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arXiv:cond-mat/0004441 · Nuclear Physics B

Ising model description of the SU(2)1 quantum critical point in a dimerized two-leg spin-1/2 ladder

Y.-J. Wang, A. A. Nersesyan

Published Sep 1, 2000• 22 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(00)00305-9

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The physical properties of the edge states of the cut two-leg spin ladder are investigated by means of the bosonization approach. By carefully treating boundary conditions, we derive the existence of spin-1/2 edge states in the spin ladder with a ferromagnetic rung exchange and for the open spin-1 Heisenberg chain. In contrast, such states are absent in the antiferromagnetic rung coupling case. The approach, based on a mapping onto decoupled semi-infinite off-critical Ising models, allows us to compute several physical quantities of interest. In particular, we determine the magnetization and dimerization profiles of the cut two-leg spin ladder and of the open biquadratic spin-1 chain in the vicinity of the SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ Wess-Zumino-Novikov-Witten critical point.
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.
In the weak-coupling regime of the continuous theories, two sets of one-loop renormalization-group equations are derived and solved to disclose the phase diagrams of the antiferromagnetic generalized two-leg spin-12\frac{1}{2}21​ ladder under the effect of (I) a staggered external magnetic field and (II) an explicit dimerization. In model (I), the splitting of the SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ critical line into U(1)U(1)U(1) and Z2{Z}_{2}Z2​ critical surfaces is observed, while in model (II), two critical surfaces arising from their underlying critical lines with SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ and Z2{Z}_{2}Z2​ characteristics merge into an SU(2)1\mathrm{SU}{(2)}_{1}SU(2)1​ critical surface on the line where the model attains its highest symmetry.