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Questions tagged [condensed-matter]

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

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Gutzwiller renormalization factors

I am computing the expectation value of the kinetic term of a tight-binding model, respect to the Gutzwiller wavefunction, in the limit of infinite lattice-coordination, i.e using these constraints (...
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Average number of particles in quantum well [on hold]

An ideal gas of non-relativistic particles is in a box with perodic boundary conditions. I've shown that its chemical potential is given by: $$\mu=-kT\ln \left( \left( \frac{2\pi m}{h^2} \right)^{3/...
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Long-ranged Coulomb Interaction $\Rightarrow$ Longitudinal Plasmon Modes?

I am currently taking a lecture on quantum theory of condesed matter systems. In the lecture notes it is stated that For long-ranged Coulomb interactions only longitudinal plasmon modes are ...
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Matching band momenta of zigzag and infinite graphene

Let's say the zigzag line is along the $x$-direction. The 2D 1st Brillouin zone (BZ) of an infinite graphene is a hexagon with inequivalent Dirac points located alternately at the 6 corners as shown. ...
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How can we prove that correlation function depends only on the spatial difference if Hamiltonian is translationally invariant?

If $H$ is a translationally invariant Hamiltonian, how can I convince myself that the correlation function (on the ground state $\left|G\right\rangle$) $\left\langle G|\psi(x)\psi(x’)|G\right\rangle$ ...
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Calculation of free energy for Bloch electrons

The question is based on Eq. 6-9 in this paper https://arxiv.org/abs/0704.3824. Basically the free energy is defined as $ K({\bf r}) =\sum_{n{\bf k}} f_{n{\bf k}}\text{Re}\left\{\psi_{n{\bf k}}^*({...
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+100

How does the Berry curvature relate to the hopping strengths in the Haldane model?

Take Haldane's Hamiltonian, as quoted from Fruchart et al.'s An Introduction to Topological Insulators: 3.5.3. Haldane's Hamiltonian The first quantized Hamiltonian of Haldane's model can be ...
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Magnetic Flux in Unit Cell of Haldane Model

I am trying to understand how magnetic fluxes arise due to NN and NNN hopping in Haldane's model. In An Introduction to Topological Insulators by Fruchart et al., we see the following figure: ...
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What is the difference between metallicity and semimetallicity?

I am looking for a definition of semimetallicity from an experimental point of view ( $\rho(T)$, carrier density, mean free path, scattering time, etc.) and from a theoretical point of view. Can ...
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A good instruction on Symmetry enriched Topological phases

I am looking for a good introduction to SETs, and topologically ordered phaeses it should be something describing first principles and gives a good explanation on the basics and the logic of this ...
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How to Explicitly Calculate z-Component of Berry Curvature?

While numerically playing with the 2-level Haldane model recently, I wondered how I could analytically calculate the z-component of the Berry curvature $F$. I framed my problem as needing an ...
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Molecular model of liquids

The macroscopic behavior of gasses and solids follow very intuitively from the description of matter as quasi-spherical molecules interacting with each other with attractive and repulsive forces. ...
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What is so topological about topological phase transitions?

I am studying the KT-transition, which is called a topological phase transition. The phase transition is driven by vortices in a 2-D superfluid, where it is shown that at a critical temperature $T_c$ ...
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53 views

How is atomic position expressed in QM?

I am trying to understand how DFT works. I understand how to express the position of an atom or molecule in terms of the positions of the nuclei and electrons by setting up a Hamiltonian expressed in ...
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Why hydrogen bond forming has lifetimes on picosecond scale?

According to this Research http://www.kinetics.nsc.ru/mds/downloads/2009_JSC_Naber_Vol_LifeTime.pdf hydrogen bonds are formed and destroyed within a timescale of a few picoseconds. Why hydrogen ...
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Gapless modes at the boundary between topological insulator and normal insulator

I am currently learning about topology in condensed matter physics. I think I understand most of how topological indeces come about and differences between Z and Z2 indeces and the symmetries that ...
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1answer
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Bosonic representation of $SU(N)$: what values can $n_b$ take?

In Assa Auerbach's book on page 166, he describes the construction of a bosonic representation of $SU(N)$ where the generators $S^{mn} \rightarrow b^\dagger_m b_n$. I'm a bit confused about the ...
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DMRG for Heisenberg spin chain [closed]

I am learning DMRG. I am writing a DMRG code of Heisenberg chain, which has following Hamiltonian $$H=\sum_i S_i\cdot S_{i+1}$$ The algorithm for infinite DMRG is following: Build left and right ...
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How does a super current affect ductility, maleability and the mechanical properties of a superconductor?

In metals, the ductility, malleability, tensile strength and strain are all determined in part by their free electrons. I am wondering what would happen to all of these properties of a superconductor ...
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Difference between domain size and correlation length in ferromagnetic materials?

I am getting confused about different length scales in magnetic materials. I understand that the correlation length for a ferromagnetic materials is defined as <(s(x)−<(s(x))>)(s(y)−<(s(y))>)>...
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Effective theory of hierarchial fractional quantum hall state

In describing the effective field theory picture of the hierarchical fractional quantum Hall states in Tong's lecture notes, page 165 he gives the expression for filling fraction, quasi-particle ...
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Why the ground state of the Kiteav model almost a singlet?

The interaction strengths J_x=J_y=J_z. I have checked by exact diagonalization.
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Relationship between Eigenvectors of Hamiltonian vs function of the Representations of the Group

I am trying to understand the relationship between the eigenvectors obtained from a diagonalizing a Hamiltonian and the basis functions of the Representations of the Group, $G$, used to build the ...
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Renormalization of sine gordon theory

So assume that we have a usual sine gordon theory in the the theory we have a term in the hamiltonian $$\frac{yu}{2\pi\alpha^2}\int dx \cos(\sqrt{8}\phi_\sigma(x))$$ where $\alpha$ is cut off ...
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How are the orientations and cuts of crystal substrates determined?

I have been looking at piezoelectric crystals, LiNbO3 primarily, so piezoelectric devices. But I have had trouble understanding the cuts and orientations that are referred to with the rotated cuts. ...
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Why do we use matrix product states?

Given a many body $\vert\psi\rangle$, we can express it in terms of a matrix product state. That is, $\vert\psi\rangle = \sum_{i,j..k}\psi_{i,j..k}\vert i,j..k\rangle$ can be rewritten as $\vert\...
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Choice of Unit Cell on Band Diagram (Brillouin Zone Folding)

I am looking at photonic band diagrams specifically, but my question relates to band diagrams in general. For a honeycomb lattice, I can pick a (primitive) rhombic unit cell or a hexagonal unit cell. ...
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Can Einstein relation be used to calculate mobility under equilibrium dynamics?

In weak field non-equilibrium dynamics, mobility can be calculated by Einstein relation $\mu=\frac{eD}{K_BT}$, where $D$ is diffusion constant. Mobility can also be calculated by the definition $\mu=...
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Drude model for metals

The equation of motion in the Drude model is given by: $$\frac{d\mathbf{p}}{dt} = \mathbf{F} - \frac{\mathbf{p}}{\tau},$$ where $\tau$ is the collision time, $\mathbf{F}$ an external force due to ...
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What are the allowed wavenumbers in the finite size system?

Usually, we introduce wavenumber $\textbf{q}$ by Fourier transform, for example, an operator $A_{\textbf{q}}=1/\sqrt{N}*\sum_{i}e^{i \textbf{q}\cdot \textbf{r}_{i}}A_{i}$, where $N$ is number of sites,...
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Physical Meaning of the Gutzwiller Constraints

I have a doubt on the constraints for the expecation values obtained by Bünemann et all. First i want to introduce my notation To analytically solve a tight-binding model, \begin{equation} \hat{H}= ...
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Mermin Wagner theorem proof, what does the K stand for ?

I've been reading about the Mermin-Wagner theorem recently. I think I understand pretty much every computation need to derive its result from the Bogoliub inequality, but there is one thing I don't ...
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Hall effect in superconductors

In many papers on Hall effect in superconductors (in the mixed state), experimental results are plotted as magnetic field vs Hall angle. Why we need to consider the Hall angle in these cases? Can't we ...
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Finding ground state energy using numerical real space renormalization group

I want to find ground state energy (as well as wavefunction) for spinless $tV$ model using Real-Space Renormalization Group (RSRG) approximation. The $tV$ model is defined as $$H=H_t+H_{int}=-t\sum_{i=...
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What if an ocean planet is covered by superfluid ocean? [closed]

It is possible that an ocean planet can be covered by superfluid state liquid. What will happens on this kind of planet? Will there be any changes to tide? Will there be strong magnetic field? Will ...
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Is there any relation between density matrix renormalization group (DMRG) and renormalization group (RG)?

Probably I am going to receive many down-votes for this post but I really need to ask this question here. I am new to statistical mechanics. I wanted to learn Density Matrix Renormalization Group (...
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1answer
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Is metallic hydrogen an example of exciton?

I know that in exciton an electron is excited and goes from valence band to conducting band leaving an electron hole which is positively charged, soon Jupiter came into my mind and then this question. ...
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1answer
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Can one formulate a fluctuation-dissipation theorem in presence of non-Gaussian noise sources?

The fluctuation dissipation theorem relates the linear response of a system to Gaussian fluctuations. The natural question that comes to my mind is the possible derivation of an analogous FDT in ...
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Why does semimetals (particularly nearly compensated ones) have very strong magnetoresistance?

It's well established that semimetals, i.e. metals with both electrons and holes, have a strongest enhancement of its resistance when subject to a magnetic field (namely magnetoresistance). From the ...
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Are phase and particle (photon) number in QED conjugated variables?

I found in A. Zee's book "QFT in a nutshell" (1.edition) the interesting relation (8) respectively (9) in chapter III section 5 (p.173) which states that in a collective of non-relativistic bosons the ...
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What's the explanation for Kohler's rule?

In a metal, the increase of resistivity ($\Delta\rho$) due to an applied magnetic field follows a functional form of the parameter $\rho_0/B$ (residual resistivity divided by magnetic field) i.e. $$(\...
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2answers
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How can I explicitly express the Ising Hamiltonian in matrix form?

I am reading this book about numerical methods in physics. It has the following question: Consider the Ising Hamiltonian defined as following $$H=-\sum_ {i=1}^{N-1} \sigma_i^x \sigma_ {i+1} ^x + h ...
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1answer
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What's the real-space equivalent of the Fermi surface?

So I'm familiar with the concept of Fermi surface in momentum space and all that. But if everything in the momentum space can be obtained by Fourier transforming something in the real space (e.g. ...
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Charging of a superconducting island for arbitrary junction transmission

For this question I am considering a system much like the traditional Cooper pair box shown below: we have a superconducting island, capacitively coupled to a gate electrode, and coupled to a ...
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Resource recommendation: Tensor Networks

I want to learn tensor network methods for condensed matter systems. I went through some basic papers (i.e. 1,2) and come to know that there are many things (i.e. different math, tensors, ...
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What would a non-perturbative renormalization group treatment for polymers look like?

I know that one can do perturbative renormalization for the polymer excluded volume problem or the self-avoiding walk problem corresponding to n=0 component field theory. Here in Hamiltonian, we have, ...
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Debye screening in $\mathbb{R^d}$

Consider the Poisson-Boltzmann equation $$ \nabla^2 V(r) = -\frac{1}{\epsilon_0}en\left(1 - e^{e V(r)/k_BT}\right) $$ which models the electrostatic potential in a spherically symmetric ideal gas of ...
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Why does first photonic band go to zero at the centre of the Brillouin zone?

I have been plotting photonic band diagrams of various geometries recently and I identify if it is correct by looking if it goes to zero at the Brillouin zone centre, $\Gamma$. I realised early on ...
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What is the irreducible Brillouin zone for a rhombic unit cell?

So I realised that the rhombic unit cell is in fact not the same as a hexagonal unit cell. (I thought they both gave hexagonal lattices but the rhomic unit cell with two rods gives a honeycomb lattice ...
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What is the difference between Rashba spin-orbit coupling and Drsselhaus spin-orbit coupling?

It is known that both Rashba and Dresselhaus SOC need to have an inversion asymmetry. what makes them distinctive.