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arXiv:1610.08741 · Physical review. B./Physical review. B

Field-induced quantum phases in a frustrated spin-dimer model: A sign-problem-free quantum Monte Carlo study

Kwai-Kong Ng, Min-Fong Yang

Published Feb 28, 2017• 22 citations
arXivHTMLPDF

Abstract

The magnetization process of a frustrated spin-1/2 spin-dimer model on a square lattice is investigated by means of a sign-problem-free quantum Monte Carlo algorithm developed recently. Rich field-induced quantum phases are discovered. We find two spin superfluids satisfying different symmetries upon layer permutation. There exist as well two solid phases with distinct checkerboard patterns. More interestingly, a spin supersolid phase possessing both solid and superfluid long-range orders is observed over a finite regime of magnetic fields. We find that this exotic phase can be stabilized only when small but nonzero spin anisotropy is present. Various field-induced transitions among these phases are explored. Our findings may provide guidance to the search of these interesting quantum phases in real frustrated spin-dimer compounds.

DOI
10.1103/physrevb.95.064431

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The magnetization process of a frustrated spin-1/2 spin-dimer model on a square lattice is investigated by means of a sign-problem-free quantum Monte Carlo algorithm developed recently. Rich field-induced quantum phases are discovered. We find two spin superfluids satisfying different symmetries upon layer permutation. There exist as well two solid phases with distinct checkerboard patterns. More interestingly, a spin supersolid phase possessing both solid and superfluid long-range orders is observed over a finite regime of magnetic fields. We find that this exotic phase can be stabilized only when small but nonzero spin anisotropy is present. Various field-induced transitions among these phases are explored. Our findings may provide guidance to the search of these interesting quantum phases in real frustrated spin-dimer compounds.
Using the quantum Monte Carlo method, we study, under external magnetic fields, the ground state phase diagram of the two-dimensional spin S=1/2 dimer model with an anisotropic intraplane antiferromagnetic coupling. With the anisotropy 4 greater/approximately Delta greater/approximately 3, a supersolid phase characterized by a nonuniform Bose condensate density that breaks translational symmetry is found. The rich phase diagram also contains a checkerboard solid, an antiferromagnet in the z axis, and a superfluid phase formed by S(z)= +1 spin triplets which has a finite staggered magnetization in the in-plane direction. As we show, the model can be realized as a consequence of including the next nearest neighbor coupling among dimers and our results suggest that spin dimer systems may be an ideal model system to study the supersolid phase.
Abstract In recent years, spin-1/2 dimerized antiferromagnets have become a remarkable subject since rich eld-induced quantum phases can appear. In this work, we study second order quantum phase transition caculated by this combined algorithm of the innite timeevolving block decimation method and tensor renormalization group approach. By applying an enough magnetic eld, a spin superuid phase is observed. Moreover, a supersolid phase is also observed in small regime of magnetic eld. We will show the full phase diagrams in various weaker frustrating interlayer interaction.
The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.
This work focuses on numerical studies of quantum spin systems. These simple models are known to exhibit a variety of phases, some of which have no classical counterpart. Phase transitions between them are driven by quantum fluctuations and the unconventional nature of some such transitions make them a fascinating avenue of study. Quantum Monte Carlo (QMC) is an indispensable tool in the study of these phases and phase transitions in two and higher dimensions. Nevertheless, we are limited by our inability to simulate models that suffer from the infamous sign problem. While the case of S=1/2 has been studied extensively due to availability of sign problem free models, not much progress has been made for higher S. In a first part of this dissertation, a systematic procedure to write down a large family of ``designer hamiltonians'', i.e. models constructed to be free from the sign problem (``de-signed''), for arbitrary spin-S is given. Three applications of this procedure are also presented. As a first application, a S=1 interaction is constructed on the square lattice realizing a novel ``Haldane Nematic (HN)'' phase that breaks the lattice rotational symmetry while preserving lattice translational symmetry and spin rotational symmetry. By supplementing our model with a two-spin Heisenberg interaction, a study of the transition between the antiferromagnetic and HN phase is presented, which we find to be of first order. In a second application, the antiferromagnetic to four-fold columnar valence bond solid (cVBS) phase transition in a sign free S=1 square lattice model is studied. Our simulations provide unambiguous evidence for a direct conventional first-order quantum phase transition demonstrating a sharp contrast with the S=1/2 case, where this transition is a prototypical example of an unconventional continuous transition. In our third application, all possible sign-free two-site spin-S interactions are constructed and the phases that are realized by these new nearest neighbour models are investigated on the square lattice. In a second part, the superfluid-VBS quantum phase transition is studied in a spin model in presence of easy plane anisotropy, i.e. spins preferentially align in a plane. The model studied is an interpolation of two models: (a) a rotationally symmetric model that appears to host a continuous transition even on the biggest lattices studied (b) the other is an easy plane version of the aforementioned model that clearly shows a first order transition even on relatively small lattices. In our simulations, the nature of the transition was found to be first order in the presence of an easy plane anisotropy, indicating the superfluid-VBS transition in the two-component easy plane model is generically discontinuous. In a third part, we study the SU(N) generalization of the Heisenberg antiferromagnet on the BCC lattice. Our numerical studies of the model show that magnetic order present for N=2 is destroyed for N>15 and valence bond solid order is observed for N>16. The nature of the phase at N=16 and the nature of the phase transition between different phases is investigated.
The frustrated magnet $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is one of the prime candidates for realizing a Kitaev quantum spin liquid (QSL). However, the existence of a field-induced intermediate QSL phase in this material remains under debate. Here, we employ sign-free numerically exact quantum Monte Carlo simulations to investigate the Kitaev-Heisenberg (KH) model on the honeycomb lattice with $K=\ensuremath{-}2J$ under an applied magnetic field along the zzz direction. Our findings reveal that the system undergoes a direct quantum phase transition from a zigzag magnetically ordered phase to a spin-polarized phase at zero temperature, which belongs to the 3D XY universality class. At finite temperatures, a Berezinskii-Kosterlitz-Thouless transition line separates the spin-polarized phase from a quasi-long-range ordered state, eventually terminating at the quantum critical point. Our results convincingly show that there is no intermediate QSL phase in the KH model with a zzz-direction magnetic field, which we believe will shed important light on understanding experimental observations in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.