Level crossing, spin structure factor and quantum phases of the frustrated spin-1/2 chain with first and second neighbor exchange

TL;DR

This paper investigates the quantum phase diagram of a frustrated spin-1/2 chain with first and second neighbor exchanges, using numerical methods to identify critical points and phases characterized by gapless or gapped behavior.

Contribution

It combines level crossing analysis and spin structure factor calculations with ED and DMRG to map out the phase diagram and identify quantum critical points in the frustrated chain.

Findings

Identifies a gapless QLRO(π/2) phase between specific J1/J2 ratios.

Shows agreement between numerical results and field theory at small frustration.

Reveals discrepancies in weak exchange regimes between different theoretical approaches.

Abstract

The spin-1/2 chain with isotropic Heisenberg exchange $J_1$, $J_2 > 0$ between first and second neighbors is frustrated for either sign of J1. Its quantum phase diagram has critical points at fixed $J_1/J_2$ between gapless phases with nondegenerate ground state (GS) and quasi-long-range order (QLRO) and gapped phases with doubly degenerate GS and spin correlation functions of finite range. In finite chains, exact diagonalization (ED) estimates critical points as level crossing of excited states. GS spin correlations enter in the spin structure factor $S(q)$ that diverges at wave vector $q_m$ in QLRO($q_m$) phases with periodicity $2\pi/q_m$ but remains finite in gapped phases. $S(q_m)$ is evaluated using ED and density matrix renormalization group (DMRG) calculations. Level crossing and the magnitude of $S(q_m)$ are independent and complementary probes of quantum phases, based respectively on excited and ground states. Both indicate a gapless QLRO($\pi/2$) phase between $-1.2 < J_1/|J_2| < 0.45$. Numerical results and field theory agree well for quantum critical points at small frustration $J_2$ but disagree in the sector of weak exchange $J_1$ between Heisenberg antiferromagnetic chains on sublattices of odd and even-numbered sites.