Questions tagged [condensed-matter]

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

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Pair correlation function for non-interacting spinless bosons

While trying to solve a second quantization exercise regarding a bosonic gas, I've been having trouble trying to understand the $(1-\delta_{\text{pq}})$ term in the decomposition of the following ...
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What does the term "condense" mean in the physics literature

When reading the physics literature, we often see the term "condensate". Some examples: in the string net model (Wen, Levin), one will say the string "condensate". in QCD, people ...
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Connection of Sugawara construction to the regular energy-momentum tensor

Update: As pointed out by @ConnorBehan this problem is related to the rearrangement lemma in the 'Yellow Book'. In fact this problem is already mentioned page 649 in the book in the discussion about ...
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Book Recommendation for spin-orbit coupling

I am wondering if there were any recommendations for any books that are around graduate level in regards to the discussion of spin-orbit coupling and the Rashba spin-orbit coupling
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Tight-binding model for decorated square lattice

How do I go about determining the tight-binding Hamiltonian for the crystal structure below? I have identified the primitive lattice vectors $\mathbf{a}_1=(a,0)$ and $\mathbf{a}_2=(0,a)$ for lattice ...
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What is the difference between MOKE hysteresis loop and VSM Hysteresis loop?

I need to understand what is the difference between Magneto-optical Kerr effect (MOKE) hysteresis loop and vibrating sample magnetometer (VSM) hysteresis loop? And the use of each one of them?
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Question About Exchange

Is the Exchange term, for example in a set of Hartree-Fock equations for a solid, to be interpreted as arising from electrons actually, physically, exchanging positions constantly? So, for a metal, I ...
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How an applied magnetic field breaks the inversion symmetry in a centrosymmetric system?

I want to understand why magnetic dipole transition breaks the inversion symmetry in a centrosymmetric system and gives rise to second-order nonlinearity.
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What is the physical significance of reduced zone scheme?

Different energy bands can be drawn in different zones in $k$-space is called Extended-Zone-Scheme, whereas if the different bands are drawn in first Brillouin zone, then its called Reduced Zone ...
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Order and Disorder Operators in QFT

On the wikipedia page, the 't Hooft loop operator is called a "disorder parameter," in contrast to the Wilson loop operator, which is an "order parameter." From my limited ...
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Why only the wavelength and speed of refracted light traveling inside a transparent material changes and not its frequency? [duplicate]

When monochromatic light waves travel from one medium to another the frequency never changes. A transition to a denser medium will result of a slow down of the propagation speed v of the light wave ...
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Role of Berry's curvature in nanomaterials

what is the physics behind Berry's curvature? In many papers, they are explaining topological and anomalous quantum hall effects via Berry's curvature. but what is the physics behind this curvature ...
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Why liquid helium boils as its temperature is lowered?

Water boils when heated. Liquid helium boils when cooled. Not only that. It boils initially and then stops. Why?
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Connection between the imaginary part of retarded correlation function and derivative of Fermi-Dirac distribution function

A two-particle retarded correlation function is (its derivation is not related to my question here) $$ C^R(\omega) = \sum_{kq}\bigg(f(\epsilon_k )-f(\epsilon_{k+q} )\bigg)\frac{1}{\omega+\epsilon_k-\...
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Nambu-Goldstone mode without symmetry breaking

Superfluidity is often explained in terms of spontaneous breaking of global $U(1)$ symmetry. However, we know that in real, finite-size quantum systems, this symmetry can never be broken. Quantum ...
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Electric charge of the Higgs mode in superconductivity

I have a question about the Higgs mode in superconductivity. In this doc, it is said, page 12, that the Higgs mode has no electric charge. But it couples nonlinearly with the photon (in the ...
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Enlargement of unit cell by ordering wave vector for a square (or triangular) lattice

For a square lattice we have lattice vectors $\vec{a_1}=(a,0)$ and $\vec{a_2}=(0,a)$. If we introduce an ordering by a wave vector $\vec{Q}=(\pi/a,\pi/a)$, the unit cell is doubled and the new lattice ...
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Why are time-ordered Greens functions equal to retarded Greens functions at zero temperature?

When I calculate a photon polarization diagram: I get the same answer: If I calculate it in equilibrium (retarded Greens functions) with finite chemical potential, in the limit of zero temperature, ...
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Is the phenomenon of geometrical frustration in condensed matter physics related to some kind of topological invariant?

Edit (attempt to clarify my question a little bit): I’m not thinking geometrical frustration should be necessarily associated to a topological invariant in a direct way, but maybe local geometrical ...
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Charge ordering and orbital ordering - What is the difference?

In the context of condensed matter physics, particularly phase transitions of transition metal compounds, I often encounter charge ordering (CO) and orbital ordering (OO). For me, the terms look ...
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Complex energies of non-reciprocally coupled chain with hoppings of equal absolute value

In the Hatano-Nelson chain (i.e. the simplest 1D tight-binding model with nonreciprocal hopping) for positive hoppings $t_{1,2}>0$ you get a purely real spectrum. However, as soon as you change the ...
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Phase of BCS wavefunction

Can anyone explain to me why the phase of the BCS wavefunction $|\Psi_\text{BCS}\rangle=\prod_\mathbf{k}(|u_\mathbf{k}|+|v_\mathbf{k}|e^{i\theta_\mathbf{k}} \hat{c}_{\mathbf{k}\uparrow}^\dagger\hat{c}...
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Simple explanation of the dynamical mean field theory (DMFT)?

Can someone give me a good reference article or book, that explains the dynamical mean field theory (DMFT) in a simplest possible manner? I've read quite a lot about the DMFT (and used it), but ...
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Fermionic occupation for an inhomogeneous tight-binding model

The model Consider the simple one-dimensional fermionic tight-binding chain of $N$ sites with inhomogenous hopping couplings $t_n$: $$ H = - \sum_n t_n c^\dagger_{n+1} c_n + \text{h.c.} \equiv \sum_{n,...
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$\mathbb{Z}_2$ Symmetry in Water

I have learned that the critical exponents for phase transitions is independent of the microscopic structure of the substance and is dependent on the symmetry. For instance the phase transition for a ...
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The $\rm SO(8)$ invariant interaction piece in Fidkowski and Kitaev's model

In this paper (arXiv link), the authors demonstrate the existence of a quartic interaction $W$ involving the 8 majorana operators $c_1 \ldots c_8$ (eq. 8) which is invariant under an $\rm SO(7)$ ...
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How to build a quantum model of a P-N semicondctor junction?

Literature for quantum modelling of a semicondunctor P-N junction seems to be almost completely absent. I am wondering is it because it is too complex or the justifications provided by classical ...
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How do I maximize the overlap?

I am tasked to find the extend to which the many-body eigenstates can be described by adding a single electron or hole to the ground state. or if there exists a single particle orbital $\phi_i$ such ...
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How do I compute the density of states of the non-interacting Hamiltonian?

I have to show that the trace of the non-interacting spectral function $\int dr A^{0}(r,r,\omega)$ is equal to the density of states (DOS) of the non-interacting hamiltonian. But I can't remember how ...
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Is the Integer Quantum Hall Effect a distinct phase of matter?

In the Landau classification scheme, phases of matter differ in terms of symmetry. However, we know of many instances where this classification scheme does not apply. I have often heard topological ...
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Why the value of Abrikosov beta parameter is a sum of series?

The order parameter $\psi(x,y)$ can be written as : \begin{equation} \psi(x,y)=\sum_{n=-\infty}^{\infty}c_n\exp{(inky)}\exp\left[{-\kappa^2\over2}\left(x-{nk\over\kappa^2}\right)^2\right] \end{...
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Bosonization for the Tomonaga-Luttinger liquid

I'm having a hard time understanding bosonization applied to the Tomonaga-Luttinger liquid. My difficulties appear when contrasting some references which approach the problem in different ways I can't ...
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What are units of quantum field (or creation and annihilation) operators?

Let us have a free particle Hamiltonian given as $$ \hat{H} = \sum_{k}\mathcal{E}_k c_k^\dagger c_k \quad ; \quad \mathcal{E}_k=\frac{\hbar^2k^2}{2m} $$ unit of $\hbar$ are $J\cdot s$, the units of ...
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What is the significance of the shape of the Fermi surface?

First of all, this is something that is very difficult for me to conceptualize (k-space, the BZ, and related topics). Also, currently reading Kittel. I know that the Fermi surface is defined as the ...
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What evidence can be the unambiguous proof of Majorana fermions in condensed matter?

Although in recent years many papers claimed that they observed Majorana fermions in condensed matter, most of them are questioned because of the inability to rule out alternative explanations. So is ...
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BCS Theory: why does $\langle \hat{\Delta}^{\dagger} \hat{\Delta}\rangle \approx \langle \hat{\Delta}^{\dagger}\rangle \langle \hat{\Delta}\rangle$?

My textbook (Advanced QM by Yuli V. Nazarov) defines the Cooper pair creation operator as $$Z_{k}^{\dagger}=c_{k,\uparrow}^{\dagger}c_{-k,\downarrow}^{\dagger}.$$ The text then goes on to show that ...
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Coulomb interaction in 2D crystal

My question is very simple. What is the correct way of modelling a Coulomb interaction on a 2D lattice? Usually for a system that is infinitely big $(N\to\infty)$ and not discrete $(a_0\to 0)$, the ...
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What is the physical meaning of adiabatically varying the wavevector $k$ as a parameter to calculate the Chern number for topological effects?

Could it mean something like applying a weak electric field and perturbing the band structure? Or some other weak perturbation? Or is that the wrong idea?
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How to calculate lattice hamiltonian?

I was watching White's DMRG introduction video on youtube, where he was showing the 1D lattice model as an example. He said that it's hamiltonian is (ignoring the constant factors) $$H = -\frac{\...
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Going from 2D dispersion relation to density of states

If one was to have a 2D dispersion say: $$\varepsilon(k)=k_x^2-k_y^2$$ We know the dispersion relation generally can be written as:$$ D(\varepsilon)=\sum_{k_x}\sum_{k_y}\delta(E-\varepsilon(k_x,k_y)$$ ...
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Pressure and insulator-metal transition

Why does a seemingly large class of materials become (super-)conducting (see [1]) when subjected to strong enough pressure? The issue is discusssed for specific cases in a myriad of papers, but I was ...
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Non-periodic perturbation in solid state

I want to obtain the eigenstates of a crystalline solid with a local perturbation. In other words, I want to solve the following Schrodinger Equation: $$ H(x)=\frac{\nabla^2}{2m}+V(x)+\lambda H'(x)$$ ...
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1answer
51 views

Magnitude of reciprocal-lattice vector

I'm reading "A Journey into Reciprocal Space" by Glazer where the metric tensor in reciprocal space is defined as: $$M^*=\begin{bmatrix} \textbf{a}^*\cdot\textbf{a}^* & \textbf{a}^*\...
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2answers
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$C$, $P$, $T$ symmetry of $O(3)$ non-linear sigma model

Consider the $O(3)$ nonlinear sigma model with topological theta term in 1+1 D: $$\mathcal{L}=|d\textbf{n}|^{2}+\frac{i\theta}{8\pi}\textbf{n}\cdot(d\textbf{n}\times d\textbf{n}).$$ The time reversal ...
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At absolute zero temperature, we see that the electrical resistivity of a metal is not zero - Why? [closed]

I do know that for a perfect conductor, the electrical resistivity is zero at absolute zero temperature. But for an imperfect conductor (e.g. that we use in daily life) it is not zero even at $T=0^{\...
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About "Free electron theory in metals" in Condensed Matter Physics

We study "Free electron theory in metals" in Condensed Matter Physics. While discussing this theory (both classically and quantum mechanically), we assume the electrons moving inside the ...
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1answer
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How to calculate the density of states near a point for the given dispersion relation?

The problem's statement is as follows: Given that $ E(\vec{k}) = ak_x^2 + bk_y^2 + c|k_z|$, Calculate the density of states near $(0,0,0)$. It's easy to do the integration if $E$ is quadratic in ...
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Missing minus sign when taking derivative

I'm trying to understand to get the following formula (first formula on pg 33) in Altland Simons second edition: $$\Delta S \simeq \int d^m x (1 + \partial_{x_\mu} \, (\omega_a \, \partial_{\omega_a} \...
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Why is $\rm CsCl$ simple cubic?

I'm confused with the lattice structure of $\rm CsCl$. It should be categorized as simple cubic, but I wonder why it is not body-centered-cubic (BCC)? Is that because there are two types of atoms, ...
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1answer
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Long-range correlations in transverse field Ising model

The transverse field Ising model in 1+1d has two phases: a symmetric "disordered" phase and a symmetry-breaking "ordered" phase. Both of these phases have a finite excitation gap. ...

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