$\mathbb{Z}_3$ quantum double in a superconducting wire array
- URL: http://arxiv.org/abs/2101.01720v3
- Date: Fri, 13 Aug 2021 17:43:19 GMT
- Title: $\mathbb{Z}_3$ quantum double in a superconducting wire array
- Authors: Zhi-Cheng Yang, Dmitry Green, Hongji Yu, and Claudio Chamon
- Abstract summary: We show that a quantum double can be realized in an array of superconducting wires coupled via Josephson junctions.
Our model maps to a quantum three-state Potts model under a duality transformation.
- Score: 1.3159512679346685
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We show that a $\mathbb{Z}_3$ quantum double can be realized in an array of
superconducting wires coupled via Josephson junctions. With a suitably chosen
magnetic flux threading the system, the inter-wire Josephson couplings take the
form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry
-- a local $\mathbb{Z}_3$ symmetry involving permutations and shifts by $\pm
2\pi/3$ of the superconducting phases. The sign of the star potential resulting
from the Josephson energy is inverted in this physical realization, leading to
a massive degeneracy in the non-zero flux sectors. A dimerization pattern
encoded in the capacitances of the array lifts up these degeneracies, resulting
in a $\mathbb{Z}_3$ topologically ordered state. Moreover, this dimerization
pattern leads to a larger effective vison gap as compared to the canonical case
with the usual (uninverted) star term. We further show that our model maps to a
quantum three-state Potts model under a duality transformation. We argue, using
a combination of bosonization and mean field theory, that altering the
dimerization pattern of the capacitances leads to a transition from the
$\mathbb{Z}_3$ topological phase into a quantum XY-ordered phase. Our work
highlights that combinatorial gauge symmetry can serve as a design principle to
build quantum double models using systems with realistic interactions.
Related papers
- Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
The interplay between symmetry and topological properties plays a very important role in modern physics.
How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
arXiv Detail & Related papers (2024-10-24T19:52:27Z) - Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance.
The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
arXiv Detail & Related papers (2023-05-22T11:00:25Z) - Emergence of non-Abelian SU(2) invariance in Abelian frustrated
fermionic ladders [37.69303106863453]
We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette.
Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry.
At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
arXiv Detail & Related papers (2023-05-11T15:57:27Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - Integrable Quantum Circuits from the Star-Triangle Relation [0.4305891170440042]
We construct integrable quantum circuits using the star-triangle relation.
We give two examples of circuits acting on a chain of $Q-$state qudits.
arXiv Detail & Related papers (2023-02-24T14:55:52Z) - Intrinsically Interacting Higher-Order Topological Superconductors [19.52773844535185]
We propose a minimal interacting lattice model for two-dimensional class-$D$ higher-order topological superconductors.
A Lieb-Schultz-Mattis-type constraint is proposed and applied to guide our lattice model construction.
arXiv Detail & Related papers (2022-12-26T04:48:28Z) - Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
We introduce a class of quantum optical Hamiltonian characterized by three-body couplings.
We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
arXiv Detail & Related papers (2022-04-07T15:39:21Z) - Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d [0.0]
We study a lattice gauge theory where the gauge fields, represented by spin-$frac12$ operators are coupled to a single flavor of staggered fermions.
Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in $(2+1)$-d.
Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase.
arXiv Detail & Related papers (2021-12-01T19:00:03Z) - Chiral waveguide optomechanics: first order quantum phase transitions
with $\mathbb{Z}_3$ symmetry breaking/ [0.0]
We present a direct mapping between the quantum optomechanical problem of the atoms harmonically trapped in the vicinity of a chiral waveguide and a generalized quantum Rabi model.
We extend the class of the superradiant phase transitions for the systems possessing $mathbbZ_3$ rather than parity $mathbbZ$ symmetry.
arXiv Detail & Related papers (2020-09-02T18:34:21Z) - A superconducting circuit realization of combinatorial gauge symmetry [0.0]
We propose a superconducting quantum circuit based on a general principle -- gauge symmetry -- designed to emulate topologically-ordered quantum liquids.
A key feature of the exact gauge symmetry is that amplitudes connecting different $mathbb Z$ loop states arise from paths having zero classical energy cost.
arXiv Detail & Related papers (2020-06-17T18:00:02Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.