The antiferromagnetic Ising model on the pyrochlore lattice exhibits a quantum phase transition in an applied transverse field from the low-field quantum spin-ice phase to the high-field polarized regime. Recent field-theoretical analysis and series expansion results indicate this to be a discontinuous, first-order transition. Here, we explore this transition using quantum Monte Carlo simulations in order to assess this scenario and study the thermodynamic properties in the vicinity of the quantum phase transition. For this purpose, we also consider several variants of extended cluster-update schemes for the transverse-field Ising antiferromagnet on frustrated lattices and compare their performance to the conventional bond-based algorithm for the transverse-field Ising model on the pyrochlore lattice.
Abstract We propose an eigen microstate approach (EMA) for analyzing quantum phase transitions in quantum many-body systems, introducing a novel framework that does not require prior knowledge of an order parameter. Using the transverse-field Ising model (TFIM) as a case study, we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates. Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition, as reflected in the behavior of specific components ξ i ( k ) within the eigen microstates. This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.
We study the ground state and low-lying polaritonic excitation states in the Ising-Rabi lattice model (IRLM), where the transverse field in the quantum transverse field Ising model is replaced by a quantized local photon field. The competition among the photon-hopping coupling, the intrasite Rabi interaction, and the Ising interaction drives the system across a quantum phase transition from the insulating phase to the delocalized superradiant phase. Mean-field theory confirms the existence of the quantum phase transition and the analytical expressions for the phase boundary are derived. The spectra of low-lying polaritonic excitations and Bose-Einstein condensation are further explored by a unitary transformation method. The deep strong-coupling analysis reveals a quantum criticality, where the IRLM belongs to the universality class of the
XYZ model. When the hopping strength
t=0, the properties of the ground state in the IRLM are investigated by the symmetry analysis and the density-matrix renormalization-group method. It turns out that the photon field cannot alone serve as a global transverse field in the quantum transverse field Ising model without the presence of hopping coupling since a crossover behavior instead of a quantum phase transition is confirmed.