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arXiv:1012.4518 · Physical Review B

Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field

Salvatore R. Manmana, Andreas Martin Läuchli, Fabian H. L. Eßler, Frédéric Mila

Published May 31, 2011• 46 citations
arXivHTMLPDF

Abstract

We investigate the properties of the Heisenberg $S=1$ 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.

DOI
10.1103/physrevb.83.184433

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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 investigate the effect of a single-ion anisotropy on the bilinear-biquadratic spin-1 J1-J2 chain, focusing on the quantum phase transitions out of the trimerized phase. Using large-scale density matrix renormalization group simulations, we uncover a rich phase diagram comprising five gapped phases and, remarkably, two critical floating phases. These incommensurate Luttinger liquid phases emerge from the proliferation of non-magnetic domains - 0-states and dimers - within a trimerized background and are confined to the zero magnetization sector, while magnetic excitations remain gapped. We show that the transition between the topological Haldane phase and the floating phases are governed by a composite critical line with central charge c=2, consistent with a coexistence of magnetic and non-magnetic critical modes. Our results shed new light on the long-standing problem of the Haldane-trimerized transition.
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.
We study the zero-temperature properties of a spin-1/21/21/2 Heisenberg chain with an additional three-site chiral term of strength ggg. The model is known to be integrable and previous work using Bethe ansatz has identified a phase transition from the usual critical state for g<gc=2/πg< g_c = 2/πg<gc​=2/π to a chiral phase for g>gcg>g_cg>gc​. Here we combine analytical and computational approaches to demonstrate that the transition point comprises an unusual Lifshitz transition with dynamical critical exponent z=3z=3z=3, and the chiral phase is a partially spin-polarized phase which spontaneously breaks SU(2) symmetry. We derive a strongly interacting chiral boson field theory for the critical point, and show that even its small-momentum, low-energy response is non-trivial. We also determine the universal properties of the chiral phase, and specifically show that it has a simultaneous quadratically dispersing ferromagnetic "magnon" mode coexisting with the power-law singularities and linearly dispersing excitations typical of a Luttinger liquid. Our conclusions are validated using numerics based on matrix product state methods and exact diagonalization.
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The ground state phase diagrams and thermodynamic properties of a spin-1 bond-alternating Heisenberg antiferromagnetic chain with a single-ion anisotropy in longitudinal and transverse magnetic fields are investigated jointly by means of the infinite time evolving block decimation, the linearized tensor renormalization group, and the density matrix renormalization group methods. It is found that in the magnetic field--bond alternating ratio plane six phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2 magnetization plateau, and spin-polarized phases are identified in a longitudinal field, while in a transverse field there are five phases including singlet dimer, Haldane, Z2{Z}_{2}Z2​ symmetry breaking, quasi-1/2 magnetization plateau, and quasi-spin-polarized phases. A reentrant behavior of the staggered magnetization in a transverse field is observed. The quantum critical behaviors in longitudinal and transverse magnetic fields are disclosed to fall into different universality classes with corresponding conformal field central charge c=1c=1c=1 and 1/21/21/2, respectively. The experimental data of the compound NTENP under both longitudinal and transverse magnetic fields are nicely fitted, and the Luttinger liquid behavior of low-temperature specific heat experimentally observed is also confirmed.
We investigate spin chains with bilinear-biquadratic (BLBQ) spin interactions as a function of an applied magnetic field hhh. At the Uimin-Lai-Sutherland (ULS) critical point we find a gapless to gapless transition revealed by the dynamical structure factor $S(q,\ensuremath{\omega})$ as a function of hhh. At h=0h=0h=0, the envelope of the lowest-energy excitations goes soft at two points, ${q}_{1}=2\ensuremath{\pi}/3$ and ${q}_{2}=4\ensuremath{\pi}/3$, dubbed the phase A. With increasing field, the spectral peaks at each of the gapless points bifurcate, making in total four soft modes, and combine to form a new set of excitations that soften at a single point $q=\ensuremath{\pi}$ at ${h}_{c1}\ensuremath{\approx}0.94$. Beyond hc1{h}_{c1}hc1​ the system enters another gapless B phase until the transition at hc2=4{h}_{c2}=4hc2​=4 to the fully polarized phase. We compare the ULS model results with those for the Affleck-Kennedy-Lieb-Tasaki model as a representative of the gapped Haldane phase. We explain the mechanism of the gapless to gapless transition in the ULS model using its conserved charges and a spinon band picture. We also discuss the universality of central charges of the BLBQ family of models subjected to a magnetic field.