# 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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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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### $\mathbb{Z}_2$ 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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### $C$, $P$, $T$ 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 ...