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

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 ${\mathbb{Z}}_2$ 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 ${\mathbb{Z}}_2$ symmetry sets in, exhibiting a net charge imbalance and non-zero 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.

18 pages, 9 figures. Close to the published version

References in corpus (37)

• The density-matrix renormalization group in the age of matrix product states
• Probing many-body dynamics on a 51-atom quantum simulator
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• The ITensor Software Library for Tensor Network Calculations
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• From density-matrix renormalization group to matrix product states
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Hidden order in 1D Bose insulators
• Rise and fall of hidden string order of lattice bosons
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• Applying matrix product operators to model systems with long-range interactions
• Microwave-engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Quench Dynamics of a Fermi Gas with Strong Non-Local Interactions
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Artificial gauge fields with ultracold atoms
• Realizing distance-selective interactions in a Rydberg-dressed atom array
• Non-local order parameters for the 1D Hubbard model
• Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model
• Gauge-theoretic origin of Rydberg quantum spin liquids
• Competing phases, phase separation and co-existence in the extended one-dimensional bosonic Hubbard model
• Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Observation of brane parity order in programmable optical lattices
• Phase diagram of an interacting staggered Su-Schrieffer-Heeger two-chain ladder close to a quantum critical point
• Phase diagram of Rydberg-dressed atoms on two-leg triangular ladders
• Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice
• Topological Lifshitz Transitions, Orbital Currents, and Interactions in Low-dimensional Fermi Gases in Synthetic Gauge Fields
• Topological chiral currents in the Gross-Neveu model extension
• Spectrum, Lifshitz transitions and orbital currents in frustrated fermionic ladders with a uniform flux

Cited by in corpus (4)

• Tunable quantum criticality in multicomponent Rydberg arrays
• Interaction dependence of the Hall response for the Bose-Hubbard triangular ladder
• Exploring Frustration Effects of Strongly Interacting Bosons via the Hall Response
• The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux