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Register a new userFourth-Order Exceptional Points in Correlated Quantum Many-Body Systems
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Non-Hermtian (NH) Hamiltonians effectively describing the physics of dissipative systems have become an important tool with applications ranging from classical meta-materials to quantum many-body systems. Exceptional points, the NH counterpart of spectral degeneracies, are among the paramount phenomena unique to the NH realm. While realizations of second-order exceptional points have been reported in a variety of microscopic models, higher-order ones have largely remained elusive in the many-body context, as they in general require fine tuning in high-dimensional parameter spaces. Here, we propose a microscopic model of correlated fermions in three spatial dimensions and demonstrate the occurrence of interaction-induced fourth-order exceptional points that are protected by chiral symmetry. We demonstrate their stability against symmetry breaking perturbations and investigate their characteristic analytical and topological properties.
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Dynamical phase transitions extend the notion of criticality to non-stationary settings and are characterized by sudden changes in the macroscopic properties of time-evolving quantum systems. Investigations of dynamical phase transitions combine aspects of symmetry, topology, and non-equilibrium physics, however, progress has been hindered by the notorious difficulties of predicting the time evolution of large, interacting quantum systems. Here, we tackle this outstanding problem by determining the critical times of interacting many-body systems after a quench using Loschmidt cumulants. Specifically, we investigate dynamical topological phase transitions in the interacting Kitaev chain and in the spin-1 Heisenberg chain. To this end, we map out the thermodynamic lines of complex times, where the Loschmidt amplitude vanishes, and identify the intersections with the imaginary axis, which yield the real critical times after a quench. For the Kitaev chain, we can accurately predict how the critical behavior is affected by strong interactions, which gradually shift the time at which a dynamical phase transition occurs. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems, and our approach can immediately be applied in higher dimensions.
Exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce, are ubiquitous and unique features of non-Hermitian systems. Second-order EPs are by far the most studied due to their abundance, requiring only the tuning of two real parameters, which is less than the three parameters needed to generically find ordinary Hermitian eigenvalue degeneracies. Higher-order EPs generically require more fine-tuning, and are thus assumed to play a much less prominent role. Here, however, we illuminate how physically relevant symmetries make higher-order EPs dramatically more abundant and conceptually richer. More saliently, third-order EPs generically require only two real tuning parameters in presence of either $PT$ symmetry or a generalized chiral symmetry. Remarkably, we find that these different symmetries yield topologically distinct types of EPs. We illustrate our findings in simple models, and show how third-order EPs with a generic $sim k^{1/3}$ dispersion are protected by PT-symmetry, while third-order EPs with a $sim k^{1/2}$ dispersion are protected by the chiral symmetry emerging in non-Hermitian Lieb lattice models. More generally, we identify stable, weak, and fragile aspects of symmetry-protected higher-order EPs, and tease out their concomitant phenomenology.
We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative systems. The space of controllable parameters of isolated quantum many-body systems is endowed with a Riemannian quantum metric structure, which can be exploited when such systems are driven adiabatically. Here, we use this metric structure to construct optimal protocols in order to accomplish the task of adiabatic ground-state preparation in a fixed amount of time. Such optimal protocols are shown to be geodesics on the parameter manifold, maximizing the local fidelity. Physically, such protocols minimize the average energy fluctuations along the path. Our findings are illustrated on the Landau-Zener model and the anisotropic XY spin chain. In both cases we show that geodesic protocols drastically improve the final fidelity. Moreover, this happens even if one crosses a critical point, where the adiabatic perturbation theory fails.
A numerical approach is presented that allows to compute nonequilibrium steady state properties of strongly correlated quantum many-body systems. The method is imbedded in the Keldysh Greens function formalism and is based upon the idea of the variational cluster approach as far as the treatment of strong correlations is concerned. It appears that the variational aspect is crucial as it allows for a suitable optimization of a reference system to the nonequilibrium target state. The approach is neither perturbative in the many-body interaction nor in the field, that drives the system out of equilibrium, and it allows to study strong perturbations and nonlinear responses of systems in which also the correlated region is spatially extended. We apply the presented approach to non-linear transport across a strongly correlated quantum wire described by the fermionic Hubbard model. We illustrate how the method bridges to cluster dynamical mean-field theory upon coupling two baths containing and increasing number of uncorrelated sites.
Quantum phase transitions are a ubiquitous many-body phenomenon that occurs in a wide range of physical systems, including superconductors, quantum spin liquids, and topological materials. However, investigations of quantum critical systems also represent one of the most challenging problems in physics, since highly correlated many-body systems rarely allow for an analytic and tractable description. Here we present a Lee-Yang theory of quantum phase transitions including a method to determine quantum critical points which readily can be implemented within the tensor network formalism and even in realistic experimental setups. We apply our method to a quantum Ising chain and the anisotropic quantum Heisenberg model and show how the critical behavior can be predicted by calculating or measuring the high cumulants of properly defined operators. Our approach provides a powerful formalism to analyze quantum phase transitions using tensor networks, and it paves the way for systematic investigations of quantum criticality in two-dimensional systems.
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