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Annalen der Physik

Magnetic Phase Transition Driven by Frustrated Interactions in a Longitudinal‐Field Ising Chain

Yan‐Li Zhou

Published Aug 13, 2018• 0 citations
Publisher

Abstract

Abstract The ground‐state magnetic phase transitions in a classical spin chain with long‐range interactions in a system of trapped ions are investigated. The tunable competing interactions, mediated by both longitudinal and transverse photon modes, lead to competition among different spins, due to which magnetic frustration occurs. Various ground‐state spin configurations are separated by multiple phase transitions when the strength and sign of these interactions are tuned continuously. The spin chains are highly degenerated because of the frustration, so there is some melting of several magnetic phases.

DOI
10.1002/andp.201800072

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Abstract The ground‐state magnetic phase transitions in a classical spin chain with long‐range interactions in a system of trapped ions are investigated. The tunable competing interactions, mediated by both longitudinal and transverse photon modes, lead to competition among different spins, due to which magnetic frustration occurs. Various ground‐state spin configurations are separated by multiple phase transitions when the strength and sign of these interactions are tuned continuously. The spin chains are highly degenerated because of the frustration, so there is some melting of several magnetic phases.
We present a scheme of quantum simulation of many-body interactions with trapped ions via the exchange of virtual phonons, where the motion from both the longitudinal and the transverse directions is considered. By tuning the detunings of Raman lasers, the long-range and locally tunable interaction is easily obtained between different spins. We show that the competing spin-spin couplings mediated by all motion modes can give rise to higher levels of frustration and richer phase transitions than the conventional approaches based on the longitudinal or the transverse phonon modes alone.
We show that a trapped-ion chain interacting with an optical spin-dependent force shows strong frustration effects due to the interplay between long range interactions and the dressing by optical phases. We consider a strong spin-phonon coupling regime and predict a quantum phase diagram with different competing magnetic and structural orders. In a highly frustrated region, the system shows enhanced quantum fluctuations and entanglement, which are characteristic of spin-liquid phases. We propose and describe within a mean-field approach a quantum annealing process to induce a quasiadiabatic evolution towards the ground state.
Abstract In this paper we study an Ising spin chain with short-range competing interactions in the presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic-phase diagram. We compare our results with the limit in which one of two local interactions is turned off, which was previously studied in the literature. Eight regions of parameters with qualitatively distinct properties are featured, with different first- and second-order phase transition lines and critical points.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.
We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Because of the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil's staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems.
The ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed into the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg–Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the ‘classical’ Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal–transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of a two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin–spin correlations.