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Physical Review A

Hopping-induced quantum phase transition in the Ising-Rabi lattice model

Gaoke Hu, Zhiguo Lü, Hai‐Qing Lin, Hang Zheng

Published Aug 23, 2023• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.108.023723

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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 XYZXYZXYZ model. When the hopping strength t=0t=0t=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.
The unitary transformation method is used to study the properties of the polaritonic states and Bose-Einstein condensation in the Rabi lattice model, where the on-site two-level systems (TLSs) are coupled with the intersite hopping photons. It is shown that the counter-rotating coupling (CRC) between TLS and photon, which breaks down the conservation of the excitation numbers, may induce a long-range Ising-like interaction among intersite TLSs. We have shown that the coupled TLSs and photons are hybridized to form the polaritonic states, and the corresponding ground state and polaritonic excitation spectra are calculated by diagonalizing our transformed Hamiltonian. When the photon hopping JJJ is weak, the excitation spectrum is gapped. But the gap decreases with increasing JJJ, and at critical value J=JcJ={J}_{c}J=Jc​ the gap becomes zero at the $\mathrm{\ensuremath{\Gamma}}$ point and the ground state becomes instable. Thus, Jc{J}_{c}Jc​ is the phase transition point where the polaritons are condensed at the $\mathrm{\ensuremath{\Gamma}}$ point to form the delocalized superradiant phase. The results show that the larger detuning between TLS and photon favors the disorder insulator phase, which requires the stronger Jc{J}_{c}Jc​ to get the long-range order phase. The phase diagram of the delocalized superradiant phase transition has been obtained where there are no Mott lobes since the CRC breaks down the number conservation. The ground state and the excitation spectra of the delocalized superradiant phase are also calculated. It is shown that in the delocalized superradiant state the order parameter is the nonzero ground-state average of the photon annihilation operator. The polaritonic excitation has a finite excitation gap because the CRC breaks down the number conservation but leaves only a discrete symmetry, the parity conservation.
Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.
Abstract We investigate the ground-state properties of a disorderd Ising model with uniform transverse field on the Bethe lattice, focusing on the quantum phase transition from a paramagnetic to a glassy phase that is induced by reducing the intensity of the transverse field. We use a combination of quantum Monte Carlo algorithms and exact diagonalization to compute Rényi entropies, quantum Fisher information, correlation functions and order parameter. We locate the transition by means of the peak of the Rényi entropy and we find agreement with the transition point estimated from the emergence of finite values of the Edwards–Anderson order parameter and from the peak of the correlation length. We interpret the results by means of a mean-field theory in which quantum fluctuations are treated as massive particles hopping on the interaction graph. We see that the particles are delocalized at the transition, a fact that points towards the existence of possibly another transition deep in the glassy phase where these particles localize, therefore leading to a many-body localized phase.
Recent studies of the global phase diagram of quantum-critical heavy-fermion metals prompt consideration of the interplay between the Kondo interactions and quantum fluctuations of the local moments alone. Toward this goal, we study a Bose-Fermi Kondo model (BFKM) with Ising anisotropy in the presence of a local transverse field that generates quantum fluctuations in the local-moment sector. We apply the numerical renormalization-group method to the case of a sub-Ohmic bosonic bath exponent and a constant conduction-electron density of states. Starting in the Kondo phase at zero transverse field, there is a smooth crossover with increasing transverse field from a fully screened to a fully polarized impurity spin. By contrast, if the system starts in its localized phase, then increasing the transverse field causes a continuous, Kondo-destruction transition into the partially polarized Kondo phase. The critical exponents at this quantum phase transition exhibit hyperscaling and take essentially the same values as those of the BFKM in zero transverse field. The many-body spectrum at criticality varies continuously with the bare transverse field, indicating a line of critical points. We discuss implications of these results for the global phase diagram of the Kondo lattice model.
In this work, we investigate the quantum phase transition of light in the dissipative Rabi-Hubbard lattice under the framework of the mean-field theory and quantum dressed master equation. The order parameter of photons in strong qubit-photon coupling regime is derived analytically both at zero and low temperatures. Interestingly, we can locate the localization and delocalization phase transition very well in a wide parameter region. In particular for the zero-temperature limit, the critical tunneling strength approaches zero generally in the deep-strong qubit-photon coupling regime, regardless of the quantum dissipation. This is contrary to the previous results with the finite minimal critical tunneling strength based on the standard Lindblad master equation. Moreover, a significant improvement of the critical tunneling is also observed at finite temperature, compared with the counterpart under the Lindblad description. We hope these results may deepen the understanding of the phase transition of photons in the Rabi-Hubbard model.
We explore the quantum criticality of a two-site model combining quantum Rabi models with hopping interaction. Through a combination of analytical and numerical approaches, we find that the model allows the appearance of a superradiant quantum phase transition (QPT) even in the presence of strong A2{\mathbf{A}}^{2}A2 terms, preventing single-site superradiance. In the two-site model the effect of A2{\mathbf{A}}^{2}A2 terms can be surmounted by the photon delocalization from hopping, and a reversed superradiant QPT occurs as a consequence of the competition between A2{\mathbf{A}}^{2}A2 terms and the hopping interaction. We characterize the phase diagram and scaling functions and extract the critical exponents in the vicinity of the critical point, thus establishing the universal behavior of the second-order phase transition. Remarkably the effective hopping strength will be enhanced if more cavities are cascaded. We also prove that the multiqubit counterpart of the quantum Rabi dimer, i.e., the Dicke dimer, has the same properties in beating the A2{\mathbf{A}}^{2}A2 effect. Our work provides a path to the study of phase transitions in the presence of the A2{\mathbf{A}}^{2}A2 terms and offers the prospect of investigating quantum-criticality physics and quantum devices in many-body systems.