28 votes
Accepted

Topological insulators: why K-theory classification rather than homotopy classification?

Very loosely speaking the reasoning is this. Imagine a two band system in which the fermi sea has one filled band with Chern number $n$ and another system with $N$ filled bands but also with Chern ...
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  • 5,051
27 votes
Accepted

Relation between cohomology and the BRST operator

Ghostly Lie algebra cohomology Let $\mathfrak{g}$ be our Lie algebra and $V_\rho$ a representation space with representation map $\rho : \mathfrak{g} \to \mathrm{End}(V_\rho)$. $V_\rho$ is, by the ...
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  • 105k
17 votes
Accepted

How does physics research work?

Is there a group of (paid) researchers that work on M-Theory 24/7, hoping that someday they'll finally unify physics? Or is it more like a thing that passionate people do in their spare time? ...
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  • 3,663
16 votes

A pedestrian explanation of conformal blocks

A conformal field theory is a quantum field theory which is invariant under conformal transformations. Due to this invariance, correlation functions must obey linear equations called conformal Ward ...
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16 votes

Definition of short range entanglement

A quote from http://en.wikipedia.org/wiki/Symmetry_protected_topological_order : The SPT order (for both frermionic and bosonic systems) has the following defining properties: Distinct SPT states ...
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12 votes
Accepted

Is the recent Nature paper by Minev et al. evidence of new physics?

The trick here in "observing a quantum jump" is that this is not equivalent to doing a strong measurement that "collapses" the wavefunction. The archetypal quantum jump is a two ...
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  • 105k
11 votes

QCD and QED with unlimited computational power - how precise are they going to be?

Part b) is a big mathematical physics topic in its own right. The divergent tail of an asymptotic series is not garbage, rather it contains a lot of information that together with some additional ...
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  • 9,640
10 votes
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What is spontaneous symmetry breaking in quantum systems?

Bei Zeng and I wrote a paper http://arxiv.org/abs/1406.5090 , which addresses this question: A symmetry breaking phase for finite group G is a gLU equivalent class formed by symmetric many-body ...
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9 votes
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On a rigorous definition of Feynman's functional integral$.$

The definition you are using in your question is the one that everybody who does rigorous perturbative renormalization uses. The particular choice of method BPHZ vs. Epstein-Glaser, etc. doesn't ...
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8 votes
Accepted

Adiabatic theorem and Berry phase

The adiabatic theorem is required to derive the Berry phase equation in quantum mechanics. Therefore the adiabatic theorem and the Berry phase must be compatible with one another. (Though geometric ...
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  • 2,628
7 votes
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Self-dual Maxwell equations, the second homology group, and topological invariants of a four manifold

I'm not an expert in algebraic topology by the stretch of anyones imagination, but hopefully I can shed some light on this. The starting point is, as you mention, the Maxwell equations themselves. ...
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7 votes

Definition of short range entanglement

Yes, this is a known problem in the condensed matter community. There are two different definitions of short range entangled (SRE) states. The key difference is whether the fermion symmetry protected ...
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7 votes
Accepted

SLE applied to theoretical physics (eg. CFT), too untractable? not informative enough?

My name is Raoul Santachiara and I am a CNRS researcher at the Paris-Saclay university. My core expertise are the CFTs and their applications to 2D critical statistical model. I have worked (and I am ...
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7 votes

Lindblad and Input-Output Formalism in Quantum Optics

There is already a nice answer but I feel that some important aspects deserve additional attention. My answer is simply a list of observations: Master equations involve approximations: It is ...
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  • 10.8k
6 votes

What is the use of a Universal-NOT gate?

A Universal-Not allows FTL communication I added a Universal-Not gate to my toy circuit simulator and played around with it, trying to find interesting things. I was experimenting with "measuring ...
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  • 5,894
6 votes

Seiberg-Witten theory and Superconductivity

The connection between superconductivity and Seiberg-Witten theory can be understood through the observation that superconductivity is related to the Meissner effect, which is the exclusion of ...
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6 votes
Accepted

Hamiltonian for the Periodic Kitaev Model

First, watch out for the factors of 2 and $\sin(k)$s in your line 3 (after doing the fourier transform). Second, you do not want to set those terms to zero. Instead, remember that $k$ is just a ...
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  • 5,165
6 votes

Is a gapless system always conducting and a gapped system insulating?

The statement is not true, because there are counter examples. A U(1) spin liquid is gapless, but it is insulating. An $s$-wave superconductor is fully gapped, but it is (super)conducting.
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6 votes

Does recent paper show Bohmian mechanics is correct?

Bohmian Quantum Mechanics doesn't make different predictions than any other interpretation. The trajectories of Bohmian Mechanics are simply a particular choice of probability current. You could ...
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  • 24.6k
6 votes
Accepted

Perturbative Results Kitaev Model with Magnetic Field

Yes, the precise result can be found in Eq. (30) of our paper arXiv:1109.4155: $$\kappa = \frac{h_xh_yh_z}{8 u_0^2 J^2},$$ where $u_0$ is a numerical factor obtained by solving the mean field ...
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5 votes

Regularization of the Casimir effect

(This argument is for a one-dimensional system, but similar arguments can be given in higher dimensions. We work in units with $c = \hbar = e = 1$). Suppose we have some regulator procedure ...
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  • 2,976
5 votes

What is the upper-limit on intrinsic heating due to dark matter?

Dark matter is not the only possible source of heat in ordinary matter: cosmic rays and similar would also heat ordinary matter. Experiments searching for dark matter see a great deal of heat from ...
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  • 257
5 votes

Wormholes & Time Machines - for *experts* in GR/maths

Can someone explain how the wormhole motion is valid as a diffeomorphism, which my limited understanding suggests is the only permitted type of manifold transformation in relativity. Diffeomorphisms ...
5 votes

Apparent failure of SUSY nonrenormalization theorem

There actually can be a violation of no-renormalization theorem in case where massless fields are involved in the the computation as in the first and second graphs. These inconsistencies appear as ...
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  • 767
5 votes

Essentials to learn before reading condensed matter papers?

If you have graduate level understanding of quantum physics, make sure you have an advanced understanding of statistical mechanics as well. Pathria is a classic, as is Huang, although the latter can ...
5 votes

Relationship between different $Z_{16}$ classifications

Besides the obvious relationship that the representation theory of Majorana zero modes is the leverage point for each, the two are related in an intricate network of bosonization and dimensional ...
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5 votes
Accepted

Relation between cobordism and unitary fusion category classification of TQFT/ SPT phase

The Turaev-Viro state sums are for constructing non-invertible 3d TQFTs, since there are no nontrivial invertible ones without adding extra symmetry. You can do that, and it leads to a G-equivariant ...
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5 votes
Accepted

What does 3D buckling reconstruction mean?

In the "structural reconstruction" context it means that the crystal structure has changed -- often at a surface. In particular a "buckling reconstrction" means that the ...
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  • 41.3k
5 votes

What does 3D buckling reconstruction mean?

Surfaces of materials don't look like the inside of the bulk, otherwise you'd have dangling bonds and a ton of energy. So the dangling bonds combine in a certain way to minimize that energy. This is ...
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  • 1,469

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