We study the ground-state phase diagram of a two-dimensional kagome-lattice spin-1/2 $XY$ model ( $J$ ) with a four-site ring-exchange interaction ( $K$ ) 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 ${\mathbb{Z}}_{2}$ 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 $z$ and $\ensuremath{\nu}$ falling in the three-dimensional $XY$ universality class, making it a candidate for an exotic $XY$ * quantum critical point, mediated by the condensation of bosonic spinons.We study the ground-state phase diagram of a two-dimensional kagome-lattice spin-1/2 $XY$ model ($J$) with a four-site ring-exchange interaction ($K$) 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 ${\mathbb{Z}}_{2}$ 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 $z$ and $\ensuremath{\nu}$ falling in the three-dimensional $XY$ universality class, making it a candidate for an exotic $XY$* quantum critical point, mediated by the condensation of bosonic spinons.

arXiv:1106.0761Physical Review BOct 14, 201123 citations

Spin Correlations in Quantum Spin Liquids on the Kagome Lattice

Tyler Dodds, Yong Baek Kim

Bulletin of the American Physical SocietyMar 21, 20130 citations

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

Nguyễn Thị Kim Ánh

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.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.

Vietnam Journal of Science and Technology/Science and TechnologyMar 16, 20180 citations

Multi-spin exchange model for a quantum spin liquid on the honeycomb lattice

Yifei Wang, D. N. Sheng, Chang-De Gong

Bulletin of the American Physical SocietyMar 25, 20110 citations

Breathing kagome XY quantum magnet with four-site ring exchange

Niklas Casper, Wolfram Brenig

We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin- $1/2$ ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a ${\mathbb{Z}}_{2}$ quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua.We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-$1/2$ ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a ${\mathbb{Z}}_{2}$ quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua.

arXiv:2010.00014Physical review. B./Physical review. BMar 22, 20210 citations

We study the ground-state phase diagram of a two-dimensional kagome-lattice spin-1/2

XY

model (

J

) with a four-site ring-exchange interaction (

K

) 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

{\mathbb{Z}}_{2}

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

z

and $\ensuremath{\nu}$ falling in the three-dimensional

XY

universality class, making it a candidate for an exotic

XY

* quantum critical point, mediated by the condensation of bosonic spinons.

We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-

1/2

ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a

{\mathbb{Z}}_{2}

quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua.