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Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain | | Luca Lepori
; Davide Vodola
; Guido Pupillo
; Giacomo Gori
; Andrea Trombettoni
; | | Date: |
17 Nov 2015 | | Abstract: | We deal with the problem of studying the effective theories and the
symmetries of long-range models around their critical points. A prominent issue
is to determine whether they possess (or not) conformal symmetry (CS) at
criticality and how the presence of CS depends on the range of the
interactions. To have a model, both simple to treat and interesting, where to
investigate these questions, we focus on the Kitaev chain with long-range
pairings decaying with distance as power-law with exponent $alpha$. This is a
quadratic solvable model, yet displaying non-trivial quantum phase transitions.
By means of a renormalization group approach, we derive its effective theory
close to criticality. The effective action is the sum of two terms: a Dirac
action $S_D$, found in the short-range Ising universality class, and a CS
breaking term $S_{AN}$. While the Dirac action originates from low-energy
excitations in the spectrum, the CS breaking term $S_{AN}$ originates from
high-energy modes. At criticality, $S_{AN}$ flows to zero for $alpha > 2$,
while for $alpha < 2$ it dominates and determines the breakdown of the CS.
From the effective theory one can also see that new phases emerge for
$alpha<1$. Out of criticality $S_{AN}$ breaks, in the considered
approximation, the effective Lorentz invariance (ELI) for every finite
$alpha$. In the short-range limit the ELI is restored. In order to test the
validity of the determined effective theory, we compared the two-fermion static
correlation functions and the von Neumann entropy obtained from it with the
ones calculated on the lattice, finding agreement. The proposed scenario is
expected to hold in other long-range models displaying quasiparticle
excitations in ballistic regime. | | Source: | arXiv, 1511.5544 | | Services: | Forum | Review | PDF | Favorites | |
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