Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice

Emonts, Patrick; Wessel, Stefan

doi:10.1103/physrevb.98.174433

Cited by 10 publications

(12 citation statements)

References 33 publications

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“…Thus spin-active non-Kramers systems can arise from two nearby non-degenerate states well separated from the rest, or, from a lattice-symmetry protected dou- blet ground state which will be split by impurities. These systems can be modelled by random-transverse field Ising models [27][28][29][30][31][32]. Indeed the material Pr 2 Zr 2 O 7 is a realization of this model [33].…”

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confidence: 99%

“…We also find that the confining phase [32] The data is for 16 and 32-site clusters and 4 th and 5 th order NLC. The vertical black lines denote the transition point [30,31] between QSL and the paramagnetic phase. NLC does not converge within the QSL phase, and for this reason NLC results are not shown for small h values.…”

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confidence: 99%

“…The ED results for 16− and 32−site clusters are also shown. In the thermodynamic limit, there may be a small discontinuity at the transition [30,31], but finite size effects are small in the paramagnetic phase right down to the transition. This first order transition point from previous studies [30,31] is indicated by the vertical black lines.…”

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confidence: 99%

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Local entanglement and confinement transitions in the random transverse-field Ising model on the pyrochlore lattice

et al. 2019

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We use Numerical Linked Cluster Expansions (NLC) and Exact Diagonalization (ED) to study confinement transitions out of the Quantum Spin Liquid (QSL) phase in the pyrochlore-lattice Ising antiferromagnet with random transverse fields. We calculate entanglement entropies associated with local regions defined by single tetrahedra to observe these transitions. The randomness-induced confinement transition is marked by a sharp reduction in the local entanglement and a concomitant increase in Ising correlations. In NLC, it is studied through the destruction of loop resonances due to random transverse-fields. The confining phase is characterized by a distribution of local entanglement entropies, which persists to large random fields.

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Local entanglement and confinement transitions in the random transverse-field Ising model on the pyrochlore lattice

et al. 2019

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“…1, where the enlarged dimer basis gives a fully sign-free problem, and the same situation arises in our current trimer-based model. Second, enlarged bases can also assist calculations for sign-free models that nevertheless pose a challenge to the efficiency of SSE QMC updates because of high energy barriers, as encountered in the case of Ising-type frustration [51][52][53][54][55]. Third, changes of basis can make observables that are very difficult to compute in one basis readily accessible in another; we will meet an example of this in Sec.…”

Section: Arbitrary-basis Qmcmentioning

confidence: 99%

Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets

et al. 2022

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The phase diagrams of highly frustrated quantum spin systems can exhibit first-order quantum phase transitions and thermal critical points even in the absence of any long-ranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loop-update scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin-1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spin-trimer basis are sign-problem-free when the intertrimer couplings are fully frustrated. This model features a first-order quantum phase transition, from which a line of first-order transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the first-order line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime.

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“…The transverse field Ising magnet (TFIM) is now the archetypal example of a system displaying a quantum phase transition [5]. Its widespread use relies on the fact that the application of a transverse field is a simple -and controllable -way to introduce quantum dynamics in an otherwise classical (Ising) system [6], [7]. It is a customary tool in many relevant topics like quantum magnetism [8], [9], or novel topological excitations [10], but also for understanding materials with unconventional properties, such as heavy fermion systems [11] and high-temperature superconductors [12].…”

Section: Introductionmentioning

confidence: 99%

BiMnTeO6 : A multiaxis Ising antiferromagnet

et al. 2019

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The crystal and magnetic properties of honeycomb BiMnTeO 6 have been studied between 1.5 K and 300 K using synchrotron X-rays and neutron scattering experiments. Commensurate magnetic ordering is observed below T N = 10 K, and corresponds to a non collinear spin arrangement, with spins tilted away from the anisotropy easy-axis set by the Jahn-Teller distortion of the MnO 6 octahedra. Inelastic scattering experiments show two main nearly localised magnetic excitations, which can be well described by an exchange Hamiltonian involving weak Mn-Mn magnetic interactions and a crystal field Hamiltonian characterizing the strong easy-axis anisotropy associated with the d z2 orbital ordering of Mn 3+ . The crystal field levels can be accurately calculated, taking into account a transverse molecular field imposed by the magnetic ordering of the neighbouring atoms below T N . This makes of BiMnTeO 6 an interesting example of a multi-axis Ising system in a self-imposed transverse magnetic field.

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Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice

Cited by 10 publications

References 33 publications

Local entanglement and confinement transitions in the random transverse-field Ising model on the pyrochlore lattice

Local entanglement and confinement transitions in the random transverse-field Ising model on the pyrochlore lattice

Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets

BiMnTeO6 : A multiaxis Ising antiferromagnet

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