Abstract
We discuss quantum phase transition by a solvable model in the dual gravity setup. By considering the effect of the scalar condensation on the fermion spectrum near the quantum critical point(QCP), we find that there is a topologically protected fermion zero mode associated with the metal to insulator transition. Unlike the topological insulator, our zero mode is for the bulk of the material, not the edge. We also show that the strange metal phase with T-linear resistivity emerges at high enough temperature as far as a horizon exists. The phase boundaries calculated according to the density of states allow us understanding the structures of the phase diagram near the QCP.
Highlights
We will show that when the fermion couples to the scalar with condensation in the holographic bulk space, the fermion can get a topologically protected zero mode localized at the Anti-de Sitter (AdS) boundary, at the bulk of the material, and it can be used to provide an analytic solution to the prototype quantum transition like that of metal to insulator
It is interesting to notice that the scalar is associated with the chiral symmetry breaking in the bulk
There is no chiral symmetry in 2+1 boundary, since Lorentz group of 2+1 does not contain two copies of SU(2)
Summary
Let the bulk fermion ψ be the dual field to the boundary fermion χ and ΦI be the dual bulk field of the operator χΓI χ, where I is an index set for arbitrary type of tensor:. For m2Φ = −2 the solution for the scalar in the zero temperature limit near the boundary is given by. We can prove the existence of the zero modes by solving above Dirac equation explicitly to find the boundary Green functions whose poles give us the full information of the spectrum. This is a surprising aspect of the holographic theory because such phenomena can never happen in flat spacetime or in weakly interacting system where the scalar order always introduces a gap. Such fermion zero mode has not been reported in holographic context as far as we know. We are forced to ask, if an ordered state is gapless, how the order can be protected? We want to understand its origin
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