In this paper, we propose a method to understand the nature of the quantum disorder phase of the two-dimensional (2D) high-spin frustrated model. The ground state and excitation properties of a fully frustrated 2D spin-1 model are studied based on a model whose ground state can be found exactly. By analogy to the pseudopotential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valence-bond solid (VBS) states along the horizontal or vertical direction of the square lattice. We also find that the ground state could be characterized by a nonzero string order, which rarely happened in the 2D case. The method that we used reveals the connection between the fractional quantum Hall effect and the frustrated 2D antiferromagnetism system. The VBS states capture the main character of the disordered phase in the 2D spin-1 frustrated system and can be verified by a numerical method.In this paper, we propose a method to understand the nature of the quantum disorder phase of the two-dimensional (2D) high-spin frustrated model. The ground state and excitation properties of a fully frustrated 2D spin-1 model are studied based on a model whose ground state can be found exactly. By analogy to the pseudopotential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valence-bond solid (VBS) states along the horizontal or vertical direction of the square lattice. We also find that the ground state could be characterized by a nonzero string order, which rarely happened in the 2D case. The method that we used reveals the connection between the fractional quantum Hall effect and the frustrated 2D antiferromagnetism system. The VBS states capture the main character of the disordered phase in the 2D spin-1 frustrated system and can be verified by a numerical method.

arXiv:cond-mat/0611170Physical Review BAug 24, 20076 citations

Towards quantum simulation of spin dynamics in frustrated systems

Ippei Nakamura, Ryuta Yamamoto, Takeshi Fukuhara

Bulletin of the American Physical SocietyMay 29, 20180 citations

Critical exponents of the fully frustrated two-dimensionalXYmodel

Guillermo Ramı́rez-Santiago, Jorge V. José

We present a detailed study of the critical properties of the two-dimensional (2D) XY model with maximal frustration in a square lattice. We use extensive Monte Carlo simulations to study the thermodynamics of the spin and chiral degrees of freedom, concentrating on their correlation functions. The gauge-invariant spin-spin correlation functions are calculated close to the critical point for lattice sizes up to 240\ifmmode\times\else\texttimes\fi{}240; the chiral correlation functions are studied on lattices up to 96\ifmmode\times\else\texttimes\fi{}96. We find that the critical exponents of the spin-phase transition are \ensuremath{\nu}=0.3069 and \ensuremath{\eta}=0.1915, which are to be compared with the unfrustrated XY model exponents \ensuremath{\nu}=1/2 and \ensuremath{\eta}=0.25. We also find that the critical exponents of the chiral transition are ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\chi}}}$=0.875, 2\ensuremath{\beta}=0.1936, 2\ensuremath{\gamma}=1.82, and 2\ensuremath{\gamma}'=1.025, which are different from the expected 2D Ising critical exponents. The spin-phase transition occurs at ${\mathit{T}}_{\mathit{U}(1)}$ =0.446, which is about 7% above the estimated chiral critical temperature ${\mathit{T}}_{\mathit{Z}2}$ =0.4206. However, because of the size of the statistical errors, it is difficult to decide with certainty whether the transitions occur at the same or at slightly different temperatures. Finally, the jump in the helicity modulus in the fully frustrated system is found to be about 23% below the unfrustrated universal value. The most important consequence of these results is that the fully frustrated XY model appears to be in a novel universality class. Recent successful comparisons of some of these results with experimental data are also briefly discussed.We present a detailed study of the critical properties of the two-dimensional (2D) XY model with maximal frustration in a square lattice. We use extensive Monte Carlo simulations to study the thermodynamics of the spin and chiral degrees of freedom, concentrating on their correlation functions. The gauge-invariant spin-spin correlation functions are calculated close to the critical point for lattice sizes up to 240\ifmmode\times\else\texttimes\fi{}240; the chiral correlation functions are studied on lattices up to 96\ifmmode\times\else\texttimes\fi{}96. We find that the critical exponents of the spin-phase transition are \ensuremath{\nu}=0.3069 and \ensuremath{\eta}=0.1915, which are to be compared with the unfrustrated XY model exponents \ensuremath{\nu}=1/2 and \ensuremath{\eta}=0.25. We also find that the critical exponents of the chiral transition are ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\chi}}}$=0.875, 2\ensuremath{\beta}=0.1936, 2\ensuremath{\gamma}=1.82, and 2\ensuremath{\gamma}'=1.025, which are different from the expected 2D Ising critical exponents. The spin-phase transition occurs at ${\mathit{T}}_{\mathit{U}(1)}$=0.446, which is about 7% above the estimated chiral critical temperature ${\mathit{T}}_{\mathit{Z}2}$=0.4206. However, because of the size of the statistical errors, it is difficult to decide with certainty whether the transitions occur at the same or at slightly different temperatures. Finally, the jump in the helicity modulus in the fully frustrated system is found to be about 23% below the unfrustrated universal value. The most important consequence of these results is that the fully frustrated XY model appears to be in a novel universality class. Recent successful comparisons of some of these results with experimental data are also briefly discussed.

arXiv:cond-mat/9402100Physical review. B, Condensed matterApr 1, 199487 citations

Numerical Experiments on Frustrated Quantum Spin Systems

Sanzo Miyazawa, M. S. Makivić, T. Horiki +1 more

Springer proceedings in physicsJan 1, 19920 citations

Finite temperature numerical simulations of frustrated spin systems

Cynthia J. Olson, Gergely Zaránd, Gergely T. Zimányi

APSMar 1, 20000 citations

Observing frustrated quantum magnetism in two-dimensional ion crystals

Mu Qiao, Zhengyang Cai, Ye Wang +10 more

Two-dimensional (2D) quantum magnetism is a paradigm in strongly correlated many-body physics. The understanding of 2D quantum magnetism can be expedited by employing a controllable quantum simulator that faithfully maps 2D-spin Hamiltonians. The 2D quantum simulators can exhibit exotic phenomena such as frustrated quantum magnetism and topological order and can be used to show quantum computational advantages. Many experimental platforms are being developed, including Rydberg atoms and superconducting annealers. However, with trapped-ion systems, which showed the most advanced controllability and quantum coherence, quantum magnetism was explored in one-dimensional chains. Here, we report simulations of frustrated quantum magnetism with 2D ion crystals. We create a variety of spin-spin interactions for quantum magnets, including those that exhibit frustration by driving different vibrational modes and adiabatically prepare the corresponding ground states. The experimentally measured ground states are consistent with the theoretical predictions and are highly degenerate for geometrically frustrated spin models in two dimensions. Quantum coherence of the ground states is probed by reversing the time evolution of the B-field to the initial value and then measuring the extent to which the remaining state coincides with the initial state. Our results open the door for quantum simulations with 2D ion crystals.Two-dimensional (2D) quantum magnetism is a paradigm in strongly correlated many-body physics. The understanding of 2D quantum magnetism can be expedited by employing a controllable quantum simulator that faithfully maps 2D-spin Hamiltonians. The 2D quantum simulators can exhibit exotic phenomena such as frustrated quantum magnetism and topological order and can be used to show quantum computational advantages. Many experimental platforms are being developed, including Rydberg atoms and superconducting annealers. However, with trapped-ion systems, which showed the most advanced controllability and quantum coherence, quantum magnetism was explored in one-dimensional chains. Here, we report simulations of frustrated quantum magnetism with 2D ion crystals. We create a variety of spin-spin interactions for quantum magnets, including those that exhibit frustration by driving different vibrational modes and adiabatically prepare the corresponding ground states. The experimentally measured ground states are consistent with the theoretical predictions and are highly degenerate for geometrically frustrated spin models in two dimensions. Quantum coherence of the ground states is probed by reversing the time evolution of the B-field to the initial value and then measuring the extent to which the remaining state coincides with the initial state. Our results open the door for quantum simulations with 2D ion crystals.

arXiv:2204.07283Apr 15, 20221 citation

{\mathit{T}}_{\mathit{U}(1)}

=0.446, which is about 7% above the estimated chiral critical temperature

{\mathit{T}}_{\mathit{Z}2}

=0.4206. However, because of the size of the statistical errors, it is difficult to decide with certainty whether the transitions occur at the same or at slightly different temperatures. Finally, the jump in the helicity modulus in the fully frustrated system is found to be about 23% below the unfrustrated universal value. The most important consequence of these results is that the fully frustrated XY model appears to be in a novel universality class. Recent successful comparisons of some of these results with experimental data are also briefly discussed.