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arXiv:2402.11927 · Physical review. B./Physical review. B

Emergent SU(3) symmetry in a four-leg spin tube

E. Orignac

Published May 16, 2024• 0 citations
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Abstract

We consider an antiferromagnetic four-leg spin-1/2 tube using Abelian and non-Abelian bosonization. We show that in the limit of weak interchain coupling, the most relevant interaction gives rise to an emergent $\mathrm{SU}(3)$ symmetry, broken only by marginal interactions that can be canceled by diagonal interchain couplings. We discuss the low-energy spectrum in the semiclassical limit and using a mapping to a trimerized $\mathrm{SU}(3)$ spin chain. We establish that the correlation functions of ferroquadrupolar operators can be used to reveal the emergent symmetry.

DOI
10.1103/physrevb.109.174430

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We consider an antiferromagnetic four-leg spin-1/2 tube using Abelian and non-Abelian bosonization. We show that in the limit of weak interchain coupling, the most relevant interaction gives rise to an emergent SU(3)\mathrm{SU}(3)SU(3) symmetry, broken only by marginal interactions that can be canceled by diagonal interchain couplings. We discuss the low-energy spectrum in the semiclassical limit and using a mapping to a trimerized SU(3)\mathrm{SU}(3)SU(3) spin chain. We establish that the correlation functions of ferroquadrupolar operators can be used to reveal the emergent symmetry.
We consider a system of interacting spinless fermions on a two-leg triangular ladder with $\ensuremath{\pi}/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge and a discrete Z2{\mathbb{Z}}_{2}Z2​ symmetry---a product of parity transformation and chain permutation. Using bosonization, we show that, in the low-energy limit, the system is described by the quantum double-frequency sine-Gordon model. On the basis of this correspondence, a rich phase diagram of the system is obtained. It includes trivial and topological band insulators for weak interactions, separated by a Gaussian critical line, whereas at larger interactions a strongly correlated phase with spontaneously broken Z2{\mathbb{Z}}_{2}Z2​ symmetry sets in, exhibiting a net charge imbalance and nonzero total current. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry. This non-Abelian symmetry, absent in the microscopic description, is realized at low energies as a combined effect of the magnetic flux, frustration, and many-body correlations. The criticality belongs to the SU(2)1{}_{1}1​ Wess-Zumino-Novikov-Witten universality class. The critical point bifurcates into two Ising critical lines that separate the band insulators from the strong-coupling symmetry broken phase. We establish an analytical connection between the low-energy description of our model around the critical bifurcation point on one hand and the Ashkin-Teller model and a weakly dimerized XXZXXZXXZ spin-1/2 chain on the other. We complement our field-theory understanding via tensor network simulations, providing compelling quantitative evidences of all bosonization predictions. Our findings are of interest to up-to-date cold atom experiments utilizing Rydberg dressing that have already demonstrated correlated ladder dynamics.
We study the ground-state phase diagram of a frustrated spin-1/2 four-leg tube. Using a variety of complementary techniques, namely, density matrix renormalization group, exact diagonalization, Schwinger boson mean-field theory, quantum Monte Carlo, and series expansion, we explore the parameter space of this model in the regime of all-antiferromagnetic exchange. In contrast to unfrustrated four-leg tubes, we uncover a rich phase diagram. Apart from the Luttinger liquid fixed point in the limit of decoupled legs, this comprises several gapped ground states, namely, a plaquette, an incommensurate, and an antiferromagnetic quasispin-2 chain phase. The transitions between these phases are analyzed in terms of total energy and static structure factor calculations and are found to be of (weak) first order. Despite the absence of long-range order in the quantum case, remarkable similarities to the classical phase diagram are uncovered, with the exception of the icommensurate regime, which is strongly renormalized by quantum fluctuations. In the limit of large leg exchange, the tube exhibits a deconfinement crossover from gapped magnon-like excitations to spinons.
The frustrated three-leg antiferromagnetic spin-12\frac{1}{2}21​ tube with a weak interchain coupling in a magnetic field is investigated by means of Abelian bosonization techniques. It is clearly shown that a vector chiral long-range order and a one-component Tomonaga-Luttinger liquid coexist in a wide magnetic-field region from a state with a small magnetization to a nearly saturated one. The chiral order is predicted to still survive in the intermediate plateau state. We further predict that (even) when the strength of one bond in the three rung couplings is decreased (increased), an Ising-type quantum phase transition takes place and the chirality vanishes (no singular phenomena occur and the chiral order is maintained). Even without magnetic fields, the chiral order would also be present if the spin tube possesses easy-plane anisotropy.
We propose a mechanism of a vector chiral long-range order in two-leg spin-12\frac{1}{2}21​ and spin-1 antiferromagnetic ladders with four-spin exchanges and a Zeeman term. It is known that for one-dimensional quantum systems, spontaneous breakdown of continuous symmetries is generally forbidden. Any vector chiral order hence does not appear in spin-rotationally [SU(2)]-symmetric spin ladders. However, if a magnetic field is added along the Sz{S}^{z}Sz axis of ladders and the SU(2) symmetry is reduced to the U(1) one, the zzz component of a vector chiral order can emerge with the remaining U(1) symmetry unbroken. Making use of Abelian bosonization techniques, we actually show that a certain type of four-spin exchange can yield a vector chiral long-range order in spin-12\frac{1}{2}21​ and spin-1 ladders under a magnetic field. In the chiral-ordered phase, the Z2{Z}_{2}Z2​ interchain-parity (i.e., chain-exchange) symmetry is spontaneously broken. We also consider effects of perturbations breaking the parity symmetry.
We study the magnetization plateau state of the three-leg spin-12\frac{1}{2}21​ tube in the strong rung coupling region, where S3{S}_{3}S3​ symmetry breaking and the low-energy chirality degree of freedom play crucial roles. On the basis of the effective chirality model and density matrix renormalization group, we clarify that, as the leg coupling increases, the chirality liquid with gapless nonmagnetic excitations, the spin-imbalance phase, and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. The relevance of these results to experiments is also discussed.
Motivated by the recent discovery of the spin tube [(CuCl2tachH)3Cl]Cl2[{(\mathrm{Cu}{\mathrm{Cl}}_{2}\mathrm{tach}\mathrm{H})}_{3}\mathrm{Cl}]{\mathrm{Cl}}_{2}[(CuCl2​tachH)3​Cl]Cl2​, we investigate the properties of a frustrated three-leg spin tube with antiferromagnetic intra- and inter-ring couplings. We pay special attention to the evolution of the properties from weak to strong inter-ring coupling and show on the basis of extensive density matrix renormalization group and exact diagonalization calculations that the system undergoes a first-order phase transition between a dimerized gapped phase at weak coupling that can be described by the usual spin-chirality model and a gapless critical phase at strong coupling that can be described by an effective spin-3∕23∕23∕2 model. We also show that there is a magnetization plateau at 1∕31∕31∕3 in the whole gapped phase and slightly beyond. The implications for [(CuCl2tachH)3Cl]Cl2[{(\mathrm{Cu}{\mathrm{Cl}}_{2}\mathrm{tach}\mathrm{H})}_{3}\mathrm{Cl}]{\mathrm{Cl}}_{2}[(CuCl2​tachH)3​Cl]Cl2​ are discussed, with the conclusion that this system behaves essentially as a spin-3∕23∕23∕2 chain.