We investigate a phase transition in an SU(3) symmetric spin-1 chain. To study this transition, we numerically diagonalize an SU(3) symmetric Hamiltonian combining the Uimin-Lai-Sutherland (ULS) model Hamiltonian with the Hamiltonian of the exact trimer ground state ( ${\mathbb{Z}}_{3}$ symmetry breaking). Our numerical results are discussed on the basis of the conformal field theory (CFT) and the renormalization group (RG). We then show the phase transition between a trimer liquid phase (massless, no long-range order) and a trimer phase (spontaneously ${\mathbb{Z}}_{3}$ symmetry breaking). Next, we find the central charge $c=2$ in the massless phase, and $c<2$ in the ${\mathbb{Z}}_{3}$ symmetry broken phase. From these results, we identify the universality class of the critical trimer liquid phase, as well as the phase boundary between these two phases.We investigate a phase transition in an SU(3) symmetric spin-1 chain. To study this transition, we numerically diagonalize an SU(3) symmetric Hamiltonian combining the Uimin-Lai-Sutherland (ULS) model Hamiltonian with the Hamiltonian of the exact trimer ground state (${\mathbb{Z}}_{3}$ symmetry breaking). Our numerical results are discussed on the basis of the conformal field theory (CFT) and the renormalization group (RG). We then show the phase transition between a trimer liquid phase (massless, no long-range order) and a trimer phase (spontaneously ${\mathbb{Z}}_{3}$ symmetry breaking). Next, we find the central charge $c=2$ in the massless phase, and $c<2$ in the ${\mathbb{Z}}_{3}$ symmetry broken phase. From these results, we identify the universality class of the critical trimer liquid phase, as well as the phase boundary between these two phases.

arXiv:2108.01882Physical review. B./Physical review. BOct 4, 20212 citations

Universality Relations in Non-solvable Quantum Spin Chains

G. Benfatto, V. Mastropietro

arXiv:0907.2837Journal of Statistical PhysicsJan 8, 201022 citations

Charge-6e superconductivity from doping SU(3) spin liquids

Yanqi Wang, Boran Zhou, Hui Ying Yang +1 more

We propose doping $SU(3)$ -symmetric spin liquids as a route toward charge- $6e$ superconductivity. This generalizes the idea of constructing charge- $4e$ superconductivity from doped $SU(4)$ -symmetric phases. As a concrete platform, we study a bilayer triangular-lattice Hubbard model with $SU(3)$ spin symmetry and interlayer antiferromagnetic exchange. Using complementary parton constructions, we analyze doped $\mathbb{Z}_3$ quantum spin liquid and $SU(3)$ -related chiral spin liquids. Doping a $\mathbb{Z}_3$ quantum spin liquid can produce an orthogonal metal with a gauge invariant fermi surface of charge- $3e$ fermionic trions. Pairing these trions gives a time-reversal-symmetric charge- $6e$ superconductor. Doping Abelian $SU(3)_1$ and $SU(6)_1$ chiral spin liquids yields chiral charge- $6e$ superconductors with and without residual Abelian topological order, respectively. Doping a non-Abelian $SU(3)_2$ chiral spin liquid leads to a non-Abelian chiral charge- $6e$ superconductor intertwined with $SO(3)_{-3}$ topological order and supporting non-Abelian $h/(6e)$ superconducting vortices. We also identify several other phases, including $\mathbb{Z}_3$ orthogonal metal, quantum anomalous Hall (crystal) phases enriched by $\mathbb{Z}_3$ or $\mathbb{Z}_2$ topological order, $SU(3)$ -breaking charge- $2e$ superconductors, composite fermi liquid coupled to non-Abelian gauge field, and descendant chiral spin liquids. Our results identify doped $SU(3)$ spin liquids as a natural setting where symmetry, fractionalization, and topology cooperate to produce charge- $6e$ superconductivity.We propose doping $SU(3)$-symmetric spin liquids as a route toward charge-$6e$ superconductivity. This generalizes the idea of constructing charge-$4e$ superconductivity from doped $SU(4)$-symmetric phases. As a concrete platform, we study a bilayer triangular-lattice Hubbard model with $SU(3)$ spin symmetry and interlayer antiferromagnetic exchange. Using complementary parton constructions, we analyze doped $\mathbb{Z}_3$ quantum spin liquid and $SU(3)$-related chiral spin liquids. Doping a $\mathbb{Z}_3$ quantum spin liquid can produce an orthogonal metal with a gauge invariant fermi surface of charge-$3e$ fermionic trions. Pairing these trions gives a time-reversal-symmetric charge-$6e$ superconductor. Doping Abelian $SU(3)_1$ and $SU(6)_1$ chiral spin liquids yields chiral charge-$6e$ superconductors with and without residual Abelian topological order, respectively. Doping a non-Abelian $SU(3)_2$ chiral spin liquid leads to a non-Abelian chiral charge-$6e$ superconductor intertwined with $SO(3)_{-3}$ topological order and supporting non-Abelian $h/(6e)$ superconducting vortices. We also identify several other phases, including $\mathbb{Z}_3$ orthogonal metal, quantum anomalous Hall (crystal) phases enriched by $\mathbb{Z}_3$ or $\mathbb{Z}_2$ topological order, $SU(3)$-breaking charge-$2e$ superconductors, composite fermi liquid coupled to non-Abelian gauge field, and descendant chiral spin liquids. Our results identify doped $SU(3)$ spin liquids as a natural setting where symmetry, fractionalization, and topology cooperate to produce charge-$6e$ superconductivity.

arXiv:2607.25909Jul 28, 20260 citations

Anomalous quantum information scrambling for Z3 parafermion chains

Shun-Yao Zhang, Dong-Ling Deng

Parafermions are exotic quasiparticles with non-Abelian fractional statistics that could be exploited to realize universal topological quantum computing. Here, we study the scrambling of quantum information in one-dimensional parafermionic chains, with a focus on ${\mathbb{Z}}_{3}$ parafermions in particular. We use the generalized out-of-time-ordered correlators (OTOCs) as a measure of the information scrambling and introduce an efficient method based on matrix product operators to compute them. With this method, we compute the OTOCs for ${\mathbb{Z}}_{3}$ parafermions chains up to 200 sites for the entire early growth region. We find that, in stark contrast to the dynamics of conventional fermions or bosons, the information scrambling light cones for parafermions can be both symmetric and asymmetric, even for inversion-invariant Hamiltonians involving only hopping terms. In addition, we find a deformed light cone structure with a sharp peak at the boundary of the parafermion chains in the topological regime, which gives unambiguous evidence of the strong zero modes at infinite temperature.Parafermions are exotic quasiparticles with non-Abelian fractional statistics that could be exploited to realize universal topological quantum computing. Here, we study the scrambling of quantum information in one-dimensional parafermionic chains, with a focus on ${\mathbb{Z}}_{3}$ parafermions in particular. We use the generalized out-of-time-ordered correlators (OTOCs) as a measure of the information scrambling and introduce an efficient method based on matrix product operators to compute them. With this method, we compute the OTOCs for ${\mathbb{Z}}_{3}$ parafermions chains up to 200 sites for the entire early growth region. We find that, in stark contrast to the dynamics of conventional fermions or bosons, the information scrambling light cones for parafermions can be both symmetric and asymmetric, even for inversion-invariant Hamiltonians involving only hopping terms. In addition, we find a deformed light cone structure with a sharp peak at the boundary of the parafermion chains in the topological regime, which gives unambiguous evidence of the strong zero modes at infinite temperature.

arXiv:2103.13450Physical review. B./Physical review. BMay 27, 20213 citations

Symmetry of the Spin Systems

Roman Boča

Elsevier eBooksJan 1, 20120 citations

{\mathbb{Z}}_{3}

symmetry breaking). Our numerical results are discussed on the basis of the conformal field theory (CFT) and the renormalization group (RG). We then show the phase transition between a trimer liquid phase (massless, no long-range order) and a trimer phase (spontaneously

{\mathbb{Z}}_{3}

symmetry breaking). Next, we find the central charge

c=2

in the massless phase, and

c<2

in the

{\mathbb{Z}}_{3}

symmetry broken phase. From these results, we identify the universality class of the critical trimer liquid phase, as well as the phase boundary between these two phases.

We propose doping

SU(3)

-symmetric spin liquids as a route toward charge-

6e

superconductivity. This generalizes the idea of constructing charge-

4e

superconductivity from doped

SU(4)

-symmetric phases. As a concrete platform, we study a bilayer triangular-lattice Hubbard model with

SU(3)

spin symmetry and interlayer antiferromagnetic exchange. Using complementary parton constructions, we analyze doped

\mathbb{Z}_3

quantum spin liquid and

SU(3)

-related chiral spin liquids. Doping a

\mathbb{Z}_3

quantum spin liquid can produce an orthogonal metal with a gauge invariant fermi surface of charge-

3e

fermionic trions. Pairing these trions gives a time-reversal-symmetric charge-

6e

superconductor. Doping Abelian

SU(3)_1

and

SU(6)_1

chiral spin liquids yields chiral charge-

6e

superconductors with and without residual Abelian topological order, respectively. Doping a non-Abelian

SU(3)_2

chiral spin liquid leads to a non-Abelian chiral charge-

6e

superconductor intertwined with

SO(3)_{-3}

topological order and supporting non-Abelian

h/(6e)

superconducting vortices. We also identify several other phases, including

\mathbb{Z}_3

orthogonal metal, quantum anomalous Hall (crystal) phases enriched by

\mathbb{Z}_3

\mathbb{Z}_2

topological order,

SU(3)

-breaking charge-

2e

superconductors, composite fermi liquid coupled to non-Abelian gauge field, and descendant chiral spin liquids. Our results identify doped

SU(3)

spin liquids as a natural setting where symmetry, fractionalization, and topology cooperate to produce charge-

6e

superconductivity.

{\mathbb{Z}}_{3}

parafermions in particular. We use the generalized out-of-time-ordered correlators (OTOCs) as a measure of the information scrambling and introduce an efficient method based on matrix product operators to compute them. With this method, we compute the OTOCs for

{\mathbb{Z}}_{3}

parafermions chains up to 200 sites for the entire early growth region. We find that, in stark contrast to the dynamics of conventional fermions or bosons, the information scrambling light cones for parafermions can be both symmetric and asymmetric, even for inversion-invariant Hamiltonians involving only hopping terms. In addition, we find a deformed light cone structure with a sharp peak at the boundary of the parafermion chains in the topological regime, which gives unambiguous evidence of the strong zero modes at infinite temperature.