Magnetic phase diagram of the spin-1/2 antiferromagnetic zigzag ladder

TL;DR

This paper maps the magnetic phase diagram of a spin-1/2 antiferromagnetic zigzag ladder, identifying multiple gapped and gapless phases, and develops effective theories to explain their correlation functions and critical properties.

Contribution

It provides a comprehensive numerical and theoretical analysis of the phase diagram, including effective low-energy theories for various TLL phases and their correlation functions.

Findings

Identification of three gapped phases and four TLL phases.

Development of effective low-energy theories for TLL phases.

Good agreement between numerical results and theoretical predictions.

Abstract

We study the one-dimensional spin-1/2 Heisenberg model with antiferromagnetic nearest-neighbor J_1 and next-nearest-neighbor J_2 exchange couplings in magnetic field h. With varying dimensionless parameters J_2/J_1 and h/J_1, the ground state of the model exhibits several phases including three gapped phases (dimer, 1/3-magnetization plateau, and fully polarized phases) and four types of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2, spin-density-wave (SDW_2), and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various (multiple-)spin correlation functions in detail, and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1, SDW_2, and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs, and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons (central charge c=1+1), which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-one-dimensional compounds are also discussed.