This paper proposes a non-Hermitian class of dynamic critical phenomenon beyond the classification by Hohenberg and Halperin triggered by the coalescence of the collective eigenmodes to the Goldstone mode. The authors find an anomalous enhancement of fluctuations that diverge at $d\ensuremath{\le}4$, and many-body correlation effects that become relevant at $d<8$.
This paper proposes a non-Hermitian class of dynamic critical phenomenon beyond the classification by Hohenberg and Halperin triggered by the coalescence of the collective eigenmodes to the Goldstone mode. The authors find an anomalous enhancement of fluctuations that diverge at d\ensuremath≤4, and many-body correlation effects that become relevant at d<8.
In recent years, two independent research fields, i.e. non-Hermitian andstrongly correlated systems have been merged, forming an important researchfield in physics. The progress of relevant theories and experiments hasreshaped our understanding of matter. In this field, the research object isnot limited to the influence of non-Hermiticity on the energy spectrum andthe eigenstate properties of many-body systems. Researchers have paid more attentionto the manipulation of quantum states. It is universally received that the exceptional point is the most significant featurethat distinguishes non-Hermitian quantum mechanics from Hermitian quantum mechanics. In addition to the recent advances in non-Hermitian topological band theory and quantum sensing around the exceptional points, this paper concentrates on the non-Hermitian critical dynamical phenomenon and its application to the quantum many-body system. When the system has an exceptional point, an arbitrary initial state belonging to the coalescent subspace will be projected on the coalescent state. Based on the directionality of the evolved quantum state, this paper reviews our several representative researches in recent years, including local-field-induced dynamical magnetization, quantum phase transition in transverse field, Ising model at non-zero temperature, quantum mold casting in the center-environment system, as well as superconducting state preparation in the non-Hermitian strongly correlated system. We also focus on the new preparation methods and detection schemes of non-equilibrium quantum states related to exception points.
Critical exceptional points (CEPs) are nonequilibrium critical points in open many-body systems at which multiple collective excitation modes coalesce. CEPs are known to amplify classical fluctuations, but their effect on genuinely \textit{quantum} fluctuations remains unclear. Here, we show that dissipative collective-spin systems hosting CEPs exhibit parametrically enhanced steady-state \textit{quantum} spin squeezing. Close to the CEP, the optimally squeezed variance scales as ∣Z∣, whereas the anti-squeezed variance diverges as ∣Z∣−1, with Z the dimensionless order parameter. Importantly, the anti-squeezed fluctuation direction asymptotically aligns with the coalescing eigenvector of the stability matrix, reflecting the defective nature of the CEP dynamics. These scalings are robust against dephasing channels generated by spin components orthogonal to the coalesced critical collective mode. Our results identify CEPs as a route to engineering steady-state anisotropic quantum fluctuations and correlations in driven-dissipative platforms.
Real-time dynamics of strongly correlated systems, in particular its critical dynamics near phase transitions, have been always on the cutting edge of studies in diverse fields of physics, e.g., high energy physics, condensed matter, holography, etc. In this work, we investigate the critical damping of collective modes associated with spontaneous breaking of approximate symmetries, which are called pseudo-Goldstone modes, in strongly correlated systems. Using the Schwinger-Keldysh field theory, we find a universal pseudo-Goldstone damping via the critical O(N) model that has never been found before by other approaches. Different from the conventional damping found in holography and hydrodynamics, the new one is controlled by critical fluctuations, hence is invisible in mean-field systems or strongly correlated systems with classical gravity duals. Since the critical damping depends solely on the universalities of the critical point, irrespective of the microscopic details, our conclusion should be applicable to a wide class of interacting systems. Strongly correlated systems exhibit universal dynamics near phase transitions, from particle to condensed matter physics. However, despite the successes of various theoretical approaches, systematic treatments of fluctuations are scarce. Here the authors unveil a universal damping of pseudo-Goldstone modes in systems with approximate symmetries, advancing our understanding of near-critical dynamics in several contexts.
Exceptional points (EPs) represent non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to enhanced sensitivity and critically damped dynamics. We demonstrate that when an EP coincides with a dissipative phase transition in an extended open Dicke model of two cavities coupled to a collective spin, the critical fluctuations are strongly amplified and governed by modified critical exponents. Numerical results reveal enhanced critical scaling in both the normal and superradiant phases, in agreement with an analytical theory based on the Jordan-block structure of the linearized dynamical matrix at the EP. Our results establish EPs as a mechanism to engineer critical scaling in open quantum systems, with potential applications to critical quantum sensing.
Exceptional points describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier et al., Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose–Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of superfluidity and to the scattering of classical particles. We propose an experimental set-up to directly probe this exceptional point, and demonstrate its feasibility with the aid of numerical calculations. Our work fosters the observation of exceptional points in nonequilibrium many-body quantum systems.
In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of O ( N ) field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of 2 N − 3 Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions d < 4 they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for N = 2 , and a generalization for arbitrary N , which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an x y magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium. Published by the American Physical Society 2024