Competing Orders and Hidden Duality Symmetries in Two-leg Spin Ladder Systems

Abstract

A unifying approach to competing quantum orders in generalized two-leg spin ladders is presented. Hidden relationship and quantum phase transitions among the competing orders are thoroughly discussed by means of a low-energy field theory starting from an SU(4) quantum multicritical point. Our approach reveals that the system has a relatively simple phase structure in spite of its complicated interactions. On top of the U(1)-symmetry which is known from previous studies to mixes up antiferromagnetic order parameter with that of the p-type nematic, we find an emergent U(1)-symmetry which mixes order parameters dual to the above. On the basis of the field-theoretical- and variational analysis, we give a qualitative picture for the global structure of the phase diagram. Interesting connection to other models (e.g. bosonic t-J model) is also discussed.

33 pages incl. 8 figures, accepted for publication in Phys.Rev.B

References in corpus (4)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Algebraic spin liquid as the mother of many competing orders
• Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange

Cited by in corpus (21)

• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Quantum magnetism on the Cairo pentagonal lattice
• Quantum phase transitions in multileg spin ladders with ring exchange
• Magnetic properties of the spin-1/2 Ising-Heisenberg diamond chain with the four-spin interaction
• Diamond chains with multiple-spin exchange interactions
• Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach
• Competing orders in the generalized Hund chain model at half-filling
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
• Duality approach to one-dimensional degenerate electronic systems
• Semiclassical Approach to Competing Orders in Two-leg Spin Ladder with Ring-Exchange
• Four-spin-exchange- and magnetic-field-induced chiral order in two-leg spin ladders
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Antiferromagnetic ordering of energy levels for spin ladder with four-spin cyclic exchange: Generalization of the Lieb-Mattis theorem
• Exact models for trimerization and tetramerization in spin chains
• Spin nematics in frustrated spin-dimer systems with bilayer structure
• Energy-level ordering and ground-state quantum numbers for frustrated two-leg spin-1/2 ladder model
• Abundant quadrupolar or nematic phases driven by the Heisenberg interactions in a spin-1 dimer system forming a bilayer
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• On the ground state energy scaling in quasi-rung-dimerized spin ladders
• Phase diagram of a spin-1/2 Heisenberg ladder with a chirality-chirality interaction