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arXiv:2407.03612 · Physical Review A

Quantum phase transition in a quantum Rabi square with next-nearest-neighbor hopping

Yilun Xu, Feng-Xiao Sun, Qiongyi He, Han Pu, Wei Zhang

Published Aug 1, 2024• 5 citations
arXivHTMLPDF

Abstract

We propose a quantum Rabi square model where both the nearest-neighbor and the next-nearest-neighbor photon hopping are allowed among four quantum Rabi systems located at the vertices of a square. By tuning the next-nearest hopping strength, we realize a first-order phase transition between the antiferromagnetic superradiant phase and the frustrated superradiant phase, as well as a second-order phase transition between the normal and the superradiant phases. To understand the emergence of such phases, we show analytically that the effect induced by next-nearest hopping is equivalent to that of an artificial gauge phase. Our findings suggest that the next-nearest-neighbor hopping can serve as an alternative for the gauge phase to realize quantum control in applications of quantum simulation and quantum materials and that our model represents a basic building block for the frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ quantum spin model on square lattices.

DOI
10.1103/physreva.110.023702

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•Jan 1, 2012•0 citations
We propose a quantum Rabi square model where both the nearest-neighbor and the next-nearest-neighbor photon hopping are allowed among four quantum Rabi systems located at the vertices of a square. By tuning the next-nearest hopping strength, we realize a first-order phase transition between the antiferromagnetic superradiant phase and the frustrated superradiant phase, as well as a second-order phase transition between the normal and the superradiant phases. To understand the emergence of such phases, we show analytically that the effect induced by next-nearest hopping is equivalent to that of an artificial gauge phase. Our findings suggest that the next-nearest-neighbor hopping can serve as an alternative for the gauge phase to realize quantum control in applications of quantum simulation and quantum materials and that our model represents a basic building block for the frustrated J1\ensuremath-J2{J}_{1}\text{\ensuremath{-}}{J}_{2}J1​\ensuremath-J2​ quantum spin model on square lattices.
We present the phase diagram of a one-dimensional quantum Rabi zigzag chain under an artificial gauge field, which is implemented via phase-modulated next-nearest-neighbor (NNN) hopping. For a system size of N=8N=8N=8, we analytically determine the order parameters and critical thresholds, identifying five distinct superradiant phases. For strong nearest-neighbor (NN) coupling, the system exhibits either a ferro-superradiant (FSR) or an antiferro-superradiant (AFSR) phase depending on its sign. Increasing NNN coupling induces a stripe antiferro-superradiant (sAFSR) phase with antiparallel NNN and parallel NN displacements, which is distinct from the conventional AFSR phase. Tuning the magnetic flux drives the system into chiral or antichiral superradiant phases with opposite ground-state photon currents, which are different from the conventional superradiant phases. Remarkably, geometric frustration within each triangular plaquette stabilizes chiral phases even at small magnetic flux while suppressing the sAFSR phase, which vanishes for N=6N=6N=6. Mapping the system onto an effective magnetic Hamiltonian yields an analogous phase diagram featuring distinct magnetic phases, offering insight into the anomalous superradiant phases. This equivalence establishes a quantum optical platform for simulating chiral magnetism.
The Jordan–Wigner transformation is applied to the spatially anisotropic spin-1/2 Heisenberg model on a square lattice with the nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions. The transformed Hamiltonian describes the interacting spinless fermions that hop between neighbor sites in a gauge field. Using the mean-field-type approximation to both the direct interaction between fermions and the phase factors, which represent the gauge field, the problem is reduced to that concerning a free Fermi gas. Two types of antiferromagnetic ordering (the N´eel and collinear ones) are considered. By calculating the ground-state energies, the phase transitions induced by the interaction frustration were analyzed.
We present exotic quantum phases in a quantum Rabi hexagonal ring. A remarkable finding is that the application of an artificial magnetic field to the ring induces long-range interactions, yielding effective next-nearest-neighbor photon hopping in the subrings. This phenomenon gives rise to two chiral superradiant phases in addition to a ferro-superradiant and an antiferro-superradiant phase. As evidence, there appear chiral ground-state currents of photons in the subrings with opposite signs in different chiral phases. The degenerate configurations of the complex order parameters in chiral phases are similar to the in-plane magnetizations of a chiral magnetic. The critical exponents governing the excitation energy in the two chiral phases are identical to those of the Rabi triangle, which depend on the size of the subrings rather than the size of the ring. It is important to classify the universality class of the multiple chiral phase transitions as the size of Rabi ring increases. Furthermore, the implementation of the proposed system is an exciting prospect in quantum simulations for exploring intriguing quantum phases.
We map a quantum Rabi ring, consisting of N cavities arranged in a ring geometry, into an effective magnetic model containing the XY exchange and the Dzyaloshinskii-Moriya (DM) interactions. The analog of the latter is induced by an artificial magnetic field, which modulates photon hopping between nearest-neighbor cavities with a phase. This mapping facilitates the description and understanding of the different phases in the quantum optical model through simple arguments of competing magnetic interactions. For the square geometry (N=4) the rich phase diagram exhibits three superradiant phases denoted as ferro-superradiant, antiferro-superradiant, and chiral superradiant. In particular, the DM interaction is responsible for the chiral phase in which the energetically degenerate configurations of the order parameters are similar to the in-plane magnetizations of skyrmions with different helicities. The antiferro-superradiant phase is suppressed in the triangle geometry (N=3) as geometric frustration contributes to stabilize the chiral phase even for small values of the DM interaction. The chiral phases for odd and even N show a different scaling behavior close to the phase transition. The equivalent behavior on both systems opens the possibility of simulating chiral magnetism in a few-body quantum optical platform, as well as understanding one system using the insights gained from the other.
We analyze the phase transition of the frustrated J1{J}_{1}J1​-J2{J}_{2}J2​ Ising model with antiferromagnetic nearest- and strong next-nearest-neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for $1/2<{J}_{2}/{J}_{1}\ensuremath{\lesssim}1$ is not of the weakly universal type---as commonly believed---but we conclude from the clearly doubly peaked structure of the energy histograms that the transition is of weak first order. Motivated by these results, we analyze the phase transitions via field-theoretic methods; i.e., we calculate the central charge of the underlying field theory via transfer-matrix techniques and present, furthermore, a field-theoretic discussion on the phase-transition behavior of the model. Starting from the conformally invariant fixed point of two decoupled critical Ising models (J1=0{J}_{1}=0J1​=0), we calculate the effect of the nearest-neighbor coupling term perturbatively using operator product expansions. As an effective action we obtain the Ashkin-Teller model.
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.