Frustration-induced quantum phase transitions in a quasi-one-dimensional ferrimagnet: Hard-core boson map and the Tonks-Girardeau limit

Abstract

We provide evidence of a superfluid-insulator transition (SIT) of magnons in a quasi-one-dimensional quantum ferrimagnet with isotropic competing antiferromagnetic spin interactions. This SIT occurs between two distinct ferrimagnetic phases due to the frustration-induced closing of the gap to a magnon excitation. It thus causes a coherent superposition of singlet and triplet states at lattice unit cells and a power-law decay on the staggered spin correlation function along the transverse direction to the spontaneous magnetization. A hard-core boson map suggests that asymptotically close to the SIT the magnons attain the Tonks-Girardeau limit. The quantized nature of the condensed singlets is observed before a first-order transition to a singlet magnetic spiral phase accompanied by critical antiferromagnetic ordering. In the limit of strong frustration, the system undergoes a decoupling transition to an isolated gapped two-leg ladder and a critical single linear chain.

Spontaneously magnetized Tomonaga-Luttinger liquid in frustrated quantum antiferromagnets

“…Since λ > 0 the transition cannot be first order. We emphasize that our derivation of the spontaneous magnetization (22) fully respects the SU (2) rotational symmetry and M can point in an arbitrary direction.…”

“…A very good possibility to realize such a spontaneously magnetized TLL (SMTLL) is offered by ferrimagnetic systems. Several numerical studies [18][19][20][21][22][23][24] have followed this route and found incommensurate ferrimagnetic phases which can be candidates for the SMTLL. However besides the numerical results, there is still no microscopic theory that explains the nature of the incommensurate phase and could relate it to a SMTLL.…”

Haldane Phases and Ferrimagnetic Phases with Spontaneous Translational Symmetry Breakdown in Distorted Mixed Diamond Chains with Spins 1 and 1/2

“…For example, partial ferrimagnetic phases are found in various onedimensional frustrated quantum spin models. [45][46][47][48][49][50][51] However, some of them are only numerically confirmed and no physical explanation has been given so far. We hope that the present study paves the way to the general understanding of these partial ferrimagnetic states.…”

“…The ferrimagnetic phase of this kind has been found in various frustrated one-dimensional quantum spin systems. [45][46][47][48][49][50][51] In contrast, between the nonmagnetic phase and the FDC3 phase, we find no partial ferrimagnetic phase for small B .…”

The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field

“…Ferrimagnetic systems İn particular, the behavior of the edge states associated with the 1/3 magnetization plateau of the AB 2 anisotropic chain was recently investigated [45]. Furthermore, rich phase diagrams are observed through doping [46][47][48][49][50] or adding geometric frustration [51][52][53][54][55][56][57][58] to the ferrimagnetic models. In particular, ferrimagnetic spin-(1/2, S) chains under an applied magnetic field present magnetization plateaus at m = S − 1/2 (ferrimagnetic plateau) and m = S + 1/2 (saturation plateau), where m is the magnetization per unit cell [59][60][61][62][63][64].…”