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

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Ising model on lattices with (vertical side length) $\neq$ (horizontal side length)

Consider the Ising model with nearest neighbours interactions on a rectangular lattice $L\times M$. If $L=M$ (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit ...
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80 views

Why are most ferromagnets metals while antiferromagnets are insulators?

This seems to be experimentally true, but I don't quite have an intuition as the why. In the Ising model, we usually consider an insulating ferromagnet if $J>0$, where $J$ is the exchange coupling. ...
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35 views

Does the q-states Potts become the XY model in large q state?

I have met several times in papers, the order of the phase transition of the $q$-state Potts model depends on $q$. E.g., in two dimensions, for $q = 2$ (the Ising model), $3$, $4$ the order-disorder ...
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34 views

Does the relation between entropy and temperature depend on the ensemble?

If we change the temperature of a given system, there will be a relation between its entropy and temperature S(T). Is S(T) the same in a canonical ensemble and a grand canonical ensemble? If not, is ...
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217 views

Non-trivial solution for a linear set of coefficients involved in the phonon modes of a semiconductor quantum dot

I am trying to use the method outlined in this linked paper (T. Takagahara, Journal of Luminescence, 70 (1996), pp. 129-143) to find the phonon-exciton coupling in a spherical PbS quantum dot. In Eq ...
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42 views

1st order phase transition, superheating/supercooling, metastable state

I read that superheating and supercooling characterize 1st order phase transitions in papers. Some of them also use the metastable state at the same time as the superheating/supercooling. Are ...
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63 views

Disclinations, dislocations, lattices, Displacement fields and scaling

I am looking up Frank, and Burger vectors and associated material on dislocation/disclination. It seems straightforward describing a lattice and what dislocation means. It is even possible to restrict ...
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62 views

A puzzle of thermalization in simulating the 3D XY-model

I am learning the classical Monte Carlo simulation. When I simulate the 3D XY-model $$ \beta H = -\beta J \sum_{<i,j>} cos(\theta_i-\theta_j) $$ where $\beta$ is the inverse of the temperature ...
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24 views

Packing fraction of atoms in a HCP structure

I am looking to find the ratio of atomic sphere to unit cell volume in a HCP (hexagonal close packing) arrangement. Some sources I have say it is 0.74 My unit cell structure is that shown below. I ...
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22 views

Torque between Nematic Disclinations

I am looking at a liquid crystal system in 2 dimensions well in the nematic phase. Say the system has been quenched rapidly or is confined on some geometry due to which there are disclinations ...
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66 views

Projection Method in Hubbard model

This is a question from Altland and Simons book "Condensed Matter Field Theory". In the second exercise on page 64, the book claims that if we define $\hat P_s, \hat P_d$ to be the operators that ...
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33 views

Why do some ionic compounds form in the NaCl structure vs the CsCl structure?

Everything else the same, I'd expect two monoatomic ions to form an ionic structure in the CsCl structure because with more atoms bonded to each atom, it would seem to be more stable. And yet I ...
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compressibility of cold atoms in optical lattices

The compressibility of cold bosons in an optical lattice is defined as $\kappa = \frac{\partial \langle n\rangle}{\partial \mu}$, where $\langle n\rangle$ is the density and $\mu$ is the chemical ...
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184 views

Definition of short range entanglement

When studying Symmetry Protected Topological phases, one needs to define what a short range entangled (SRE) states means. But there appears to be different definitions that are not equivalent to each ...
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133 views

Strange definition of microcanonical partition function

I always thought that the microcanonical partition function would measure the number of states that correspond to some fixed energy. Despite, I found in this paper (equation 3.4) that we integrate ...
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Rigorous distinction between quasiparticles and collective excitations

I would like to hear your opinion on the question whether there is an accepted distinction between both concepts in condensed matter physics. I would tend to use the word quasiparticle for dressed ...
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106 views

Confusion about duality transformation in 1+1D Ising model in a transverse field

In 1+1D Ising model with a transverse field defined by the Hamiltonian \begin{equation} H(J,h)=-J\sum_i\sigma^z_i\sigma_{i+1}^z-h\sum_i\sigma_i^x \end{equation} There is a duality transformation which ...
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Can someone explain LO-TO Splitting?

LO-TO splitting occurs in an ionic (i.e. polar) solid such as GaAs or NaCl. What happens is that the degeneracy of the transverse optical (TO) and longitudinal optical (LO) phonons at $k=0$ is broken ...
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246 views

How is Meissner effect explained by BCS theory?

Someone says we can derive the GL equations from BCS theory, which can explain Meissner effect, but I want a more clear physical picture of this phenomena.
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Monte carlo simulation for continuous spin model (e.g. XY or Heisenberg model)

Unlike the Ising model, the XY model and the Heisenberg model have a continuous spectrum. So one need discretize them for a numerical simulation. But how to make sure the discretization procedure ...
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37 views

Does the real part of the inverse dielectric function have to be negative at some point for Cooper pairs to form?

Electrons naturally repel one another. However, in a superconductor, a phonon-mediated interaction causes the electrons to have a weak attractive interaction. Suppose that the interaction between two ...
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1answer
57 views

Superfluid-Mott insulator transition in Bose-Hubbard model in terms of vortex condensation

I have heard that there is some effective field theoretic type understanding of the superfluid-Mott insulator transition in Bose-Hubbard model. It says if the system is in a superfluid phase where the ...
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87 views

Topological insulator vs. topological superconductors in any dimension

My question today is simple. What is the difference between a topological insulator and a topological superconductor? How that difference depends on the dimensionality of space(time)? What is the ...
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1answer
33 views

Is there Johnson noise in superconductor?

For conductor, the Johnson Noise is $v_n = \sqrt { 4 k_B T R \Delta f }$. It is clear that the noise depends on $R$. I'm curious whether this noise will appear in supercondutor? That is for ...
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30 views

Benefit of using Matsubara Green function

Physicists often calculate Matsubara Green function and then perform an analytic continuation $i\omega_n \rightarrow \omega +i\eta$ to obtain the retarded Green function. Why is doing so better than ...
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26 views

Maximum voltage on metal sphere? [duplicate]

What is the maximum voltage that can be put on a metal sphere before electrons fly off it or the metal itself explodes due to electrostatic forces?
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102 views

Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...
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47 views

Why we never observe superposition of up and down ferromagnetic ground state of Ising model?

I thought it is due to spontaneous symmetry breaking. But isn't that because we never observe the superposition states, then we claim that there is spontaneous symmetry breaking. It looks like ...
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98 views

Is there a way to obtain an RG flow equation for Quantum spin systems using MERA

We restrict ourselves to ground states of translationally invariant 1d quantum systems. I understand that there is the scale invariant MERA(multiscale entanglement renormalization ansatz) which ...
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88 views

Are constant terms in second-quantization relevant?

I have a rather broad question and a specific problem. Let's take a orthonormal single-particle basis $\{ \vert i \rangle \}$, a simple single-particle Hamiltonian $$\tilde{H} = \sum_{i, j} h_{i j} ...
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3answers
262 views

Axioms behind entropy!

The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of ...
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43 views

kitaev-honeycomb : can't get wilson loop squared to yield +1

I'm new here, loving this website and I'm having some difficulty with the wilson-loop operator in kitaev's honeycomb model. problem statement The Kitaev model (Kitaev, 2006 is the original paper) ...
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honeycomb lattice in continuum limit

for TB model when we want to go to the continuum limit in real space in magnetic field (on square lattice) we use this relation and if we expand the bracket the current operator will appear now i ...
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Thermal fluctuations in metals

My professor said that the $k_BT$ displacement in the energy levels of the band electrons is due to the space-thermal displacement of the potential of the ion host. I think that this displacement is ...
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75 views

Optical absorption in a semiconductor for $E<E_g$ [duplicate]

Quoting from Solid State Electronic Devices (by Ben G. Streetman and Sanjay Banerjee): A photon with energy less than $E_g$ is unable to excite an electron from the valence band to the ...
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39 views

Tight binding operators in 2D lattice system

I have a very naive problem about lattice system, how to translate common operators defined in the bulk ($\hat{x}$, $\hat{p}$...) into their lattice analogues. In a single- band tight-binding ...
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79 views

Energy of an Electron in a One Dimensional Periodic Potential

First, we consider the time independent Schrodinger equation of the form: $$\bigg(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+u(x) \bigg)\phi_A(x)=E_A\phi_A(x)$$ Where $u(x)$ is a potential created by a ...
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32 views

Quantum description of Raman effect

In the classical description of Raman effect the object of study is the electric polarizability of the system. Since I'm interested in learning the quantum description of the Raman effect and in ...
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72 views

About SU(2) gauge symmetry of the large U limit of the Hubbard model

I have been studying about the SU(2) symmetry in Heisenberg Hamiltonian with a paper 'SU(2) gauge symmetry of the large U limit of the Hubbard model' written by Ian Affleck et al(Phys. Rev. B 38, 745 ...
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36 views

Energy from the Feynman-Kikuchi Partition Function

The Feynman-Kikuchi Partition function is given as $$Z_{FK}=K_\beta \int dx \eta(x) \exp \left(-\frac{x}{\beta}\right) $$ where $K_\beta$ is a normalization constant and ...
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55 views

What is spin on a lattice site is it electrons or atom as a whole?

Hi I wanted to know what is spin half in lattice site means? Is it electron or atom or total spins half of electrons in a atomic 1d chain or 2d?
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Green's function for moving solidification front

Consider a liquid solid interface $z =\zeta(x,t)$ moving at constant speed $v$, for a two dimensional problem. Due to solidification interface is changing it position. For simplicity heat ...
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2answers
70 views

Quantity to measure order in crystals

Imagine a cubic lattice for simplicity and put some atomic configuration inside of each unit cell. Lattice is of course a highly ordered entity (long range order). Please, how could I quantitatively ...
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83 views

Construction of a spin chain Hamiltonian invariant under a finite subgroup of SO(3)

I would like to construct a 2-local Hamiltonian that acts on a 1D spin chain where each spin transforms as the 3D irrep of $A_4$ which is a subgroup of $SO(3)$. I know that an $SO(3)$ invariant ...
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23 views

Effective Theory of FQH Edge State

When I was learning Xiao-Gang Wen's paper about the edge theory of Fractional Quantum Hall(FQH) state, I had one question. The paper's link is as below:\ http://dao.mit.edu/~wen/pub/edgere.pdf As ...
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42 views

Logarithmic discretization in Anderson´s model

Is there some motivation for the construction of Ladder operator that compound the recursive halmitonian of the Anderson model for numerical renormalization contained is this paper?
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Magnetic field associated with edge currents in IQHE?

According to some theory, currents in IQHE are due to the edge states. The edge current on the upper edge flows from left to right, that on the lower edge flows from right to left. Did anyone detect ...
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What exactly are crystal planes and how do they reflect x-rays?

What exactly are crystal planes and how do they reflect x-rays? Are crystal planes real physical planes or just an abstract concept? What are these planes made of? If they are an abstraction, what ...
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Is it possible to change one quantum state to another state by a cyclic adiabatic process?

An example is applying magnetic flux through the axis of a cylinder (2D system with periodic boundary condition). When changing flux from 0 to 1 flux quanta adiabatically, it seems that we can ...
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How to check the ohmic contact to the film?

I have a thin semiconductor film deposited on an isolating substrate. I would like to check different metals to find out do they form the ohmic contact or Schottky barrier. What is the best way to do ...