Topological Interfaces of Luttinger Liquids
- URL: http://arxiv.org/abs/2312.05566v1
- Date: Sat, 9 Dec 2023 12:41:50 GMT
- Title: Topological Interfaces of Luttinger Liquids
- Authors: Ananda Roy and Hubert Saleur
- Abstract summary: Topological interfaces of two-dimensional conformal field theories exhibit striking spectral and entanglement characteristics.
We show that a topological interface of two Luttinger liquids can be realized by coupling special one-dimensional superconductors.
The proposed lattice model provides an experimentally-realizable alternative to spin and anyon chains for the analysis of several conjectured conformal fixed points.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Topological interfaces of two-dimensional conformal field theories contain
information about symmetries of the theory and exhibit striking spectral and
entanglement characteristics. While lattice realizations of these interfaces
have been proposed for unitary minimal models, the same has remained elusive
for the paradigmatic Luttinger liquid {\it i.e.,} the free, compact boson
model. Here, we show that a topological interface of two Luttinger liquids can
be realized by coupling special one-dimensional superconductors. The gapless
excitations in the latter carry charges that are specific integer multiples of
the charge of Cooper-pairs. The aforementioned integers are determined by the
windings in the target space of the bosonic fields -- a crucial element
required to give rise to nontrivial topological interfaces. The latter occur
due to the perfect transmission of certain number of Cooper-pairs across the
interface. The topological interfaces arise naturally in Josephson junction
arrays with the simplest case being realized by an array of
experimentally-demonstrated~$0-\pi$ qubits, capacitors and ordinary Josephson
junctions. Signatures of the topological interface are obtained through
entanglement entropy computations. In particular, the subleading contribution
to the so-called interface entropy is shown to differ from existing field
theory predictions. The proposed lattice model provides an
experimentally-realizable alternative to spin and anyon chains for the analysis
of several conjectured conformal fixed points which have so far eluded
ab-initio investigation.
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