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Vietnam Journal of Science and Technology/Science and Technology

THE PHYSICS OF SPIN-1/2 XY MODEL WITH FOUR-SITE EXCHANGE INTERACTION ON THE KAGOME LATTICE

Nguyễn Thị Kim Ánh

Published Mar 16, 2018• 0 citations
Publisher

Abstract

The quantum spin liquid (QSL) state, proposed more than three decades ago by Fazekas and Anderson remains surprisingly elusive. Although recent experiments provide a strong evidence of their existence in the frustrated spin systems, the microscopic model for this state is still rare. The extensive theoretical framework, developed over decades, continues to extend further motivated by these and other discoveries from large-scale computer simulations of a relatively small number of models. In this work, we discuss the physics of the ground-state phase diagram of a two-dimensional Kagome lattice spin-1/2 XY model with a four-site ring-exchange interaction using quantum Monte Carlo simulation. We found the second order phase transition from superfluid state to a Z2 quantum spin liquid phase driven by the four-site ring exchange interaction. We have characterized the QSL by its vanishing order parameters such as the spin-spin structure factor, the plaquette-plaquette structure factor. Moreover, we have found the large anomalous exponent ηXY* ≈ 1.325 which belongs to a different universality class other than 3D XY universality class. There is no signal of supersolid phase intervening between the superfluid state and QSL state.

DOI
10.15625/2525-2518/54/1a/11801

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The quantum spin liquid (QSL) state, proposed more than three decades ago by Fazekas and Anderson remains surprisingly elusive. Although recent experiments provide a strong evidence of their existence in the frustrated spin systems, the microscopic model for this state is still rare. The extensive theoretical framework, developed over decades, continues to extend further motivated by these and other discoveries from large-scale computer simulations of a relatively small number of models. In this work, we discuss the physics of the ground-state phase diagram of a two-dimensional Kagome lattice spin-1/2 XY model with a four-site ring-exchange interaction using quantum Monte Carlo simulation. We found the second order phase transition from superfluid state to a Z2 quantum spin liquid phase driven by the four-site ring exchange interaction. We have characterized the QSL by its vanishing order parameters such as the spin-spin structure factor, the plaquette-plaquette structure factor. Moreover, we have found the large anomalous exponent ηXY* ≈ 1.325 which belongs to a different universality class other than 3D XY universality class. There is no signal of supersolid phase intervening between the superfluid state and QSL state.
We study the ground-state phase diagram of a two-dimensional kagome-lattice spin-1/2 XYXYXY model (JJJ) with a four-site ring-exchange interaction (KKK) using quantum Monte Carlo simulations. We find that the superfluid phase, existing in the regime of small ring exchange, undergoes a direct transition to a Z2{\mathbb{Z}}_{2}Z2​ quantum spin liquid phase at ${(K/J)}_{c}\ensuremath{\approx}22$, which is related to the phase proposed by L. Balents, M. P. A. Fisher, and S. M. Girvin [Phys. Rev. B 65, 224412 (2002)]. The quantum phase transition between the superfluid and the spin liquid phase has exponents zzz and $\ensuremath{\nu}$ falling in the three-dimensional XYXYXY universality class, making it a candidate for an exotic XYXYXY* quantum critical point, mediated by the condensation of bosonic spinons.
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By means of quantum Monte Carlo simulations, combined with a stochastic analytic continuation, we examine the spin dynamics of the spin-1/2 planar (XYXYXY) ferromagnet on the kagome lattice with additional four-site ring exchange terms. Such exchange processes were previously considered to lead into an extended Z2{Z}_{2}Z2​ quantum spin liquid phase beyond a quantum critical point from the XYXYXY ferromagnet. We examine the dynamical spin structure factor in the nonmagnetic regime and probe for signatures of spin fractionalization. Furthermore, we contrast our findings and the corresponding energy scales of the excitation gaps in the ring exchange model to those emerging in a related Balents-Fisher-Girvin model with a Z2{Z}_{2}Z2​ quantum spin liquid phase, and monitor the softening of the magnon mode upon approaching the quantum critical point from the XYXYXY-ferromagnetic regime.
Abstract Spin-1/2 kagome antiferromagnets are leading candidates for realizing quantum spin liquid (QSL) ground states. While QSL ground states are predicted for the pure Heisenberg model, understanding the robustness of the QSL to additional interactions that may be present in real materials is a forefront question in the field. Here we employ large-scale density-matrix renormalization group simulations to investigate the effects of next-nearest neighbor exchange couplings J 2 and Dzyaloshinskii-Moriya interactions D , which are relevant to understanding the prototypical kagome materials herbertsmithite and Zn-barlowite. By utilizing clusters as large as XC12 and extrapolating the results to the thermodynamic limit, we precisely delineate the scope of the QSL phase, which remains robust across an expanded parameter range of J 2 and D . Direct comparison of the simulated static and dynamic spin structure factors with inelastic neutron scattering reveals the parameter space of the Hamiltonians for herbertsmithite and Zn-barlowite, and, importantly, provides compelling evidence that both materials exist within the QSL phase. These results establish a powerful convergence of theory and experiment in this most elusive state of matter.
We present the zero-temperature phase diagram of a square lattice quantum spin-1/2 XY\mathrm{XY}XY model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the XY\mathrm{XY}XY order, striped or valence bond solid, staggered N\'eel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.
Quantum Fisher information (QFI) is a measure of multipartite quantum entanglement that can be obtained from inelastic neutron scattering data on quantum magnets. In this work, we demonstrate that the QFI can distinguish an unconventional quantum critical point (QCP) with fractionalization and emergent gauge structure from conventional ones within the Landau paradigm. We compute the QFI, via large-scale quantum Monte Carlo (QMC) simulations and exact diagonalization, in a kagome lattice quantum spin liquid (QSL) model with an XY and a cluster-Ising interactions. When the XY interaction is ferromagetic, the QFI obtained by QMC reveals a large anomalous dimension, which is a fingerprint of the (2+1)d XY∗^\ast∗ universality class for the transition from the ferromagnetic phase to the Z2\mathbb{Z}_2Z2​ QSL. The investigation of thermal and dynamical properties of QFI is further extended to the case of antiferromagnetic XY interaction via exact diagonalization. In this regime, a transition to a possibly distinct QSL phase is suggested via both entanglement-based probes, such as QFI and genuine multipartite negativity, and analyses of the energy spectrum and structure factors. These results not only demonstrate the versatility of QFI in identifying QSL states and unconventional QCPs but also provide useful guidance for future theoretical and experimental studies of frustrated magnets.