Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders

Year: 2023

Authors: Beradze B., Tsitsishvili M., Tirrito E., Dalmonte M., Chanda T., Nersesyan A.

Autors Affiliation: Andronikashvili Inst Phys, GE-0177 Tbilisi, Georgia; Ilia State Univ, GE-0162 Tbilisi, Georgia; Abdus Salam Int Ctr Theoret Phys ICTP, I-34151 Trieste, Italy; Int Sch Adv Studies SISSA, I-34136 Trieste, Italy; Univ Trento, Pitaevskii BEC Ctr, CNR INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Indian Inst Technol Indore, Dept Phys, Indore 453552, India.

Abstract: We consider a system of interacting spinless fermions on a two-leg triangular ladder with 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 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 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 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 XXZ 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.

Journal/Review: PHYSICAL REVIEW B

Volume: 108 (7)      Pages from: 75146-1  to: 75146-17

More Information: We thank Poetri S. Tarabunga for precious discussions and collaborations during the implementations of the TTN codes. We are grateful to Simone Montangero, Simone Notarnicola, Pietro Silvi, and Colin Egan for the useful discussions regarding the developments of the code. M.D. thanks M. Fabrizio and P. Fendley for discussions. A.N. thanks F. H. L. Essler and O. Starykh for their interest in our work and useful comments. B.B. and A.N. acknowledge fruitful cooperation with G. Japaridze on projects related to frustrated one-dimensional quantum systems. T.C. acknowledges the support of PL-GRID infrastructure for the computational resource. M.T. thanks the Simons Foundation for supporting his Ph.D. studies through Award No. 284558FY19 to the ICTP. The work of M.D. was partly supported by the ERC under Grant No. 758329 (AGEnTh) , and by the Munich Institute for Astro-, Particle and BioPhysics (MIAPbP) which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2094 – 390783311. The support of B.B and A.N. from the Shota Rustaveli National Science Foundation of Georgia, SRNSF, Grant No. FR-19-11872, is gratefully acknowledged. M.D. and E.T. further acknowledge support from the MIUR Programme FARE (MEPH), and from QUANTERA DYNAMITE PCI2022-132919. The iDMRG simulations have been performed with the TeNPy library [110] , while the TTN simulations use the C++ ITensor library [111] as its backbone.
KeyWords: Critical Exponents; Ultracold Atoms; Quantum; Model; Fields; Chains; Line
DOI: 10.1103/PhysRevB.108.075146

Citations: 1
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