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Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes | | Davide Vodola
; Luca Lepori
; Elisa Ercolessi
; Guido Pupillo
; | | Date: |
4 Aug 2015 | | Abstract: | We analyze the quantum phases, correlation functions and edge modes for a
class of spin-1/2 and fermionic models related to the one-dimensional Ising
chain in the presence of a transverse field. These models are the Ising chain
with anti-ferromagnetic long-range interactions that decay with distance as
$1/r^alpha$, as well as a related class of fermionic Hamiltonians that
generalise the Kitaev chain, where both the hopping and pairing terms are
long-range and their relative strength can be varied. For these models, we
provide the complete phase diagram for all exponents $alpha$, based on an
analysis of the entanglement entropy, the decay of correlation functions, and
the edge modes in the case of open chains. We demonstrate that violations of
the area law can occur for $alpha lesssim1$, while connected correlation
functions can decay with a hybrid exponential and power-law behaviour, with a
power that is $alpha$-dependent. Interestingly, for the fermionic models we
provide an exact analytical derivation for such a behaviour at every $alpha$.
Along the critical lines, for all models breaking of conformal symmetry is
argued at low enough $alpha$. For the fermionic models we show that the edge
modes, massless for $alpha gtrsim 1$, can acquire a mass for $alpha < 1$.
The mass of these states can be tuned by varying the relative strength of the
kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising
chain a similar edge localization appears for excited bulk states on the
paramagnetic side of the phase diagram, where edge modes are not expected. We
argue that, at least for the fermionic chains, these massive states correspond
to the appearance of new phases, notably approached via quantum phase
transitions without mass gap closure. Finally, we discuss the possibility to
detect some of these effects in experiments with cold trapped ions. | | Source: | arXiv, 1508.0820 | | Services: | Forum | Review | PDF | Favorites | |
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