The Canted Spiral: An Exact Ground State of XXZ Zigzag Ladders

Abstract

We derive the exact ground states for a one dimensional family of $S=1/2$ XXZ Hamiltonians on the zigzag ladder. These states exhibit true long range spiral order that spontaneously breaks the U(1) invariance of the Hamiltonian. Besides breaking a continuous symmetry in $d=1$, this spiral ordering has a ferromagnetic component along the symmetry axis that can take any value between zero and full saturation. In this sense, our canted spiral solutions are a generalization of the SU(2) Heisenberg ferromagnet to non-zero ordering wave-vectors of the transverse spin components. We extend this result to the $d=2$ anisotropic triangular lattice.

5 pages

References in corpus (8)

• Electronic Orbital Currents and Polarization in Mott Insulators
• Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study
• Field-induced chiral phase in isotropic frustrated spin chains
• Vector chiral order in frustrated spin chains
• Weakly anisotropic frustrated zigzag spin chain
• On calculation of vector spin chirality for zigzag spin chains
• Quantum Fluctuations of Chirality in One-Dimensional Spin-1/2 Multiferroics: Gapless Dielectric Response from Phasons and Chiral Solitons
• Multi-magnon bound states in easy-axis ferromagnetic zigzag spin chain

Cited by in corpus (18)

• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• The mother of all states of the kagome quantum antiferromagnet
• Motif magnetism and quantum many-body scars
• Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability
• Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
• Condensation of Anyons in Frustrated Quantum Magnets
• Exact solutions of few-magnon problems in the spin-$S$ periodic XXZ chain
• State preparation of AGP on a quantum computer without number projection
• Anyonic Liquids in Nearly Saturated Spin Chains
• The spiral spin state in a zigzag spin chain system
• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• All product eigenstates in Heisenberg models from a graphical construction
• Chirality in spin-1/2 zigzag XY chain: Low-temperature density-matrix renormalization group study
• Phase diagram of a frustrated asymmetric ferromagnetic spin ladder
• An exact real-space renormalization method and applications
• Spontaneous time-reversal symmetry breaking without magnetism in a $S=1$ chain
• Are degenerate groundstates induced by spontaneous symmetry breakings in quantum phase transitions?
• Construction of asymptotic quantum many-body scar states in the SU($N$) Hubbard model