We study the effect of coupling a spin-bath environment to a system which, at low energies, can be modeled as a quantum Ising system. A field theoretic formalism incorporating both thermal and quantum fluctuations is developed to derive results for the thermodynamic properties and response functions, both for a toy model and for the ${\text{LiHoF}}_{4}$ system, in which spin-8 electronic spins couple to a spin- $7/2$ nuclear spin bath: The phase transition then occurs in a system of electronuclear degrees of freedom, coupled by long-range dipolar interactions. The quantum Ising phase transition still exists, and one hybridized mode of the Ising and bath spins always goes soft at the transition.We study the effect of coupling a spin-bath environment to a system which, at low energies, can be modeled as a quantum Ising system. A field theoretic formalism incorporating both thermal and quantum fluctuations is developed to derive results for the thermodynamic properties and response functions, both for a toy model and for the ${\text{LiHoF}}_{4}$ system, in which spin-8 electronic spins couple to a spin-$7/2$ nuclear spin bath: The phase transition then occurs in a system of electronuclear degrees of freedom, coupled by long-range dipolar interactions. The quantum Ising phase transition still exists, and one hybridized mode of the Ising and bath spins always goes soft at the transition.

arXiv:1711.05438Physical review. B./Physical review. BJun 26, 201819 citations

Dynamical quantum phase transitions in presence of a spin bath

Álvaro Gómez-León, Philip C. E. Stamp

We derive an effective time independent Hamiltonian for the transverse Ising model coupled to a spin bath, in the presence of a high frequency AC magnetic field. The spin blocking mechanism that removes the quantum phase transition can be suppressed by the AC field, allowing tunability of the quantum critical point. We calculate the phase diagram, including the nuclear spins, and apply the results to quantum Ising systems with long-range dipolar interactions; the example of ${\text{LiHoF}}_{4}$ is discussed in detail.We derive an effective time independent Hamiltonian for the transverse Ising model coupled to a spin bath, in the presence of a high frequency AC magnetic field. The spin blocking mechanism that removes the quantum phase transition can be suppressed by the AC field, allowing tunability of the quantum critical point. We calculate the phase diagram, including the nuclear spins, and apply the results to quantum Ising systems with long-range dipolar interactions; the example of ${\text{LiHoF}}_{4}$ is discussed in detail.

arXiv:1512.08315Physical review. B./Physical review. BFeb 1, 20175 citations

Phase transitions in spin-one Ising systems

Hans W. Capel

Physics LettersOct 1, 196625 citations

Phase transition in an Ising model with many-spin interaction

Fa Yueh Wu

Physics Letters ANov 1, 19733 citations

Fluctuations and phase transitions in quantum Ising systems

R. H. McKenzie

The quantum Ising model is perhaps the simplest possible model of a quantum magnetic material. Despite its simplicity, its versatility and wide range of applications, from quantum computation, to combinatorial optimization, to biophysics, make it one of the most important models of modern physics. In this thesis, we develop a general framework for studying quantum Ising systems with an arbitrary single ion Hamiltonian, with emphasis on the effects of quantum fluctuations, and the quantum phase transition between paramagnetic and ferromagnetic states that occurs when a magnetic field is applied transverse to the easy axis of the system. The magnetic insulating crystal LiHoF₄ is a physical realization of the quantum Ising model, with the additional features that the dominant coupling between spins is the long range dipolar interaction, and each electronic spin is strongly coupled to a nuclear degree of freedom. These nuclear degrees of freedom constitute a spin bath environment acting on the system. In this thesis, we present an effective low temperature Hamiltonian for LiHoF₄ that incorporates both these features, and we analyze the effects of the nuclear spin bath on the system. We find the lowest energy crystal field excitation in the system is gapped at the quantum critical point by the presence of the nuclear spins, with spectral weight being transferred down to a lower energy electronuclear mode that fully softens to zero at the quantum critical point. Furthermore, we present a toy model, the spin half spin half model, that illustrates the effects of an anisotropic hyperfine interaction on a quantum Ising system. We find the critical transverse field is increased when the longitudinal hyperfine coupling is dominant, as well as an enhancement of both the longitudinal electronic susceptibility and an applied longitudinal field. In addition, we present a field theoretic formalism for incorporating the effects of fluctuations beyond the random phase approximation in general quantum Ising systems. We find that any regular on site interaction, such as a nuclear spin bath, does not fundamentally alter the critical properties of a quantum Ising system. This formalism is used to calculate corrections to the magnetization of LiHoF₄.The quantum Ising model is perhaps the simplest possible model of a quantum magnetic material. Despite its simplicity, its versatility and wide range of applications, from quantum computation, to combinatorial optimization, to biophysics, make it one of the most important models of modern physics. In this thesis, we develop a general framework for studying quantum Ising systems with an arbitrary single ion Hamiltonian, with emphasis on the effects of quantum fluctuations, and the quantum phase transition between paramagnetic and ferromagnetic states that occurs when a magnetic field is applied transverse to the easy axis of the system. The magnetic insulating crystal LiHoF₄ is a physical realization of the quantum Ising model, with the additional features that the dominant coupling between spins is the long range dipolar interaction, and each electronic spin is strongly coupled to a nuclear degree of freedom. These nuclear degrees of freedom constitute a spin bath environment acting on the system. In this thesis, we present an effective low temperature Hamiltonian for LiHoF₄ that incorporates both these features, and we analyze the effects of the nuclear spin bath on the system. We find the lowest energy crystal field excitation in the system is gapped at the quantum critical point by the presence of the nuclear spins, with spectral weight being transferred down to a lower energy electronuclear mode that fully softens to zero at the quantum critical point. Furthermore, we present a toy model, the spin half spin half model, that illustrates the effects of an anisotropic hyperfine interaction on a quantum Ising system. We find the critical transverse field is increased when the longitudinal hyperfine coupling is dominant, as well as an enhancement of both the longitudinal electronic susceptibility and an applied longitudinal field. In addition, we present a field theoretic formalism for incorporating the effects of fluctuations beyond the random phase approximation in general quantum Ising systems. We find that any regular on site interaction, such as a nuclear spin bath, does not fundamentally alter the critical properties of a quantum Ising system. This formalism is used to calculate corrections to the magnetization of LiHoF₄.

Jan 1, 20161 citation

{\text{LiHoF}}_{4}

system, in which spin-8 electronic spins couple to a spin-

7/2

nuclear spin bath: The phase transition then occurs in a system of electronuclear degrees of freedom, coupled by long-range dipolar interactions. The quantum Ising phase transition still exists, and one hybridized mode of the Ising and bath spins always goes soft at the transition.

{\text{LiHoF}}_{4}

is discussed in detail.