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A key difference between spontaneously broken symmetries and "emergent symmetries" is that emergent symmetries are never exact while spontaneously broken symmetries are backed by exact maths although the ground state isn't invariant. In most cases, the "emergent symmetries" only emerge if some parameters are fine-tuned, and even if it is so, they are only ...


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The superfluid phonons have the linear dispersion $\omega=ck$, and the low-energy effective theory is Lorentz invariant. So the superfluid is an example of emergent Lorentz symmetry. The statement: The velocity of sound in the superfluid is the same for all inertial observers, regardless of their relative motion to the superfluid is valid if the clock and ...


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This is an example from hydrodynamics. When the effects of viscosity can be ignored (inviscid flow), a uniform incident flow can exert on immersed bodies only lift forces perpendicular to the asymptotic flow velocity. However, there exist an infinite number of solutions of the flow equations of motion satisfying the asymptotic conditions at infinity and the ...


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The group of rotations of an $N$-dimensional space is $SO(N)$. Being a symmetry of nature, classical systems transform according to representations of $SO(N)$. Quantum mechanics, on the other hand, allows systems which transform according to the universal covering groups of classical symmetries. This is the reason why we get in three dimensional quantum ...


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Your second sentence is not correct in our current understanding of physics. Photons are not an "emergent property of space-time" - photons appear even when we take space-time to be a fixed object. Photons are "not due to electrons... jumping around" - they can be created by the motion of charges but they are independent objects. Photons are just as real as ...


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The simplest model is the spin-1/2 chain with Majumdar–Ghosh interaction: $$H=\sum_i P_{3/2}(i-1,i,i+1),$$ where $P_{3/2}(i,j,k)$ is the projection operator that projects a state onto the subspace with total spin-3/2 on sites $i,j,k$. The ground states are two dimer states (see the figure on wikipedia Majumdar–Ghosh model): ...


3

I have to admit that I do not know anything about the model you are working on, but the standard way to determine whether a gauge theory is confining or not is to calculate the vacuum expectation value of Wilson loops. The latter are gauge invariant operators that describe parallel transport around a closed loop in spacetime. If the vacuum expectation of a ...


2

I was wondering something similar few month ago. Then I concluded that most of the topological staffs appear at the boundary between two different topological sector. A sector being characterised by a Chern number, or if you prefer a topological charge, one needs a boundary / an interface between two systems characterised by different topological charge. ...


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As Ron noted, there are many, many examples within condensed matter; they often share a very similar story where the microscopic laws are known well (exactly, for the case of simulations), but the macroscopic laws are derived by symmetry concerns. Take for example, liquid crystals. We could simulate a collection of hard rods or ellipsoids - this is our ...


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If you Google for something like complexity emergent properties you'll lots of interesting background reading on the subject. An executive summary is that physics is deterministic and therefore that all emergent properties are in principle predictable from a knowledge of the microsocpic behaviour. However in practice the complexity of the systems is so ...


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Any problem that requires solving of non-trivial Schroedinger equations. For example, protein folding problem. It is known what equations the system should satisfy and those equations can be written down. Yet they cannot be solved with modern computers which would take millions of years tor that.



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