Decoupled phase of frustrated spin-1/2 antiferromagnetic chains with and without long range order in the ground state

Abstract

The quantum phases of one-dimensional spin $s=1/2$ chains are discussed for models with two parameters, frustrating exchange $g=J_2>0$ between second neighbors and normalized nonfrustrating power-law exchange with exponent $\alpha$ and distance dependence $r^{-\alpha }$. The ground state (GS) at $g=0$ has long-range order (LRO) for $\alpha <2$, long-range spin fluctuations for $\alpha >2$. The models conserve total spin $S=S_A+S_B$, have singlet GS for any $g$, $\alpha \ge 0$ and decouple at $1/g=0$ to linear Heisenberg antiferromagnets on sublattices $A$ and $B$ of odd and even-numbered sites. Exact diagonalization of finite chains gives the sublattice spin $<S_A^2>$, the magnetic gap $E_m$ to the lowest triplet state and the excitation $E_{\sigma }$ to the lowest singlet with opposite inversion symmetry to the GS. An analytical model that conserves sublattice spin has a first order quantum transition at $g_c=1/4ln2$ from a GS with perfect LRO to a decoupled phase with $S_A=S_B=0$ for $g\ge 4/{\pi }^2$ and no correlation between spins in different sublattices. The model with $\alpha =1$ has a first order transition to a decoupled phase that closely resembles the analytical model. The bond order wave (BOW) phase and continuous quantum phase transitions of finite models with $\alpha \ge 2$ are discussed in terms of GS degeneracy where $E_{\sigma }(g)=0$, excited state degeneracy where $E_{\sigma }(g)=E_m(g)$, and $<S_A^2>$. The decoupled phase at large frustration has nondegenerate GS for any exponent $\alpha$ and excited states related to sublattice excitations.

10 pages 8 figures

References in corpus (9)

• New Trends in Density Matrix Renormalization
• Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
• Ground states of a frustrated quantum spin chain with long-range interactions
• Quantum spin liquid in frustrated one dimensional LiCuSbO4
• Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
• Tuning the bond order wave (BOW) phase of half-filled extended Hubbard models
• Bond-order wave phase, spin solitons and thermodynamics of a frustrated linear spin-1/2 Heisenberg antiferromagnet
• Modified DMRG algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large $J_2/J_1$
• Spinons and helimagnons in the frustrated Heisenberg chain

Cited by in corpus (8)

• Numerical study of incommensurate and decoupled phases of spin-1/2 chains with isotropic exchange J1, J2 between first and second neighbors
• Multipolar phase in frustrated spin-1/2 and 1 chains
• Deconfined quantum criticality in spin-1/2 chains with long-range interactions
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Matrix product state approach to a frustrated spin chain with long-range interactions
• Quantum phase diagram of a frustrated spin-1/2 system on a Trellis Ladder
• Frustrated spin-1/2 ladder with ferro- and antiferromagnetic legs
• Spin Peierls transition of $J_1-J_2$ and extended models with ferromagnetic $J_1$.Sublattice dimerization and thermodynamics of zigzag chains in $\beta$-TeVO${}_4$