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Simple questions on the symmetric eigenstate and time-reversal (TR) breaking eigenstate?

Followings are two independent questions as implied by the title: (1) Considering a quantum Hamiltonian $H$ possesses some symmetries described by a symmetry group $G=\left \{ g_1,g_2,...,g_n \right ...
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14 views

Conductivity Matrix (Symmetry Information)

I'm trying to understand the symmetry content of the conductivity matrix: one information is, presence of time-reversal symmetry causes the off-diagonal terms to vanish. When this is broken (e.g. in ...
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0answers
24 views

Discrete Symmetries: Breaking and Preserving

This is not a question, let's list down all the effects resulting from breaking or preserving of various discrete symmetries, on various observables, be it in condensed matter or in high energy. ...
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1answer
87 views

Why doesn't topological phase transition break any symmetry? Hidden symmetry?

This question may be superficial. However why all people saying this without a proof? Just like the "hidden variables" assumption in quantum mechanics, can one disproof that there is no hidden ...
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0answers
14 views

Mean-field approach to quantum phase transitions in Fermi systems

I have a basic confusion concerning the mean-field theory of quantum phase transitions in Fermi systems. Consider as an example the BCS theory of superconductivity in a Dirac fermion system, ...
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0answers
21 views

What are spin and valley symmetries in graphene?

I have been assigned a presentation on a part of a paper ( http://arxiv.org/ftp/arxiv/papers/1303/1303.6942.pdf ). My task is to present on the spin and valley symmetries in graphene, and relate it ...
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0answers
36 views

What is the relation between pseudogap and time reversal symmetry breaking?

Some papers concerning high-$T_c$ superconductor discuss the pseudogap and time reversal symmetry breaking. My questions are: What is the characteristic of order-parameter in pseudogap? How to ...
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0answers
17 views

Hamiltonian governing liquid to a solid transition

What is the Hamiltonian 'H' (at the atomic or molecular level) that governs the phase transition from a liquid to a solid state? Actually, I want to explicitly verify the Hamiltonian 'H' admits the ...
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1answer
71 views

Origin of quark masses

Does all the mass of the quarks in the standard model come from the Higgs sector or is there also a contribution to quark masses due to QCD chiral symmetry breaking?
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1answer
97 views

Dilaton field and Scale symmetry breaking

I have read at some places that a dilaton field is associated with the spontaneous breaking of scale symmetry in a theory. (While others would be difficult to trace right now, the most easily ...
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0answers
42 views

Why doesn't Graphene have a band gap?

Is there any simple justification about graphene having no band gap? How bout its linear E-K? Why bilayer graphene has a quadratic E-K and electric field can open a band gap there? I do not ...
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1answer
67 views

Intuitive explanation of how hadron mass emerges from the strong force

I'm not familiar with QCD, but I'm looking for intuitive explanation of this phenomenon (it could be that easy explanation does not exist). What I've read is that large part of hadron masses arises ...
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1answer
58 views

Ambiguous points in spontaneous symmetry breaking of discrete symmetry

For a discrete symmetry: At the minimum value of the potential, $V$, in the Lagrangian density, why do we take $\phi= \langle v\rangle + \eta$? Aren't we deliberately breaking the symmetry? If we ...
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2answers
317 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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0answers
16 views

Symmetry breaking under isothermal expansion

Is there any example of a symmetry breaking phase transition in a system of particles under isothermal expansion?
3
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1answer
72 views

Group theoretic way to find charges after SSB

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev. In the case of the EW symmetry breaking, one can directly read the ...
2
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1answer
151 views

Superconductor symmetry breaking

When water freezes continuous translational symmetry is broken. When a metal becomes superconducting, what is the symmetry that gets broken?
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2answers
57 views

Tachyonic field

i'm working on a paper about symmetron cosmology. symmetron is a scalar field that by its symmetry breaking can explain the dark energy. the action is: ans A , V are assumed to be: where M ...
2
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1answer
60 views

How do gauginos and scalars gain masses after gauge-mediated symmetry breaking?

In the minimal-GMSB model, the messenger fields transform under the MSSM gauge group and connect a so-called hidden sector to the visible sector. These meesenger fields (left-handed chiral ...
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1answer
137 views

Spontaneous symmetry breaking and time-reversal symmetry

In most textbooks on field theory you read that "spontaneous symmetry breaking implies degeneracy of the ground state". (Like for example in ...
2
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1answer
51 views

Glashow-Weinberg-Salam mass terms

At the end of spontaneous symmetry breaking I get these mass terms: $$W_{\mu}^{\pm}=\frac{1}{\sqrt{2}}\bigl(W_{\mu}^{1} \mp i W_{\mu}^{2} \bigr )$$ $$\mathcal{L}_{mass}=\frac{1}{2} g^2 \frac{v^2}{4} ...
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83 views

Why is there a 'loophole' in Mermin Wagner for rotations?

I'm just starting out in my mathematics career by looking at some simple stuff on broken symmetries in statistical mechanics. Since 3D is 'hard' it would be very nice to look at 2D toy models of ...
3
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1answer
99 views

What is physical meaning of $|\phi|^2$ in quantum field theory and pedagogical spontaneous symmetry breaking?

If wavefunction is $\phi$, we know that $|\phi (x)|^2$ represents probability of finding a particle at $x$. Now let us talk about some pedagogical example in spontaneous symmetry breaking in QFT, ...
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2answers
162 views

Do the standard cosmology models spontaneously break Lorentz symmetry?

In standard cosmology models (Friedmann equations which your favorite choice of DM and DE), there exists a frame in which the total momenta of any sufficiently large sphere, centered at any point in ...
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0answers
45 views

Spontaneous breaking of a discrete non-Abelian symmetry

Can someone give an example of an one dimensional local gapped quantum lattice model with a discrete non-Abelian global internal symmetry that is spontaneously broken in the ground state? In ...
3
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1answer
125 views

Renormalizability of standard model

I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities: The renormalizability of all of the interaction described by the Lagrangian before ...
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1answer
43 views

What is the general conditions for non-zero polarization?

I only know that for a system to have non-zero polarization it should break inversion symmetry. What about others requirements?
5
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1answer
122 views

What do we mean when we say Bose condensation? And why can't fermions condense if they don't pair?

In common textbooks, we are told that bosons can condense in a single-particle state because of bose statistics and when the system undergoes a bose condensation, the bose field operator obtains a ...
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2answers
360 views

Are there massless bosons at scales above electroweak scale?

Spontaneous electroweak symmetry breaking (i.e. $SU(2)\times U(1)\to U(1)_{em}$ ) is at scale about 100 Gev. So, for Higgs mechanism, gauge bosons $Z$ & $W$ have masses about 100 GeV. But before ...
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0answers
30 views

How does the choice of a particular vacuum in a field theory problem decide the number of Goldstone bosons?

How does the field expansion method (by this I mean expanding your fields about a chosen VEV and plugging into a given potential so that the masses of the fields are given by the coefficients in ...
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0answers
16 views

How does the choice of a basis decide how many Goldstone bosons there are under spontaneous symmetry breaking?

I have a question about how the basis you choose in a field theory problem semmingly decides how many Goldstone bosons you get after spontaneous symmetry breaking. For SU(2), if you choose the 3 Pauli ...
5
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2answers
83 views

Coupling constant in electroweak theory

Electroweak theory has two coupling constants before and after Spontaneous Symmetry Breaking (SSB) each one for $SU(2)_L$ and $U(1)_Y$, though they are connected by Weinberg angle after SSB. My ...
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2answers
277 views

Naive questions on Goldstone modes and a possible duality relation?

For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\sum_{i=1}^{N}\mathbf{S}_i\cdot\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low ...
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0answers
55 views

What is the minimal symmetry required for a spin Hamiltonian to describe a spin-liquid ground state?

Let's restrict to the case of spin-1/2 system. As we know, a spin-liquid (SL) state is the ground state of a lattice spin Hamiltonian with no spontaneous broken symmetries (sometime it may ...
3
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1answer
79 views

How does one prove that the current of a spontaneously broken symmetry generates a particle?

I am having a hard time arguing that, after spontaneous breaking of a continuous symmetry of a field Lagrangian, local fluctuations around the vacuum can be interpreted as particles (without referring ...
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1answer
76 views

Symmetry breaking of the hidden sector

Lately, I have some read some papers about the hidden sector of particle physics which combines with the Standard Model through the so-called Higgs portal. Let the Lagrangian for this be composed of ...
4
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1answer
66 views

Number of Goldstone bosons in paramagnetic-to-ferromagnetic phase transitions

In paramagnetic-to-ferromagnetic phase transitions, the symmetry spontaneously breaks down from SO(3) to the subgroup SO(2) below $T_\text{crit}$. This implies that there should be two Goldstone modes ...
2
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1answer
45 views

Why does the symmetry breaking parameter `$v$' have dimensions of mass

A symmetry is spontaneously broken by an operator $\hat{O}$ which acquires a non-zero vacuum expectation value. This is expressed as $$ \langle 0 | \hat{O} | 0 \rangle = v$$ The parameter $v$ is ...
3
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1answer
176 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
3
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2answers
245 views

Domain walls intersection

I was reading this article(On domain shapes and processes in supersymmetric theories). In the paragraph about domain walls intersection (paragraph $4$, page $7$) the authors say: In a one-field ...
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0answers
56 views

Is there a soft Goldstino theorem?

For ordinary spontaneously broken symmetries, you can demonstrate relations between S-matrix elements with a soft goldstone emission and another S-matrix element without the emission. If I break ...
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0answers
100 views

Examples of symmetric field collapse to produce asymmetry

It would really help me with an idea I have if I could see how something such as a symmetric field could collapse to something asymmetric. I know that if $x$ occures before $y$ is symmetric, then $y$ ...
9
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1answer
180 views

A graphical proof that the $SU(2)/\mathbb{Z}_2$ vortex is non-orientable

The text, see [1], compares the vortex solutions of a spontaneously broken symmetry $U(1) \rightarrow 1$ and $SU(2)\rightarrow U(1) \rightarrow \mathbb{Z}_2$. The vortices can be classified by ...
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1answer
86 views

Goldstone boson couple to conserved current

The Goldstone boson in spontaneous symmetry breaking problem couples naturally to the associated conserved current of the broken symmetry. How can I see a rigorous (mathematical) derivation for that?
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266 views

Finding the vacuum which breaks a symmetry

I will start with an example. Consider a symmetry breaking pattern like $SU(4)\rightarrow Sp(4)$. We know that in $SU(4)$ there is the Standard Model (SM) symmetry $SU(2)_L\times U(1)_Y$ but depending ...
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2answers
227 views

In what sense do Goldstone bosons live in the coset?

Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. ...
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3answers
679 views

Why is the Symmetry Group for the Electroweak force SU(2)xU(1) and not U(2)

Let me first say that I'm a layman who's trying to understand group theory and gauge theory, so excuse me if my question doesn't make sense. Before symmetry breaking, the Electroweak force has 4 ...
4
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1answer
153 views

Spontaneous Symmetry Breaking

In Spontaneous symmetry breaking we have got that, a field $$\phi= \pm \sqrt{\frac{-m^2}{\lambda}}.$$ Now in order to get the unstable minima we need to guess the mass $m^2 <0 $. But can mass be ...
9
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2answers
371 views

Understanding Elitzur's theorem from Polyakov's simple argument?

I was reading through the first chapter of Polyakov's book "Gauge-fields and Strings" and couldn't understand a hand-wavy argument he makes to explain why in systems with discrete gauge-symmetry only ...
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1answer
96 views

Amplitudes involving Goldstone bosons

Does anyone know some theorem or statement about amplitudes involving only Goldstone bosons in theories with spontaneous symmetry breaking in the limit of low energies?