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arXiv:cond-mat/0302105 · Physical review. B, Condensed matter

Interplay of quantum and thermal fluctuations in a frustrated magnet

Sergei V. Isakov, Roderich Moessner

Published Sep 10, 2003• 131 citations
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Abstract

We demonstrate the presence of an extended critical phase in the transverse field Ising magnet on the triangular lattice, in a regime where both thermal and quantum fluctuations are important. We map out a complete phase diagram by means of quantum Monte Carlo simulations, and find that the critical phase is the result of thermal fluctuations destabilising an order established by the quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions from the paramagnet on one hand and the quantum-fluctuation driven three-sublattice ordered phase on the other. Our work provides further evidence that the zero temperature quantum phase transition is in the three-dimensional XY universality class.

DOI
10.1103/physrevb.68.104409

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We demonstrate the presence of an extended critical phase in the transverse field Ising magnet on the triangular lattice, in a regime where both thermal and quantum fluctuations are important. We map out a complete phase diagram by means of quantum Monte Carlo simulations, and find that the critical phase is the result of thermal fluctuations destabilising an order established by the quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions from the paramagnet on one hand and the quantum-fluctuation driven three-sublattice ordered phase on the other. Our work provides further evidence that the zero temperature quantum phase transition is in the three-dimensional XY universality class.
We study the combined effects of fluctuations and frustration in frustrated antiferromagnets described by the spin-1/2 easy-axis XXZ model with transverse magnetic fields, and propose its promising quantum simulation with a coherently coupled binary mixture of Fermi atoms in a triangular optical lattice. We perform a cluster mean-field plus scaling analysis to show that the ground state exhibits several nontrivial magnetic phases and a spin reorientation transition caused by the quantum order-by-disorder mechanism. Moreover, we find from Monte Carlo simulations that thermal fluctuations induce an unexpected coexistence of Berezinskii-Kosterlitz-Thouless physics and long-range order in different correlators. These predictions, besides being relevant to present and future experiments on triangular antiferromagnetic materials, can be tested in the laboratory with the combination of the currently available techniques for cold atoms.
Quantum Ising model on a triangular lattice hosts a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry, and it will transit into an up-up-down (UUD) phase with C3{C}_{3}C3​ symmetry breaking upon an infinitesimal external field along the longitudinal direction, but the overall phase diagram spanned by the axes of external field and temperature remains opaque due to the lack of systematic investigations with controlled methodologies. By means of quantum Monte Carlo at finite temperature and ground state density matrix renormalization group simulations, we map out the phase diagram of triangular quantum Ising model. Starting from the upper BKT temperature at zero field, we obtain the phase boundary between the UUD and paramagnetic phases with its 2D q=3q=3q=3 Potts universality at weak field and weakly first order transition at strong field. Originated from the lower BKT temperature at zero field, we analyze the low temperature phase boundary between the clock phase and the UUD phase with Ising symmetry breaking at weak fields and the quantum phase transition between the UUD and fully polarized phases at strong fields. The accurate many-body numerical results are consistent with our field theoretical analysis. The experimental relevance towards the BKT magnet TmMgGaO4{\mathrm{TmMgGaO}}_{4}TmMgGaO4​ and programmable quantum simulators are also discussed.
We study the antiferromagnetic {\it XY} model on a triangular lattice by extensive Monte Carlo simulations, focusing on its ordering and critical properties. Our result clearly shows that two separate transitions occur at two distinct temperatures, the one at a higher temperature is associated with a Z2Z_2Z2​-symmetry breaking driven by the chirality, and the one at a lower temperature is associated with the onset of the quasi-long-range order of the {\it XY} spin. We carefully examine the critical properties of each transition to find that the criticality of the chiral transition is consistent with the standard two-dimensional Ising universality class, whereas that of the spin transition might differ from the conventional Kosterlitz-Thouless (KT) one. The observed non-KT nature of the spin criticality is consistent with the most recent simulation result on the fully-frustrated {\it XY} model on a square lattice.
The frustrated antiferromagnetic XY model on the triangular lattice is a simple model describing the critical phenomena of magnetic systems. By using the Monte Carlo simulation method associated with the Metropolis algorithm, we investigate phase transitions of the system at critical temperatures and near critical temperatures. To achieve a scaling form of important parameters, the finite size effect must be taken into account. Our results show clearly that the broken symmetries of the system occur at two separate critical temperatures, the Kosterlitz-Thouless temperature and the Ising-like temperature (TI). However these temperatures lie close to each other about 0.6% compared with the lower temperature. At TI, the reflection symmetry breaking transition occurs and it is known as the Ising-like transition. While at the lower temperature, the rotational symmetry breaking transition occurs and it is known as the Kosterlitz-Thouless transition. Moreover, we found the asymptotic behavior of the correlation length of the Ising-like transition with the critical exponent, ν = 0.74. Taken into account the finite size effect, this value approaches 0.83 which differs from the value, ν = 1, for the Ising universality class. It is likely that the Ising-like transition may not belong to the Ising universality class. Also the other parameters such as the energy of the system, the order parameters, the specific heat, the magnetic susceptibility and the correlation functions have been calculated and their properties near the critical temperatures and at the critical temperatures have been studied.
We present results of extensive quantum Monte Carlo simulations of the three-dimensional S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature ${T}_{\mathrm{c}}/J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.946\ifmmode\pm\else\textpm\fi{}0.001$. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuations at a continuous Tc>0{T}_{\mathrm{c}}>0Tc​>0 phase transition.
We consider the finite-temperature phase diagram of the S=1/2 frustrated Heisenberg bilayer. Although this two-dimensional system may show magnetic order only at zero temperature, we demonstrate the presence of a line of finite-temperature critical points related to the line of first-order transitions between the dimer-singlet and -triplet regimes. We show by high-precision quantum Monte Carlo simulations, which are sign-free in the fully frustrated limit, that this critical point is in the Ising universality class. At zero temperature, the continuous transition between the ordered bilayer and the dimer-singlet state terminates on the first-order line, giving a quantum critical end point, and we use tensor-network calculations to follow the first-order discontinuities in its vicinity.