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arXiv:2510.05988 · Physical Review Letters

Commensurate-Incommensurate Mott Transition without Magnetic Field: Emergence of Nematic Luttinger Liquid in XXZ Chain

Julien Fitouchi, Natalia Chepiga

Published May 21, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the zero magnetization and ground state phase diagram of a spin-1/2 chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange couplings in the strongly interacting regime. Using density matrix renormalization group (DMRG) simulations, we discover two successive commensurate-incommensurate transitions of the nonconformal Pokrovsky-Talapov universality class, occurring even at zero magnetic field. We argue that the first transition marks the proliferation of solitonic discommensurations (kink-antikink pairs) in a critical phase with central charge c=2, emerging from a period-4 gapped phase. At the second transition, an incommensurate quadrupolar (or nematic) Luttinger liquid forms out of a gapped phase separation, via the condensation of two-magnon bound pairs. In the strongly interacting limit, the location of the two Pokrovsky-Talapov transitions can be analytically predicted with degenerate perturbation theory. Our results demonstrate that frustration alone is sufficient to drive continuous commensurate-incommensurate transitions of Mott type and stabilize complex objects with incommensurate quasi-long-range order without doping.

DOI
10.1103/5j3k-hztz

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We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest-neighbor range.In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbor and next-nearest-neighbor interactions.Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations.The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles.In relation with recent studies, we show several emergent transition lines with a central charge c = 3/2 between the Luttinger liquid and the cluster Luttinger liquid phases.These results could be experimentally investigated using highly tunable quantum simulators.
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We investigate the properties of the Heisenberg S=1S=1S=1 chain with bilinear and biquadratic interactions in a magnetic field using the density- matrix renormalization-group, Bethe ansatz, and field-theoretical considerations. In a large region of the parameter space, we identify a magnetized ferroquadrupolar Luttinger liquid consisting of a quasicondensate of bound magnon pairs. This liquid undergoes a continuous pair-unbinding transition to a more conventional Luttinger liquid region obtained by polarizing the system above the Haldane gap region. This pair-unbinding transition is shown to be in the Ising universality class on top of a Luttinger liquid, leading to an effective central charge 3/2. We also revisit the nature of the partially polarized Luttinger liquid around and above the Uimin-Lai-Sutherland point. Our results confirm that this is a two-component liquid and rule out the formation of a single-component vector-chiral phase.
We study a system with spin-Peierls dimerization in next-nearest-neighbor (NNN) interaction and also the presence of nearest-neighbor (NN) interaction under a magnetic field. We predict the existence of different fractionally quantized magnetization plateaus with many interesting physical properties. The effect of the frustrating NNN interaction and the role of quantum fluctuations are also explored for different magnetization plateaus. We explain more physically the gapless state of spin spectrum for small values of the frustrating NNN interaction. The transition from commensurate gapped phase to incommensurate Luttinger liquid phase is of Mott-δ type.