Recent experiments on a one-dimensional chain of trapped alkali-metal atoms [Bernien et al., Nature (London) 551, 579 (2017)] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous ${\mathbb{Z}}_{3}$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the ${\mathbb{Z}}_{3}$ chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order--disorder transition in these models and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization-group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $\ensuremath{\nu}$. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with $z\ensuremath{\ne}1$, implying an underlying nonconformal critical-field theory.Recent experiments on a one-dimensional chain of trapped alkali-metal atoms [Bernien et al., Nature (London) 551, 579 (2017)] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous ${\mathbb{Z}}_{3}$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the ${\mathbb{Z}}_{3}$ chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order--disorder transition in these models and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization-group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $\ensuremath{\nu}$. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with $z\ensuremath{\ne}1$, implying an underlying nonconformal critical-field theory.

arXiv:1806.01867Physical Review AAug 13, 2018107 citations

Phase diagram in the generalized chiral clock models

Helen Au-Yang, Jacques H. H. Perk

Physica A Statistical Mechanics and its ApplicationsJun 1, 19963 citations

Dynamical Quantum Phase Transitions

Ralf Schützhold

arXiv:1004.2409Journal of Low Temperature PhysicsOct 29, 200812 citations

Phase diagram of the Z3 parafermionic chain with chiral interactions

Ye Zhuang, Hitesh J. Changlani, Norm M. Tubman +1 more

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

Chiral Waveguide Optomechanics: First Order Quantum Phase Transitions with Z3 Symmetry Breaking

D. D. Sedov, Valerii K. Kozin, Ivan V. Iorsh

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, and we discuss the analogy between the self-organization of atomic chains in photonic structures and Dicke-like quantum phase transitions in the ultrastrong coupling regime. We extend the class of the superradiant phase transitions for the systems possessing Z_{3} rather than parity Z_{2} symmetry and demonstrate the emergence of the multicomponent Schrödinger-cat ground states in these systems.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, and we discuss the analogy between the self-organization of atomic chains in photonic structures and Dicke-like quantum phase transitions in the ultrastrong coupling regime. We extend the class of the superradiant phase transitions for the systems possessing Z_{3} rather than parity Z_{2} symmetry and demonstrate the emergence of the multicomponent Schrödinger-cat ground states in these systems.

arXiv:2009.01289Physical Review LettersDec 31, 202032 citations

Dynamical Signatures of Emergent Quantum Phases

Markus Drescher, Frank Pollmann, Technische Universität München

Jan 1, 20260 citations

{\mathbb{Z}}_{3}

symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the

{\mathbb{Z}}_{3}

chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order--disorder transition in these models and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization-group techniques. We use finite-size scaling to determine the dynamical critical exponent

z

and the correlation length exponent $\ensuremath{\nu}$. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with $z\ensuremath{\ne}1$, implying an underlying nonconformal critical-field theory.

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.