Magnetic phase diagram of the spin-12antiferromagnetic zigzag ladder

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 phases͒ and four types of gapless Tomonaga-Luttinger liquid ͑TLL͒ 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+1͒, 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-onedimensional compounds are also discussed.

Phase diagram of hard-core bosons on a zigzag ladder

“…20,21 Similarly, a chiral phase has been also predicted for isotropic frustrated spin chains in presence of a magnetic field. 16,22,23 On the contrary, for our unfrustrated model, we do not find any evidence of symmetry breaking for V ≥ 0, as can be seen from Lanczos spectra at low-energy (not shown). Therefore, we conclude that there is a fundamental difference between frustrated and unfrustrated bosons at these densities: for the former case, a gapless state with broken Z 2 symmetry is expected, while, in the latter one, a pure gapless Tomonaga-Luttinger liquid is realized.…”

“…In particular, the one-dimensional chain with SU(2) symmetry (i.e., V = 2|t|) but different nearest-(J 1 ) and next-nearest-neighbor (J 2 ) interactions has been widely discussed, also in presence of a finite magnetic field. [14][15][16] On the other hand, here we are interested in the case with positive hopping parameters and V > 2t, in order to describe strongly interacting bosons in low-dimensional systems that are relevant for atomic gases trapped in optical lattices. However, we will show that some features of the phase diagram do not depend upon the sign of t and can be understood on the basis of the strong-coupling (classical) limit V /t → ∞.…”

Ground states of spin-12triangular antiferromagnets in a magnetic field

“…However, they have qualitative effects in the Y and V phases, since S + r = 0 there, in contrast to Eqs. (7,8). Note that the modulation of S z r is perfectly consistent with one-dimensionality, and is expected to persist directly without qualitative modifications.…”

“…(7,8) as defining the local spin ordering, with a fluctuating quantum phase θ(x, τ ) (τ is imaginary time), that is, we make the replacement…”

“…The origin of the coordinate r in Eqs. (7,8) must be appropriately chosen to match the chosen ground state.…”