Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1906.09929 · Journal of High Energy Physics

Condensates of interacting non-Abelian SO(5)Nf anyons

Daniel Borcherding, Holger Frahm

Published Oct 1, 2019• 0 citations
arXivHTMLPDF

Abstract

Abstract Starting from a one-dimensional model of relativistic fermions with SO(5) spin and U(N f ) flavour degrees of freedom we study the condensation of SO(5)N f anyons. In the low-energy limit the quasi-particles in the spin sector of this model are found to be massive solitons forming multiplets in the SO(5) vector or spinor representations. The solitons carry internal degrees of freedom which are identified as SO(5)N f anyons. By controlling the external magnetic fields the transitions from a dilute gas of free anyons to various collective states of interacting ones are observed. We identify the generalized parafermionic cosets describing these collective states and propose a low temperature phase diagram for the anyonic modes.

DOI
10.1007/jhep10(2019)054

Related papers

Condensation of non-Abelian S U ( 3 ) N f anyons in a one-dimensional fermion model

Daniel Borcherding, Holger Frahm

Abstract The color excitations of interacting fermions carrying an color and U ( N f ) flavor index in one spatial dimension are studied in the framework of a perturbed Wess–Zumino–Novikov–Witten model. Using Bethe ansatz methods the low energy quasi-particles are found to be massive solitons forming quark and antiquark multiplets. In addition to the color index the solitons carry an internal degree of freedom with non-integer quantum dimension. These zero modes are identified as non-Abelian anyons satisfying fusion rules. Controlling the soliton density by external fields allows to drive the condensation of these anyons into various collective states. The latter are described by parafermionic cosets related to the symmetry of the system. Based on the numerical solution of the thermodynamic Bethe ansatz equations we propose a low temperature phase diagram for this model.

arXiv:1808.05808•Journal of Physics A Mathematical and Theoretical•Oct 23, 2018•0 citations

Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model

Daniel Borcherding, Holger Frahm

Abstract The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both spin and SU ( N f ) orbital degrees of freedom to the thermodynamic properties of the latter is studied based on the exact solution of the model. For sufficiently small temperatures and magnetic fields the anyons appear as zero energy modes localized at the massive kink excitations (Tsvelik 2014 Phys. Rev. Lett . 113 066401). From their quantum dimension they are identified as spin- anyons. The density of kinks (and anyons) can be controlled by an external magnetic field leading to the formation of a collective state of these anyons described by a parafermion conformal field theory for large fields. Based on the numerical analysis of the thermodynamic Bethe ansatz equations we propose a phase diagram for the anyonic modes.

arXiv:1706.09822•Journal of Physics A Mathematical and Theoretical•Mar 28, 2018•2 citations

Non-Abelian quasi-particles in electronic systems

Daniel Borcherding

Ever since the proposal of Kitaev for decoherence-free quantum computing based on non-Abelian anyons physical realizations of these exotic particles have been investigated extensively. Starting from one-dimensional models of interacting fermions with different symmetries the emergence and condensation of $\mathfrak{su}(2)_{N_f}$, $\mathfrak{su}(3)_{N_f}$ and $\mathfrak{so}(5)_{N_f}$ anyons is studied in the framework of integrable perturbed WZNW models. For sufficiently small temperatures and fields non-Abelian anyons residing on massive solitonic excitations are identified by their quantum dimension. By tuning the external fields the density of anyons can be increased continuously to study the effect of interactions between them. For each model the conformal field theories describing the various collective states of the interacting anyons are determined and a phase diagram for the anyonic modes is proposed.

•Jan 1, 2018•0 citations

Quantum spin ladders of non-Abelian anyons

Didier Poilblanc, Andreas W. W. Ludwig, Simon Trebst +1 more

Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more exotic quantum mechanical degrees of freedom, so-called non-Abelian anyons, which can be thought of as certain quantum deformations of ordinary SU(2) spins. Such non-Abelian anyons occur as quasiparticle excitations in topological quantum fluids, including ${p}_{x}+i{p}_{y}$ superconductors, certain fractional quantum Hall states, and rotating Bose-Einstein condensates. Here we use a combination of exact diagonalization and conformal field theory to determine the phase diagrams of ladders with up to four chains. We discuss how phenomena familiar from ordinary SU(2) spin ladders are generalized in their anyonic counterparts, such as gapless and gapped phases, odd and even effects with the ladder width, and elementary ``magnon'' excitations. Other features are entirely due to the topological nature of the anyonic degrees of freedom. In general, two-dimensional systems of interacting localized non-Abelian anyons are anyonic generalizations of two-dimensional quantum magnets.

arXiv:1101.1186•Physical Review B•Apr 29, 2011•22 citations

Observing anyonization of bosons in a quantum gas

Sudipta Dhar, Botao Wang, Milena S. J. Horvath +7 more

Abstract Anyons 1,2 are low-dimensional quasiparticles that obey fractional statistics, hence interpolating between bosons and fermions. In two dimensions, they exist as elementary excitations of fractional quantum Hall states 3–5 and are believed to enable topological quantum computing 6,7 . One-dimensional anyons have been theoretically proposed, but their experimental realization has proven to be difficult. Here we observed emergent anyonic correlations in a one-dimensional strongly interacting quantum gas, resulting from the phenomenon of spin–charge separation 8–10 . A mobile impurity provides the necessary spin degree of freedom to engineer anyonic correlations in the charge sector and simultaneously acts as a probe to reveal these correlations. Starting with bosons, we tune the statistical phase to transmute bosons through anyons to fermions and observe an asymmetric momentum distribution 11–14 , a hallmark of anyonic correlations. Going beyond equilibrium conditions, we observed dynamical fermionization of the anyons 15 . This study opens the door to the exploration of non-equilibrium anyonic phenomena in a highly controllable setting 15–17 .

Nature•May 27, 2025•17 citations

Z n clock models and chains of so ( n ) 2 non-Abelian anyons: symmetries, integrable points and low energy properties

Peter E. Finch, Michael Flohr, Holger Frahm

Abstract We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain Z n quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the so ( n ) 2 fusion category for odd n , both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g. their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For n = 3,5,7 we perform an extensive finite size study—both numerical and based on the exact solution—of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.

arXiv:1710.09620•Journal of Statistical Mechanics Theory and Experiment•Feb 1, 2018•11 citations
Abstract Starting from a one-dimensional model of relativistic fermions with SO(5) spin and U(N f ) flavour degrees of freedom we study the condensation of SO(5)N f anyons. In the low-energy limit the quasi-particles in the spin sector of this model are found to be massive solitons forming multiplets in the SO(5) vector or spinor representations. The solitons carry internal degrees of freedom which are identified as SO(5)N f anyons. By controlling the external magnetic fields the transitions from a dilute gas of free anyons to various collective states of interacting ones are observed. We identify the generalized parafermionic cosets describing these collective states and propose a low temperature phase diagram for the anyonic modes.
Abstract The color excitations of interacting fermions carrying an color and U ( N f ) flavor index in one spatial dimension are studied in the framework of a perturbed Wess–Zumino–Novikov–Witten model. Using Bethe ansatz methods the low energy quasi-particles are found to be massive solitons forming quark and antiquark multiplets. In addition to the color index the solitons carry an internal degree of freedom with non-integer quantum dimension. These zero modes are identified as non-Abelian anyons satisfying fusion rules. Controlling the soliton density by external fields allows to drive the condensation of these anyons into various collective states. The latter are described by parafermionic cosets related to the symmetry of the system. Based on the numerical solution of the thermodynamic Bethe ansatz equations we propose a low temperature phase diagram for this model.
Abstract The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both spin and SU ( N f ) orbital degrees of freedom to the thermodynamic properties of the latter is studied based on the exact solution of the model. For sufficiently small temperatures and magnetic fields the anyons appear as zero energy modes localized at the massive kink excitations (Tsvelik 2014 Phys. Rev. Lett . 113 066401). From their quantum dimension they are identified as spin- anyons. The density of kinks (and anyons) can be controlled by an external magnetic field leading to the formation of a collective state of these anyons described by a parafermion conformal field theory for large fields. Based on the numerical analysis of the thermodynamic Bethe ansatz equations we propose a phase diagram for the anyonic modes.
Ever since the proposal of Kitaev for decoherence-free quantum computing based on non-Abelian anyons physical realizations of these exotic particles have been investigated extensively. Starting from one-dimensional models of interacting fermions with different symmetries the emergence and condensation of su(2)Nf\mathfrak{su}(2)_{N_f}su(2)Nf​​, su(3)Nf\mathfrak{su}(3)_{N_f}su(3)Nf​​ and so(5)Nf\mathfrak{so}(5)_{N_f}so(5)Nf​​ anyons is studied in the framework of integrable perturbed WZNW models. For sufficiently small temperatures and fields non-Abelian anyons residing on massive solitonic excitations are identified by their quantum dimension. By tuning the external fields the density of anyons can be increased continuously to study the effect of interactions between them. For each model the conformal field theories describing the various collective states of the interacting anyons are determined and a phase diagram for the anyonic modes is proposed.
Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more exotic quantum mechanical degrees of freedom, so-called non-Abelian anyons, which can be thought of as certain quantum deformations of ordinary SU(2) spins. Such non-Abelian anyons occur as quasiparticle excitations in topological quantum fluids, including px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superconductors, certain fractional quantum Hall states, and rotating Bose-Einstein condensates. Here we use a combination of exact diagonalization and conformal field theory to determine the phase diagrams of ladders with up to four chains. We discuss how phenomena familiar from ordinary SU(2) spin ladders are generalized in their anyonic counterparts, such as gapless and gapped phases, odd and even effects with the ladder width, and elementary ``magnon'' excitations. Other features are entirely due to the topological nature of the anyonic degrees of freedom. In general, two-dimensional systems of interacting localized non-Abelian anyons are anyonic generalizations of two-dimensional quantum magnets.
Abstract Anyons 1,2 are low-dimensional quasiparticles that obey fractional statistics, hence interpolating between bosons and fermions. In two dimensions, they exist as elementary excitations of fractional quantum Hall states 3–5 and are believed to enable topological quantum computing 6,7 . One-dimensional anyons have been theoretically proposed, but their experimental realization has proven to be difficult. Here we observed emergent anyonic correlations in a one-dimensional strongly interacting quantum gas, resulting from the phenomenon of spin–charge separation 8–10 . A mobile impurity provides the necessary spin degree of freedom to engineer anyonic correlations in the charge sector and simultaneously acts as a probe to reveal these correlations. Starting with bosons, we tune the statistical phase to transmute bosons through anyons to fermions and observe an asymmetric momentum distribution 11–14 , a hallmark of anyonic correlations. Going beyond equilibrium conditions, we observed dynamical fermionization of the anyons 15 . This study opens the door to the exploration of non-equilibrium anyonic phenomena in a highly controllable setting 15–17 .
Abstract We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain Z n quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the so ( n ) 2 fusion category for odd n , both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g. their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For n = 3,5,7 we perform an extensive finite size study—both numerical and based on the exact solution—of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.