Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

Abstract

We report on a detailed investigation of the spin-1 $J_1-J_2-J_3$ Heisenberg model, a frustrated model with nearest-neighbor coupling $J_1$, next-nearest neighbor coupling $J_2$, and a three site interaction $J_3\left[({\mathbf{S}}_{i-1}\cdot {\mathbf{S}}_i)({\mathbf{S}}_i\cdot {\mathbf{S}}_{i+1})+\mathrm{H}.c.\right]$ previously studied in [Phys. Rev. B 93, 241108(R) (2016)]. Using DMRG and exact diagonalizations, we show that the phase boundaries between the Haldane phase, the next-nearest neighbor Haldane phase and the dimerized phase can be very accurately determined by combining the information deduced from the dimerization, the ground-state energy, the entanglement spectrum and the Berry phase. By a careful investigation of the finite-size spectrum, we also show that the transition between the next-nearest neighbor Haldane phase and the dimerized phase is in the Ising universality class all along the critical line. Furthermore, we justify the conformal embedding of the $SU(2{)}_2$ Wess-Zumino-Witten conformal field theory in terms of a boson and an Ising field, and we explicitly derive a number of consequences of this embedding for the spectrum along the $SU(2{)}_2$ transition line between the Haldane phase and the dimerized phase. We also show that the solitons along the first-order transition line between the Haldane phase and the dimerized phase carry a spin-1/2, while those between different dimerization domains inside the dimerized phase carry a spin 1. Finally, we show that short-range correlations change character in the Haldane and dimerized phases through disorder and Lifshitz lines, as well as through the development of short-range dimer correlations in the Haldane phase, leading to a remarkably rich phase diagram.

19 pages, 26 figures

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Cited by in corpus (26)

• Higher-order topological phases in a spring-mass model on a breathing kagome lattice
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Excitation spectrum and Density Matrix Renormalization Group iterations
• Vortex lattice melting in a boson-ladder in artificial gauge field
• Quantum phase transitions of a two-leg bosonic ladder in an artificial gauge field
• Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
• Spinon confinement and deconfinement in spin-1 chains
• Floating, critical and dimerized phases in a frustrated spin-3/2 chain
• Ground-state phase diagram of the frustrated spin-1/2 two-leg honeycomb ladder
• From SU(2)${}_5$ to SU(2)${}_3$ Wess-Zumino-Witten transitions in a frustrated spin-5/2 chain
• Proposal of a spin-one chain model with competing dimer and trimer interactions
• Magnetic phase separation in a frustrated ferrimagnetic chain under a magnetic field
• Exact zero modes in frustrated Haldane chains
• Entanglement spectrum as a marker for phase transitions in the density embedding theory for interacting spinless fermionic models
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• Dimerization and effective decoupling in two spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain
• Fractionally quantized Berry phases of magnetization plateaux in spin-$1/2$ Heisenberg multimer chains
• Rigorous decoupling between edge states in frustrated spin chains and ladders
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Realization of Wess-Zumino-Witten transitions with levels $k=6$ and $k=4$ in a frustrated spin-3 chain
• Probing universal critical scaling with scan-DMRG
• Phase transition of an SU(3) symmetric spin-1 chain
• Heisenberg spin chains with additional isotropic three-site exchange interactions
• ${\mathbb{Z}}_4$ transitions in quantum loop models on a zig-zag ladder
• Extended Ashkin-Teller transition in two coupled frustrated Haldane chains
• Confinement, deconfinement, and bound states in the spin-$1$ and spin-$3/2$ generalizations of the Majumdar--Ghosh chain