Point Of Quantum Phase Transition Research Articles

Analytical solution and spectral structure of the two-photon anisotropic Rabi-Stark model

Since the realization of the strong coupling between light and matter in experimental setups, the quantum Rabi model and its generalized models describing the interaction between the boson field and the two-level system have attracted extensive interest again. The study of anisotropic generalized Rabi models enables us to better understand the novel physical properties of the interaction between light and matter in the ultra-strong and deep-strong coupling regions. In this work, the two-photon anisotropic Rabi-Stark model (tpARSM) is analytically solved by using the Bogoliubov operator approach and the su(1, 1) Lie algebra. We derive the G-function, whose zeros give the regular spectrum of the system. By studying the pole structure of the G-function and the coefficients in the function, exceptional solutions, including the first-order quantum phase transition points, doubly degenerate exceptional solutions and nondegenerate exceptional solutions, are obtained. By discussing the spectral structure, we give the conditions for the first-order quantum phase transition of tpARSM. Furthermore, we find that the property that all of the lowest doubly degenerate crossing points in the two-photon Rabi-Stark model have the same energy only holds for the special case of the tpARSM in which the anisotropy parameter is equal to 1. Finally, from the perspective of first-order quantum phase transitions, concise conditions for the ground state energy level to collapse to or escape from the collapse point for the tpARSM are presented. A good understanding of the tpARSM will lay a good foundation for studying the extended two-photon systems involving multiple levels and multiple bosonic modes, and even the relevant open quantum systems.

Orthogonality catastrophe and quantum speed limit for dynamical quantum phase transition

We investigate the orthogonality catastrophe and quantum speed limit in the Creutz model for dynamical quantum phase transitions. We show that exact zeros of the Loschmidt echo can exist in finite-size systems for specific discrete values. We highlight the role of the zero-energy mode when analyzing quench dynamics near the critical point. Additionally, we examine the behaviors of the time for the first exact zeros of the Loschmidt echo and the corresponding quantum speed limit time as the system size increases. While the bound is not tight, it can be attributed to the scaling properties of the band gap and energy variance with respect to system size. As such, we establish a link between the orthogonality catastrophe and quantum speed limit by referencing the full form of the Loschmidt echo. In addition, we reveal the potential that the quantum speed limit holds to detect static quantum phase transition point and a reduced amplitude of the noise induced behaviors of quantum speed limit.

Probing quantum phase transition point by tuning an external anti trap.

Manipulation of ultracold atoms in optical lattices is one of the optimal ways to observe phase transitions of the Hubbard model which is useful in a variety of condensed-matter systems. Bosonic atoms in this model experience a phase transition from superfluids to Mott insulators by tuning systematic parameters. However, in conventional setups, phase transitions take place over a large range of parameters instead of one critical point due to the background inhomogeneity caused by the Gaussian shape of optical-lattice lasers. To probe the phase transition point more precisely in our lattice system, we apply a blue-detuned laser to compensate for this local Gaussian geometry. By inspecting the change of visibility, we find a sudden jump point at one particular trap depth of optical lattices, corresponding to the first appearance of Mott insulators in inhomogeneous systems. This provides a simple method to detect the phase transition point in such inhomogeneous systems. We believe it will be a useful tool for most cold atom experiments.

Spectral structure of two-mode Rabi–Stark model

The analytical solutions of the two-mode Rabi–Stark model (tmRSM) are obtained by using the Bogoliubov operators approach in Lie algebra space, which fit the exact numerical results well. The structure of the energy spectra is related to many fundamental physics characters such as symmetry, quantum phase transition (QPT), spectral collapse etc. In this paper, the spectral structure of tmRSM is discussed analytically. The regular energy spectra are given by the zeros of the G-function, and the poles appearing in the G-function are responsible for the exceptional solutions. The double degenerate exceptional solutions could be predicted by discussing the divergence of the coefficients in the G-function. If the numerator and denominator of vanish, the lowest double degenerate exceptional solutions for the nth energy levels would be located, including the first-order QPT point, the corresponding energy () is independent of the coupling strength and the energy level, even independent of the Bargmann index q. While, the nondegenerate exceptional solutions can be reproduced by the nondegenerate exceptional G-functions, the results show that more nondegenerate exceptional solutions would be found in the subspace with larger q. Then, the regular solution and two kinds of exceptional Juddian solutions of tmRSM are accurately located. The spectral collapse energy are dependent on the strength of Stark coupling and the frequency of two-level system, and Stark coupling could results in the limit of E 0 pole line is higher than that of E n pole lines, which may cause more energy levels separate from the collapse energy.

Renormalization of steered coherence and quantum phase transitions in the alternating Ising model

We explore net steered coherence defined with respect to the mutually unbiased bases. By using the quantum renormalization group method, we studied its scaling property for the ground state of two blocks of the alternating Ising model in the renormalized space. The results show that different patterns in the net steered coherence describe different phases of the model, and its susceptibility with respect to the magnetic field is divergent at the critical points of quantum phase transitions. As the net steered coherence exists for almost all bipartite states, it can serve as an alternative for exploring quantum criticality of the many-body systems in the parameter regions without entanglement and quantum discord.

Collapse of Superradiant Phase and Unstable Macroscopic Vacuum State in An-Optomechanical-Dual-Cavity with a Bose-Einstein Condensate

Based on spin-coherent-state variational method, we mainly study the multiple stable macroscopic quantum states and quantum phase transitions of a Bose-Einstein Condensate in an optomechanical dual-cavity by modulating the dual-cavity interaction and the nonlinear phonon-photon interaction. Especially, the collapse of superradiant phase can be tuned in the existing nonlinear photon-phonon interaction, but the critical quantum phase transition point or boundary hasn’t been influenced. As a result, the system occurs an additional phase transition from the superradiant phase to the inversely atomic populated state. Moreover, when dual-cavity coupling interaction increases to a certain value, a new quantum phase transition from the normal phase to the inversely atomic populated state will appear. Finally, the superradiant phase completely collapses and the normal phase also collapses into an unstable macroscopic vacuum state for a strong dual-cavity coupling interaction.

Driven one-dimensional noisy Kitaev chain

We study a one-dimensional Kitaev chain driven by the anisotropy parameter ${J}_{\ensuremath{-}}=t/{\ensuremath{\tau}}_{Q}$, in the presence of weak Gaussian noise in the parameter ${J}_{+}$. The system is prepared in the ground state of the Hamiltonian at the initial time $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$. The defect density and the residual energy at the end of the drive protocol reveals anti-Kibble Zurek (AKZ) behavior which deviates from the earlier reported linear in quench time dependence for the defect density. The entropy density at the end of the protocol is found to exhibit the signature of the AKZ behavior. In the context of the Kitaev chain, the two-point spin correlators are short ranged. The hidden topological order across the quantum phase transition point is probed via the nonlocal string order parameters. The two-point Majorana correlator and the hidden string correlator calculated in the final decohered state at the end of the noisy drive protocol is consistent with the AKZ picture. We have analyzed the kink statistics in the dual spin space, the first three cumulants at the end of the noisy drive also exhibit the AKZ scaling behavior for slower sweeps similar to the defect density. The kink distribution function is well approximated with the normal distribution with nonuniversal noise dependent mean and variance.

Quantum coherence and mutual information of mixed spin-(1/2, 5/2) Ising-<i>XXZ</i> model on quasi-one-dimensional lattices

The mixed spin-(1/2, 5/2) Ising-<i>XXZ</i> model on quasi-one-dimensional lattices can be used to study the properties of some materials (such as heterotrimetallic Fe-Mn-Cu coordination polymer), and the study on this model is beneficial to the practical applications of such materials in the field of quantum information. The quantum coherence and mutual information are calculated by the transfer matrix method, and the effects of Ising interaction, temperature and magnetic field on them are discussed. The results show that the quantum coherence decreases gradually with the increase of Ising interaction at extremely low temperatures, while there is one minimum value of mutual information in an isotropic system and there appear four minimum values in an anisotropic <inline-formula><tex-math id="M3">\begin{document}$\left( {\varDelta = 4} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230381_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20230381_M3.png"/></alternatives></inline-formula> system. Furthermore, quantum coherence and mutual information jump abruptly at quantum phase transition points where the first derivatives of them exhibit singular behaviors. The quantum coherence and mutual information at finite temperatures are also studied. As the temperature increases, they decrease monotonically in a weak magnetic field, but they first increase and then decrease in a higher magnetic field, which is caused by the competition between thermal fluctuation and magnetic field. Compared with quantum mutual information, quantum coherence exists over a wider range of magnetic field and temperature, which can be easily manipulated experimentally.

Universal characteristics of one-dimensional non-Hermitian superconductors

We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors. The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory. According to the particle-hole symmetry, there exist reciprocal particle and hole loops of generalized Brillouin zone. The critical point of quantum phase transition, where the energy gap closes, appears when the particle and hole loops intersect at Bloch points. If the non-Hermitian system has non-Hermitian skin effects, the non-Hermitian skin effect should be the Z 2 skin effect: the corresponding eigenstates of particle and hole localize at opposite ends of an open chain, respectively. The non-Bloch band theory is applied to two examples, non-Hermitian p- and s-wave topological superconductors. In terms of Majorana Pfaffian, a Z 2 non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence for the non-Hermitian topological superconductors.

Berry Phase of Two Impurity Qubits as a Signature of Dicke Quantum Phase Transition

In this paper, we investigate the effect of the Dicke quantum phase transition on the Berry phase of the two impurity qubits. The two impurity qubits only have dispersive interactions with the optical field of the Dicke quantum system. Therefore, the two impurity qubits do not affect the ground state energy of the Dicke Hamiltonian. We find that the Berry phase of the two impurity qubits has a sudden change at the Dicke quantum phase transition point. Therefore, the Berry phase of the two impurity qubits can be used as a phase transition signal for the Dicke quantum phase transition. In addition, the two impurity qubits change differently near the phase transition point at different times. We explain the reason for the different variations by studying the variation of the Berry phase of the two impurity qubits with the phase transition parameters and time. Finally, we investigated the variation of the Berry phases of the two impurity qubits with their initial conditions, and we found that their Berry phases also have abrupt changes with the initial conditions. Since the Dicke quantum phase transition is already experimentally executable, the research in this paper helps to provide a means for manipulating the Berry phase of the two impurity qubits.

Bond-Orbital-Resolved Piezoelectricity in Sp2-Hybridized Monolayer Semiconductors.

Sp2-hybridized monolayer semiconductors (e.g., planar group III-V and IV-IV binary compounds) with inversion symmetry breaking (ISB) display piezoelectricity governed by their σ- and π-bond electrons. Here, we studied their bond-orbital-resolved electronic piezoelectricity (i.e., the σ- and π-piezoelectricity). We formulated a tight-binding piezoelectric model to reveal the different variations of σ- and π-piezoelectricity with the ISB strength (Δ). As Δ varied from positive to negative, the former decreased continuously, but the latter increased piecewise and jumped at Δ=0 due to the criticality of the π-electrons' ground-state geometry near this quantum phase-transition point. This led to a piezoelectricity predominated by the π-electrons for a small |Δ|. By constructing an analytical model, we clarified the microscopic mechanisms underlying the anomalous π-piezoelectricity and its subtle relations with the valley Hall effect. The validation of our models was justified by applying them to the typical sp2 monolayers including hexagonal silicon carbide, Boron-X (X = N, P, As, Ab), and a BN-doped graphene superlattice.

Protected Hybrid Superconducting Qubit in an Array of Gate-Tunable Josephson Interferometers

We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers. The individual interferometers realize effective $\cos2\phi$ elements that exchange `pairs of Cooper pairs' between the superconducting islands when gate-tuned into balance and frustrated by a half flux quantum. If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset charge and magnetic field fluctuations for a sizable window around zero offset charge and half flux quantum. This protection window broadens upon increasing the number of interferometers if the individual elements are balanced. We use an effective spin model to describe the system and show that a quantum phase transition point sets the critical flux value at which protection is destroyed.

Negativity and quantum phase transition in a mixed spin-([formula omitted], [formula omitted], [formula omitted]) Ising–Heisenberg branched chain

The thermal entanglement in a mixed spin-(1/2, 5/2, 1/2) Ising–Heisenberg branched chain is investigated by employing negativity as entanglement measurement. Using transfer-matrix approach, the negativity is calculated numerically both near and at a quantum phase transition point. We establish the relationship between negativity and quantum phase transition. It is found that whether negativity can be used to detect quantum phase transition point depends on the typical thermal energy, and we show the range of temperature at which negativity can be used to signal each ground-state transition. In addition, the thermal stability of negativity is closely related to energy gap in the system. It is worth noting that the negativity exhibits distinct behavior between quantum and classical phases. Negativity decreases with the increase of temperature in the quantum phase, while it exhibits a ”regrowth” behavior in the classical phases.

Topological Quantum Phase Transitions of Anisotropic Antiferromagnetic Kitaev Model Driven by Magnetic Field

AbstractThe evolution of quantum spin liquid states (QSL) of the anisotropic antiferromagnetic (AFM) Kitaev model with the [001] magnetic field by utilizing the finite‐temperature Lanczos method (FTLM) is investigated. In this anisotropic Kitaev model with and (K is the energy unit), due to the competition between anisotropy and magnetic field, the system emerges four exotic quantum phase transitions (QPTs) when and , while only two QPTs when . At these magnetic‐field tuning quantum phase transition points, the low‐energy excitation spectrums appear level crossover, and the specific heat, magnetic susceptibility and Wilson ratio display anomalies; accordingly, the topological Chern number may also change. These results demonstrate that the anisotropic interacting Kitaev model with modulating magnetic field displays more rich phase diagrams, in comparison with the isotropic Kitaev model.

Renormalization of multipartite entanglement near the critical point of two-dimensional XXZ model with Dzyaloshinskii–Moriya interaction

We investigate the multipartite entanglement and the trace distance for the two-dimensional anisotropic spin-12 XXZ lattice with Dzyaloshinskii–Moriya interaction. It is found that for a many-body quantum system the multipartite entanglement is more advantageous than the bipartite entanglement due to the monogamy property. Both the quantifiers, the multipartite entanglement and the trace distance, decreases with an increase in the anisotropy and the Dzyaloshinskii–Moriya interaction tends to restore the spoiled entanglement. The quantum reormalization group method is used to compute the stable and the unstable fixed points. We observe that the quantum phase transition point is independent of the chosen quantifier as the thermodynamic limit is reached. After sufficient iterations of the quantum renormalization group, we observe two different saturated values of both the quantifiers that represent two separate phases, the spin-fluid phase and the Néel phase. The first derivative and the scaling behavior of the renormalized entanglement quantifiers are calculated. At quantum phase transition point, the non-analytic behavior of the first derivative of the two quantifiers as a function of lattice size is examined and it is found that the universal finite-size scaling law is obeyed. Furthermore, we observe that at the critical point the scaling exponent for the multipartite entanglement and the trace distance can describe the correlation length of the model.

Enhanced nonlinear quantum metrology with weakly coupled solitons in the presence of particle losses

The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. However, unavoidable lossy effect is commonly believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg (up to 1/N^3) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe, i.e, the entangled Fock (N00N-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible both for the linear and nonlinear metrologies with the SJJs, and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

We investigate quantum phase transitions for q-state quantum Potts models (q = 2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen–Shannon divergence, the relative entropy of coherence, and the l1 norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.

Quantum batteries at the verge of a phase transition

Starting from the observation that the reduced state of a system strongly coupled to a bath is, in general, an athermal state, we introduce and study a cyclic battery–charger quantum device that is in thermal equilibrium, or in a ground state, during the charge storing stage. The cycle has four stages: the equilibrium storage stage is interrupted by disconnecting the battery from the charger, then work is extracted from the battery, and then the battery is reconnected with the charger; finally, the system is brought back to equilibrium. At no point during the cycle are the battery–charger correlations artificially erased. We study the case where the battery and charger together comprise a spin-1/2 Ising chain, and show that the main characteristics—the extracted energy and the thermodynamic efficiency—can be enhanced by operating the cycle close to the quantum phase transition point. When the battery is just a single spin, we find that the output work and efficiency show a scaling behavior at criticality and derive the corresponding critical exponents. Due to always present correlations between the battery and the charger, operations that are equivalent from the perspective of the battery can entail different energetic costs for switching the battery–charger coupling. This happens only when the coupling term does not commute with the battery’s bare Hamiltonian, and we use this purely quantum leverage to further optimize the performance of the device.

Solitonic excitations in the Ising anisotropic chain BaCo2V2O8 under large transverse magnetic field

We study the dynamics of the quasi-one-dimensional Ising-Heisenberg antiferromagnet ${\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ under a transverse magnetic field. Combining inelastic neutron scattering experiments and theoretical analyses by field theories and numerical simulations, we mainly elucidate the structure of the spin excitation spectrum in the high-field phase, appearing above the quantum phase transition point ${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}10\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. We find that it is characterized by collective solitonic excitations superimposed on a continuum. These solitons are strongly bound in pairs due to the effective staggered field induced by the nondiagonal $g$ tensor of the compound and are topologically different from the fractionalized spinons in the weak-field region. The dynamical susceptibility numerically calculated with the infinite time-evolving block decimation method shows an excellent agreement with the measured spectra, which enables us to identify the dispersion branches with elementary excitations. The lowest-energy dispersion has an incommensurate nature and has a local minimum at an irrational wave number due to the applied transverse field.

Electrodynamics of Topologically Ordered Quantum Phases in Dirac Materials.

First-principles calculations of the electronic ground state in tantalum arsenide are combined with tight-binding calculations of the field dependence of its transport model equivalent on the graphene monolayer to study the emergence of topologically ordered quantum states, and to obtain topological phase diagrams. Our calculations include the degrees of freedom for nuclear, electronic, and photonic interactions explicitly within the quasistatic approximation to the time-propagation-dependent density functional theory. This field-theoretic approach allows us to determine the non-linear response of the ground state density matrix to the applied electromagnetic field at distinct quantum phase transition points. Our results suggest the existence of a facile electronic switch between trivial and topologically ordered quantum states that may be realizable through the application of a perpendicular electric or magnetic field alongside a staggered-sublattice potential in the underlying lattice. Signatures of the near field electrodynamics in nanoclusters show the formation of a quantum fluid phase at the topological quantum phase transition points. The emergent carrier density wave transport phase is discussed to show that transmission through the collective excitation mode in multilayer heterostructures is a unique possibility in plasmonic, optoelectronic, and photonic applications when atomic clusters of Dirac materials are integrated within nanostructures, as patterned or continuous surfaces.