the fermion $c_{n}$ via $$S c_{n} S^{-1} = \sum_{m} U_{nm} c_{m}$$ and I am interested in $S$ is both linear or anti linear, ...
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Doubts in understanding the elastic property of matter

Here the graph of potential energy and force produced due to interaction between two atoms are given . And at a particular separation between the atoms, they have their minimum potential energy. And ...
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1answer
42 views

How to write BdG equation for generalize Hamiltonian?

I am reading this parer Majorana Corner Modes in a High-Temperature Platform,The Bogoliubov–de Gennes Hamiltonian is : $\hat{H}=\sum_{k}\Psi^\dagger_kH(\vec{k})\Psi_k$with $\Psi_k=(c_{a,k\uparrow},...
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Is naturalness meaningful for non-fundamental theories?

Naturalness has been a guiding philosophy for particle physics for a long time, but a few years ago I heard a talk by Nima Arkani-Hamed where he pointed out that it seems to have failed us as it ...
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How isthe transparency of glass explained in physics? [closed]

I would like a rigorous explanation: a theory and model which describes glass as well as iron, and see why one of them is transparent; a detailed mathematical computation or a detailed reference. And,...
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The surface states and Fermi arcs in Weyl semimetals

I'm confused about surface states in Weyl semimetals. Assume that we have a single pair of Weyl points and the Fermi level turned to this points. In this https://arxiv.org/abs/1301.0330 paper the ...
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What are dark excitons and how to find them?

I am reading about excitons and I encountered a few times the term "dark exciton" but I have a hard time finding a good definition. I tried to google it but I only find scientific articles where the ...
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1answer
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How can I find edge states given a bulk Hamiltonian for a topologically ordered phase?

Suppose we have a momentum space tight binding Hamiltonian $H(\vec{k})$ that describes some topologically ordered system. It could be a Chern insulator in two dimensions, or a Weyl semimetal in three ...
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1answer
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How to (hypothetically) calculate $\tau$, the mean free time?

Referring to the Drude Model, I've seen a lot of excellent questions on whether $\tau$ should be thought of as the "average time between collisions" or the "average time until the next collision", and ...
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