The deconfined phase of ( $2+1$ )-dimensional ${\mathbb{Z}}_{k}$ gauge theory exhibits topological order, with $e$ and $m$ anyons that have a $2\ensuremath{\pi}/k$ braiding phase. Proliferating either $e$ or $m$ drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges $e$ and $m$ anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theory with a mutual Chern-Simons term at level $k$ to describe the vicinity of the multicritical point for $k\ensuremath{\ge}4$. The emergence of a global $\mathrm{U}{(1)}^{\mathrm{top}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}^{\mathrm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved U(1) current with protected scaling dimension; (2) the first-order line emanating from the critical point for $k=2$ disappears generically for sufficiently large $k$ ; (3) the correlation length exponent approaches that of the three-dimensional XY model with corrections of order $1/{k}^{2}$ in the large- $k$ limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.The deconfined phase of ($2+1$)-dimensional ${\mathbb{Z}}_{k}$ gauge theory exhibits topological order, with $e$ and $m$ anyons that have a $2\ensuremath{\pi}/k$ braiding phase. Proliferating either $e$ or $m$ drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges $e$ and $m$ anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theory with a mutual Chern-Simons term at level $k$ to describe the vicinity of the multicritical point for $k\ensuremath{\ge}4$. The emergence of a global $\mathrm{U}{(1)}^{\mathrm{top}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}^{\mathrm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved U(1) current with protected scaling dimension; (2) the first-order line emanating from the critical point for $k=2$ disappears generically for sufficiently large $k$; (3) the correlation length exponent approaches that of the three-dimensional XY model with corrections of order $1/{k}^{2}$ in the large-$k$ limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.

arXiv:2407.07941Physical review. B./Physical review. BAug 1, 20251 citation

Asymmetric and chiral dynamics of two-component anyons with synthetic gauge flux

Rui-Jie Chen, Ying-Xin Huang, Guo-Qing Zhang +1 more

In this work, we investigate the non-equilibrium dynamics in a one-dimensional two-component anyon-Hubbard model, which can be mapped to an extended Bose-Hubbard ladder with density-dependent hopping phase and synthetic gauge flux. Through numerical simulations of two-particle dynamics and the symmetry analysis, we reveal the asymmetric transport with broken inversion symmetry and two dynamical symmetries in the expansion dynamics. The expansion of two-component anyons is dynamically symmetric under spatial inversion and component flip, when the sign of anyonic statistics phase or the signs of gauge flux and interaction are changed. In the non-interacting case, we show the dynamical suppression induced by both the statistics phase and gauge flux. In the interacting case, we demonstrate that both chiral and antichiral dynamics can be exhibited and tuned by the statistics phase and gauge flux. The dynamical phase regimes with respect to the chiral-antichiral dynamics are obtained. These findings highlight the rich dynamical phenomena arising from the interplay of anyonic exchange statistics, synthetic gauge fields, and interactions in multi-component anyons.In this work, we investigate the non-equilibrium dynamics in a one-dimensional two-component anyon-Hubbard model, which can be mapped to an extended Bose-Hubbard ladder with density-dependent hopping phase and synthetic gauge flux. Through numerical simulations of two-particle dynamics and the symmetry analysis, we reveal the asymmetric transport with broken inversion symmetry and two dynamical symmetries in the expansion dynamics. The expansion of two-component anyons is dynamically symmetric under spatial inversion and component flip, when the sign of anyonic statistics phase or the signs of gauge flux and interaction are changed. In the non-interacting case, we show the dynamical suppression induced by both the statistics phase and gauge flux. In the interacting case, we demonstrate that both chiral and antichiral dynamics can be exhibited and tuned by the statistics phase and gauge flux. The dynamical phase regimes with respect to the chiral-antichiral dynamics are obtained. These findings highlight the rich dynamical phenomena arising from the interplay of anyonic exchange statistics, synthetic gauge fields, and interactions in multi-component anyons.

cond-mat.quant-gasCross-listedarXiv:2512.19139Dec 23, 20250 citations

The nature of the three-anyon wave functions

Stefan V. Mashkevich, Jan Myrheim, Kåre Olaussen +1 more

arXiv:hep-th/9412119Physics Letters BApr 1, 199513 citations

The deconfined phase of (

2+1

)-dimensional

{\mathbb{Z}}_{k}

gauge theory exhibits topological order, with

e

and

m

anyons that have a $2\ensuremath{\pi}/k$ braiding phase. Proliferating either

e

m

drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges

e

and

m

anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theory with a mutual Chern-Simons term at level

k

to describe the vicinity of the multicritical point for $k\ensuremath{\ge}4$. The emergence of a global $\mathrm{U}{(1)}^{\mathrm{top}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}^{\mathrm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved U(1) current with protected scaling dimension; (2) the first-order line emanating from the critical point for

k=2

disappears generically for sufficiently large

k

; (3) the correlation length exponent approaches that of the three-dimensional XY model with corrections of order

1/{k}^{2}

in the large-

k

limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.