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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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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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Gap closing when performing a topological phase transition

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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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 [on hold]

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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21 views

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.
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What is the charge carrier density $n$ from Hall experiment and in conductivity?

By applying a voltage and a magnetic field on a (let's say metallic to keep things as simple as possible) sample, one is able to create the Hall effect and to obtain the Hall coefficient $R_H \sim 1/n$...
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Are fractional quantum hall effect system symetry enriched topological phases?

In the papers I review they first start to talk about topologically ordered phases of matter. Their standard example of it is FQHE. Than they give another set examples which are quantum spin liquids, ...
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Is the effective magnetic moment defined for substances that follow the Curie-Weiss law?

The effective magnetic moment is defined as follows: \begin{equation} \mu_{eff} = \left(\chi_M \frac{3kT}{N_A\mu_0\mu_B^2}\right)^{\frac{1}{2}} \end{equation} where $\chi_M$ is the molar magnetic ...
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2answers
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Understanding the Su-Schrieffer-Heeger (SSH) model and Topological insulators regarding invariants

I'm studying the topic of Topological insulators, I'm having a very hard time understanding what is the relationship between the fact that topological invariants are different from $0$ and the ...
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1answer
43 views

Is numerical lattice wavefunction smooth? — graphene tight binding case

I tried to follow exactly Sec. II.K [page 112-113, Hamiltonian after Eq. (113)] of the standard Review of Modern Physics paper on graphene, which is a tight-binding model of a graphene stripe under ...
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1answer
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The notion of “Mobility Gaps” in the context of Anderson Localization

In the context of Anderson Localization, I heard statements such as the following: "Due to disorder, there is a broadening of the bands. Although spectral gaps between continuous bands may shrink or ...
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Are interacting symmetry protected topological (SPT) phases and symmetry enriched topological (SET) phases must be gapped?

I wonder are interacting SPT and SET phases gaped? Can we have a SET or interacting SPT phase in a semi metal?
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Negative Eigenvalues of the Hessian

I am calculating the eigenvalues of the Hessian for a ferromagnetic system. My energy has the zeeman term, a nearest neighbor exchange term, and a dipole-dipole term. I create the hessian where my ...
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64 views

Ising model with quantum magnetic field

Hamiltonian of the Ising model with an external magnetic field is written as $$H=-J\sum_{\langle i,j \rangle} s_i s_j + h\sum_j s_j$$ where $J$ is nearest neighbor coupling constant and $h$ is the ...
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1answer
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References to learn about Majorana Zero Modes

I'm a masters student currently trying to learn about Majorana zero modes in condensed matter physics. But so far the references I have checked have been not really useful for learning. I even read ...
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Connection between Bond dimension and Physical Lattice Sites for Tensor Networks

Does the bond dimension for a tensor network (say MERA, for argument's sake) bear any physical consequences for the lattice structure that it is approximating? More succintly: what dictates bond ...
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Couplings in the SYK model

I have read several times by now that the couplings in the SYK model are drawn randomly from a gaussian distribution. I was wondering what exactly is meant by that. To elaborate, when I compute an ...
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Topological Thouless pumping

I can't understand why the number of electrons pumped per cycle of a quantum pump is protected topologically. As for me this number is an integer in any case, because the number of electrons in ...
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On string-like excitations in (3+1)d discrete gauge theory

(3+1)d discrete $G$-gauge theory (untwisted Dijkgraaf-Witten theory) has both point-like and loop-like excitations; Point-like excitation is an electric charge labeled by an irreducible ...