Unbroken Phase Research Articles

Effective brane field theory with higher-form symmetry

We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

Parity-time symmetry characterization and dynamics of periodically modulated four-channel optical waveguides

The control of parity-time (PT) symmetry in cosmic-time PT symmetry system is of great significance, but the experimental realization of such an optical configuration using current technology faces enormous challenges. On the contrary, the periodic modulation method is a more feasible alternative. It is worth noting that periodic modulation in optical system is mainly performed through the cyclic change of complex refractive index materials. Unlike the traditional method of aligning periodically modulated waveguides in parallel to gain-dissipative waveguides to satisfy PT symmetry, an innovative physical model introduced in this work, features the cross-placement of these waveguides, marking it the first instance to use this configuration to manipulate PT symmetry. In this work, the influence of periodic modulation on the energy spectrum of the system in the high-frequency approximation is studied, and the dynamical evolution of light in a non-Hermitian four-channel optical waveguide is elucidated through a synergistic method of combining analytical method and numerical method. Adjusting the modulation parameter <i>A/ω</i> reveals a dual capability: it modulates the range of the real energy spectrum and precisely controls the PT symmetry of the system. Notably, at <i>A/ω</i>=0, this structure exhibits a completely real energy spectrum, which is different from the traditional parallel four-channel waveguide configuration. Furthermore, as <i>A/ω</i> varies from 0 to 2.4, the relative intensity and optical periodicity in each waveguide exhibit enhanced stability compared with their traditionally arranged counterparts. Furthermore, our examination of PT symmetry’s effect on light tunneling dynamics in individual waveguide reveals that in the unbroken PT symmetry phase, light oscillates periodically between waveguides, whereas in the broken PT symmetry phase, light propagation in each waveguide becomes stable. In the presence of waveguide coupling, it is observed that each waveguide in the system can obtain steady-state light regardless of the initial light injection point. Furthermore, under weak coupling between the gain-dissipative two-channel waveguide and the neutral waveguide, light, regardless of its entry point, will localize in the gain waveguide with propagation distance, disappear from other waveguides, and ultimately reach a steady-state configuration. The findings reveal that unlike the scenario of traditional four-channel optical waveguide system, the periodic modulation not only narrows the range of existence for the fully real energy spectrum but also enables its earlier observation. Furthermore, the relative light intensity and optical periodicity in the four-channel waveguide exhibit greater stability against variations of modulation parameters. Hence, this theoretical exploration not only profoundly summarizes the universal principle of PT-symmetric tetramers, but also elucidates that spontaneous PT symmetry breaking greatly changes the optical transmission characteristics, transforming periodic light propagation into steady-state illumination, and providing an enhanced and more robust configuration for the manipulation of PT symmetry.

Proving Rho Meson Is a Dynamical Gauge Boson of Hidden Local Symmetry

The rho meson has long been successfully identified with a dynamical gauge boson of Hidden Local Symmetry (HLS) Hlocal in the non-linear sigma model G/H gauge equivalent to the model having the symmetry Gglobal×Hlocal, with G=[SU(2)L×SU(2)R]≃O(4),H=SU(2)V≃O(3). However, under a hitherto unproven assumption that its kinetic term is dynamically generated, together with an ad hoc choice of the auxiliary field parameter “a=2”, we prove this assumption, thereby solving the long-standing mystery. The rho meson kinetic term is generated simply by the large N limit of the Grassmannian model G/H=O(N)/[O(N−3)×O(3)] gauge equivalent to O(N)global×[O(N−3)×O(3)]local, extrapolated to N=4, O(4)global×O(3)local, with all the phenomenologically successful “a=2 results”, i.e., ρ-universality, KSRF relation, and the Vector Meson Dominance, realized independently of the parameter “a”. This in turn establishes validity of the large N dynamics at the quantitative level directly by the experiments. The relevant cutoff reads Λ≃4πFπ for N=4, which is regarded as a matching scale of the HLS as a “magnetic dual” to QCD. Skyrmion is stabilized by such a dynamically generated rho meson without recourse to the underlying QCD, a further signal of the duality. The unbroken phase with a massless rho meson may be realized as a novel chiral-restored hadronic phase in the hot/dense QCD.

Topological Plasma Transport from a Diffusion View

Recent studies have identified plasma as a topological material. Yet, these researches often depict plasma as a fluid governed by electromagnetic fields, i.e., a classical wave system. Indeed, plasma transport can be characterized by a unique diffusion process distinguished by its collective behaviors. We adopt a simplified diffusion-migration method to elucidate the topological plasma transport. Drawing parallels to the thermal conduction-convection system, we introduce a double-ring model to investigate the plasma density behaviors in the anti-parity-time reversal (APT) unbroken and broken phases. Subsequently, by augmenting the number of rings, we have established a coupled ring chain structure. This structure serves as a medium for realizing the APT symmetric one-dimensional (1D) reciprocal model, representing the simplest tight-binding model with a trivial topology. To develop a model featuring topological properties, we should modify the APT symmetric 1D reciprocal model from the following two aspects: hopping amplitude and onsite potential. From the hopping amplitude, we incorporate the non-reciprocity to facilitate the non-Hermitian skin effect, an intrinsic non-Hermitian topology. Meanwhile, from the onsite potential, the quasiperiodic modulation has been adopted onto the APT symmetric 1D reciprocal model. This APT symmetric 1D Aubry–André–Harper model is of topological nature. Additionally, we suggest the potential applications for these diffusive plasma topological states. This study establishes a diffusion-based approach to realize topological states in plasma, potentially inspiring further advancements in plasma physics.

Comments on trace anomaly matching

The structure of type A and B trace anomalies is reanalyzed in terms of the universal behavior of dimension −2 invariant amplitudes. Based on it a general argument for trace anomaly matching between the unbroken and broken phases of a CFT is given. The structure of moduli trace anomalies and their transformations under source reparametrizations is discussed in detail.

Quantum steering in a [formula omitted]-symmetric system of three cavities with a linear coupling between the active and passive cavities

A system of three cavities connected by linear coupling is considered in which the coupling between the active and passive cavities is much weaker than the others. We show the dependence of the phase transition point of PT-symmetry on parameters characterizing our system. The generation of quantum steering is also investigated by using steering parameter calculations that show the steering ability of subsystems. We show that in the unbroken phase of PT-symmetry, quantum steering between subsystems of each pair can be one-way or two-way steering depending on the respective gain and loss of energy in the active and passive cavities. We also point out that the steering abilities of subsystems in our system are dependent on the initial states of the system which are set up with one photon in the active cavity or the passive one.

Multi-species thermalization cascade of energetic particles in the early universe

Heavy long-lived particles are abundant in BSM physics and will, under generic circumstances, get to dominate the energy density of the universe. The resulting matter dominated era has to end through the decay of the heavy matter component particles of mass M, and before the universe cools down to a temperature of a few MeV, in order not to upset the successful predictions of Big Bang Nucleosynthesis. The process of thermalization of their decay products, of initial energy ∼ M/2, into a thermal bath of temperature T primarily involves near-collinear splittings of energetic particles into two particles with lower energy. The correct treatment of these processes requires the inclusion of coherence effects which suppress the splitting rate. We write down and numerically solve the resulting coupled Boltzmann equations including all gauge bosons and fermions of the unbroken phase of the Standard Model (SM). We then comment on the dependence of the nonthermal spectra on the ratio M/T, as well as on the matter decay rate and branching ratios into various SM particles.

Rabi oscillations at the exceptional point in anti-parity-time symmetric diffusive systems

The motivation for this theoretical paper comes from recent experiments of a heat transfer system of two thermally coupled rings rotating in opposite directions with equal angular velocities that present anti-parity-time (APT) symmetry. The theoretical model predicted a rest-to-motion temperature distribution phase transition during the symmetry breaking for a particular rotation speed. In this work we show that the system exhibits a parity-time ($\mathcal{PT}$) phase transition at the exceptional point in which eigenvalues and eigenvectors of the corresponding non-Hermitian Hamiltonian coalesce. We analytically solve the heat diffusive system at the exceptional point and show that one can pass through the phase transition that separates the unbroken and broken phases by changing the radii of the rings. In the case of unbroken $\mathcal{PT}$ symmetry the temperature profiles exhibit damped Rabi oscillations at the exceptional point. Our results unveils the behavior of the system at the exceptional point in heat diffusive systems.

Experimentally Realizable PT Phase Transitions in Reflectionless Quantum Scattering.

Above-barrier quantum scattering with truncated real potentials V(x)=-|x|^{p} provides an experimentally accessible platform that exhibits spontaneous parity-time symmetry breaking as p is varied. The unbroken phase has reflectionless states that correspond to bound states in the continuum of the nontruncated potentials at arbitrarily high discrete real energies. In the fully broken phase there are no bound states. There is a mixed phase in which exceptional points occur at specific energies and values of p. These effects should be observable in cold-atom scattering experiments.

Scaling laws of the out-of-time-order correlators at the transition to the spontaneous PT -symmetry breaking in a Floquet system

We investigate both numerically and analytically the dynamics of out-of-time-order correlators (OTOCs) in a non-Hermitian kicked rotor model, addressing the scaling laws of the time dependence of OTOCs at the transition to the spontaneous $\mathcal{PT}$-symmetry breaking. In the unbroken phase of $\mathcal{PT}$ symmetry, the OTOCs increase monotonically and eventually saturate with time, demonstrating the freezing of information scrambling. Just beyond the phase transition points, the OTOCs increase in the power laws of time, with the exponent being larger than 2. Interestingly, the quadratic growth of OTOCs with time emerges when the system is far beyond the phase transition points. The above numerical findings are validated by our theoretical analysis, which provides a general framework with important implications for Floquet engineering and information scrambling in chaotic systems.

Entanglement entropy distinguishes PT-symmetry and topological phases in a class of non-unitary quantum walks

We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a non-unitary quantum walk. The model possesses a joint parity and time-reversal symmetry or PT-symmetry and supports topological phases when this symmetry is unbroken by its eigenstates. An asymptotic analysis at long times reveals that the quantum walk can indefinitely sustain hybrid entanglement in the unbroken symmetry phase even when gain and loss mechanisms are present. However, when the gain-loss strength is too large, the PT-symmetry of the model is spontaneously broken and entanglement vanishes. The entanglement entropy is therefore an effective and robust parameter for constructing PT-symmetry and topological phase diagrams in this non-unitary dynamical system.

Massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms

We compute the 2 → 2 gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass m3/2) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as {kappa}^2{E}^4/{m}_{3/2}^2 , signaling a potential breakdown of unitarity at a scale {Lambda}^2sim {m}_{3/2}/kappa sim {M}_{textrm{SUSY}}^2 . As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (sgoldstino), restoring perturbative unitarity up to the Planck scale. This is expected since supersymmetry is spontaneously broken, in analogy with the situation occuring in the Standard Model, where massive gauge bosons scattering preserves unitarity at high energy once we consider the contributions from the Higgs boson. However, when supersymmetry is broken by the new Fayet-Iliopoulos D-term, with ungauged R-symmetry, the above cancellation does not occur. In this case, the unbroken phase is singular and there is no contribution able to cancel the quartic divergences of the amplitudes, leading to a cutoff Λ ~ MSUSY where the effective theory breaks down. The same behaviour is obtained when supersymmetry is non-linearly realised.

Transmission across non-Hermitian -symmetric quantum dots and ladders

A non-Hermitian (NH) region connected to semi-infinite Hermitian lattices acts either as a source or as a sink and the probability current is not conserved in a scattering typically. Even a -symmetric region that contains both a source and a sink does not lead to current conservation plainly. We propose a model and study the scattering across a NH -symmetric two-level quantum dot (QD) connected to two semi-infinite one-dimensional lattices in a special way so that the probability current is conserved. Aharonov–Bohm type phases are included in the model, which arise from magnetic fluxes () through two loops in the system. We show that when , the probability current is conserved. We find that the transmission across the QD can be perfect in the -unbroken phase (corresponding to real eigenenergies of the isolated QD) whereas the transmission is never perfect in the -broken phase (corresponding to purely imaginary eigenenergies of the QD). The two transmission peaks have the same width only for special values of the fluxes (being odd multiples of ). In the broken phase, the transmission peak is surprisingly not at zero energy. We give an insight into this feature through a four-site toy model. We extend the model to a -symmetric ladder connected to two semi-infinite lattices. We show that the transmission is perfect in unbroken phase of the ladder due to Fabry–Pérot type interference, that can be controlled by tuning the chemical potential. In the broken phase of the ladder, the transmission is substantially suppressed.

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field – defined on the space of closed loops – that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.

Linear response for pseudo-Hermitian Hamiltonian systems: Application to PT -symmetric qubits

Motivated by the recent advances in modelling the pseudo-Hermitian Hamiltonian (pHH) systems using superconducting qubits we analyze their quantum dynamics subject to a small time-dependent perturbation. In particular, We develop the linear response theory formulation suitable for application to various pHH systems and compare it to the ones available in the literature. We derive analytical expressions for the generalized temporal quantum-mechanical correlation function $C(t)$ and the time-dependent dynamic susceptibility $\chi(t) \propto \text{Im} ~C(t)$. We apply our results to two \textit{PT}-symmetric non-Hermitian quantum systems: a single qubit and two unbiased/biased qubits coupled by the exchange interaction. For both systems we obtain the eigenvalues and eigenfunctions of the Hamiltonian, identify \textit{PT}-symmetry unbroken and broken quantum phases and quantum phase transitions between them. The temporal oscillations of the dynamic susceptibility of the qubits polarization ($z$-projection of the total spin), $\chi(t)$, relate to {\it ac} induced transitions between different eigenstates and we analyze the dependencies of the oscillations frequency and the amplitude on the gain/loss parameter $\gamma$ and the interaction strength $g$. Studying the time dependence of $\chi(t)$ we observe different types of oscillations, i.e. undamped, heavily damped and amplified ones, related to the transitions between eigenstates with broken (unbroken) $PT$-symmetry. These predictions can be verified in the microwave transmission experiments allowing controlled simulation of the pHH systems.

Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor

In this work, we study the dynamics of quantum coherence (total coherence, global coherence and local coherence) evolving under a local PT-symmetric Hamiltonian in maximally entangled bipartite and tripartite states. Our results indicate that quantum coherence in the bipartite state oscillates in the unbroken phase regime of the PT-symmetric Hamiltonian. Interestingly, in the broken phase regime, while the global coherence decays exponentially, the local and total coherences enter a “freezing” regime where they attain a stable value over time. A similar pattern is observed for the dynamics of total and local coherences in the maximally entangled tripartite state, while the dynamics of global coherence in this state differs from that of the bipartite state. Our study provides some novel insights into the independent contributions of global and local coherence to the freezing and oscillatory behavior of the total quantum coherence in both the unbroken and the broken phases, respectively. These results were experimentally validated for a maximally entangled bipartite state on a three-qubit nuclear magnetic resonance (NMR) quantum processor, with one of the qubits acting as an ancilla. The experimental results match well with the theoretical predictions, up to experimental errors.

Topological Phase Transitions and Mobility Edges in Non-Hermitian Quasicrystals.

Non-Hermiticity significantly enriches the properties of topological models, leading to exotic features such as the non-Hermitian skin effects and non-Bloch bulk-boundary correspondence that have no counterparts in Hermitian settings. Its impact is particularly illustrating in non-Hermitian quasicrystals where the interplay between non-Hermiticity and quasiperiodicity results in the concurrence of the delocalization-localization transition, the parity-time (PT)-symmetry breaking, and the onset of the non-Hermitian skin effects. Here, we experimentally simulate non-Hermitian quasicrystals using photonic quantum walks. Using dynamic observables, we demonstrate that the system can transit from a delocalized, PT-symmetry broken phase that features non-Hermitian skin effects, to a localized, PT-symmetry unbroken phase with no non-Hermitian skin effects. The measured critical point is consistent with the theoretical prediction through a spectral winding number, confirming the topological origin of the phase transition. More interestingly, we also provide the first experimental evidence for mobility edges which are induced by non-Hermiticity. Our Letter opens the avenue of investigating the interplay of non-Hermiticity, quasiperiodicity, and spectral topology in open quantum systems.

Witnessing criticality in non-Hermitian systems via entopic uncertainty relation

Non-Hermitian systems with exceptional points lead to many intriguing phenomena due to the coalescence of both eigenvalues and corresponding eigenvectors, in comparison to Hermitian systems where only eigenvalues degenerate. In this paper, we propose an alternative and accurate proposal based on the entropy uncertainty relation (EUR) to detect the exceptional points and identify different phases of the non-Hermitian systems. In particular, we reveal a general connection between the EUR and the exceptional points of non-Hermitian system. Compared to the unitary Hermitian dynamics, the behaviors of EUR in the non-Hermitian system are well defined into two different ways depending on whether the system is located in unbroken or broken phase regimes. In the unbroken phase regime where EUR undergoes an oscillatory behavior, while in the broken phase regime where the oscillation of EUR breaks down. Moreover, we identify the critical phenomena of non-Hermitian systems in terms of the EUR in the dynamical limit. It is found that the EUR can detect exactly the critical points of non-Hermitian systems beyond (anti-)PT symmetric systems. Finally, we comment on the prospective experimental situation.

Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays.

We propose two non-Hermitian arrays consisting of N = 2l + 1 waveguides and exhibiting parity-time (P T) or anti-P T symmetry for investigating light transfer dynamics based on Nth-order exceptional points (EPs). The P T-symmetric array supports two Nth-order EPs separating an unbroken and a broken phase with real and imaginary eignvalues, respectively. Light transfer dynamics in this array exhibits radically different behaviors, i.e. a unidirectional oscillation behavior in the unbroken phase, an edge-towards localization behavior in the broken phase, and a center-towards localization behavior just at Nth-order EPs. The anti-P T-symmetric array supports also two Nth-order EPs separating an unbroken and a broken phase, which refer however to imaginary and real eigenvalues, respectively. Accordingly, light transfer dynamics in this array exhibits a center-towards localization behavior in the unbroken phase and an origin-centered oscillation behavior in the broken phase. These nontrivial light transfer behaviors and their controlled transitions are not viable for otherwise split lower-order EPs and depend on the underlying SU(2) symmetry of spin-l matrices.

Experimental observation of partial parity-time symmetry and its phase transition with a laser-driven cesium atomic gas

Realization and manipulation of parity-time (PT) symmetry in multidimensional systems are highly desirable for exploring nontrivial physics and uncovering exotic phenomena in non-Hermitian systems. Here, we report the first experimental observation of partial PT (pPT) symmetry in a cesium atomic gas coupled with laser fields, where a two-dimensional pPT-symmetric optical potential for probe laser beam is created. A transition of the pPT symmetry from an unbroken phase to a broken one is observed through changing the beam-waist ratio of the control and probe laser beams, and the domains of unbroken, broken, and non-pPT phases are also discriminated unambiguously. Moreover, we develop a technique to precisely determine the location of the exceptional point of the pPT symmetry breaking by measuring the asymmetry degree of the probe-beam intensity distribution. The findings reported here pave the way for controlling multidimensional laser beams in non-Hermitian systems via laser-induced atomic coherence, and have potential applications for designing new types of light amplifiers and attenuators