Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions: An entanglement analysis

Parafermions are exotic quasiparticles with non-Abelian fractional statistics that can be realized and stabilized in one-dimensional models that are generalizations of the Kitaev $p$ -wave wire. We study the simplest generalization, i.e., the ${Z}_{3}$ parafermionic chain. Using a Jordan-Wigner transform we focus on the equivalent three-state chiral clock model, and study its rich phase diagram using the density matrix renormalization group technique. We perform our analyses using quantum entanglement diagnostics which allow us to determine phase boundaries, and the nature of the phase transitions. In particular, we study the transition between the topological and trivial phases, as well as to an intervening incommensurate phase which appears in a wide region of the phase diagram. The phase diagram is predicted to contain a Lifshitz type transition which we confirm using entanglement measures. We also attempt to locate and characterize a putative tricritical point in the phase diagram where the three above mentioned phases meet at a single point.Parafermions are exotic quasiparticles with non-Abelian fractional statistics that can be realized and stabilized in one-dimensional models that are generalizations of the Kitaev $p$-wave wire. We study the simplest generalization, i.e., the ${Z}_{3}$ parafermionic chain. Using a Jordan-Wigner transform we focus on the equivalent three-state chiral clock model, and study its rich phase diagram using the density matrix renormalization group technique. We perform our analyses using quantum entanglement diagnostics which allow us to determine phase boundaries, and the nature of the phase transitions. In particular, we study the transition between the topological and trivial phases, as well as to an intervening incommensurate phase which appears in a wide region of the phase diagram. The phase diagram is predicted to contain a Lifshitz type transition which we confirm using entanglement measures. We also attempt to locate and characterize a putative tricritical point in the phase diagram where the three above mentioned phases meet at a single point.

arXiv:1502.05049Physical Review BJul 31, 201573 citations

Entanglement Hamiltonians for chiral fermions

Israel Klich, Diana Vaman, Gabriel Wong

Jan 2, 20150 citations

Entanglement of a chiral fermion on the torus

David Blanco, Alan Garbarz, Pérez Nadal, Guillem

Sep 10, 201911 citations

Phase diagram of an extended parafermion chain

Jurriaan Wouters, Fabian Hassler, Hosho Katsura +1 more

We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin–Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral \mathbf{\mathbb{Z}_3} ℤ 3 axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin–Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral \mathbf{\mathbb{Z}_3} ℤ 3 axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.

arXiv:2106.15823SciPost Physics CoreFeb 8, 20220 citations

Approach to the quantum phase transition of spin chains in terms of pair-wise entanglement

Kaoru Shimizu, Akira Kawaguchi

Physics Letters AFeb 25, 20063 citations

Phase diagram of an extended parafermion chain

Fabian Hassler

We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin--Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral $\mathbb{Z}_3$ axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin--Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral $\mathbb{Z}_3$ axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.

Feb 1, 202213 citations

Phase diagram of the

Z_3

Parafermionic Chain with Chiral Interactions: An entanglement analysis

Parafermions are exotic quasiparticles with non-Abelian fractional statistics that can be realized and stabilized in one-dimensional models that are generalizations of the Kitaev

p

-wave wire. We study the simplest generalization, i.e., the

{Z}_{3}

parafermionic chain. Using a Jordan-Wigner transform we focus on the equivalent three-state chiral clock model, and study its rich phase diagram using the density matrix renormalization group technique. We perform our analyses using quantum entanglement diagnostics which allow us to determine phase boundaries, and the nature of the phase transitions. In particular, we study the transition between the topological and trivial phases, as well as to an intervening incommensurate phase which appears in a wide region of the phase diagram. The phase diagram is predicted to contain a Lifshitz type transition which we confirm using entanglement measures. We also attempt to locate and characterize a putative tricritical point in the phase diagram where the three above mentioned phases meet at a single point.

\mathbb{Z}_3

axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.