non-Hermitian Model Research Articles

Three perspectives on entropy dynamics in a non-Hermitian two-state system

Abstract A comparative study of entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. To begin with, we illustrate the phase portrait of this non-Hermitian model on the Bloch sphere, elucidating the changes in behavior as one moves across the phase transition boundary, as well as the emergent feature of unidirectional state evolution in the spontaneously broken PT-symmetry regime. This is followed by an examination of the purity and entropy dynamics. Here we distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping. In this it is demonstrated that their differences are rooted in the treatment of the environmental coupling mode. For unbroken PT symmetry of the system, a notable characteristic feature of the perspective taken is the presence or absence of purity oscillations, with an associated entropy revival. The description of the system is then continued from its PT-symmetric pseudo-Hermitian phase into the regime of spontaneously broken symmetry, in the latter two approaches through a non-analytic operator-based continuation, yielding a Lindblad master equation based on the PT charge operator C. This phase transition indicates a general connection between the pseudo-Hermitian closed-system and the Lindbladian open-system formalism through a spontaneous breakdown of the underlying physical reflection symmetry.

Temporal entanglement barriers in dual-unitary Clifford circuits with measurements

We study temporal entanglement in dual-unitary Clifford circuits with probabilistic measurements preserving spatial unitarity. We exactly characterize the temporal entanglement barrier in the measurement-free regime, exhibiting ballistic growth and decay and a volume-law peak. In the presence of measurements, we relate the temporal entanglement to the scrambling properties of the circuit. For “good scramblers” measurements do not qualitatively change the temporal entanglement profile but only result in a reduced entanglement velocity, whereas for “poor scramblers” the initial ballistic growth of temporal entanglement with bath size is modified to diffusive. This difference is understood through a mapping of the underlying operator dynamics to a biased and an unbiased persistent random walk, respectively. In the latter case measurements additionally modify the ballistic decay to the perfect dephaser limit, with vanishing temporal entanglement, to an exponential decay, which we describe through a spatial transfer matrix method. This spatial dynamics is shown to be described by a non-Hermitian hopping model, exhibiting a PT-breaking transition at a critical measurement rate p=1/2. In all cases the peak value of the temporal entanglement barrier exhibits volume-law scaling for all measurement rates. Published by the American Physical Society 2024

TT¯ deformation on non-Hermitian two coupled SYK model

We investigate TT¯ deformation on non-Hermitian coupled Sachdev-Ye-Kitaev (SYK) model and the holographic picture. The relationship between ground state and thermofield double state is preserved under the TT¯ deformation. We prove that TT¯ deformed theory provides a reparametrization in large N limit. We numerically calculate the deformation effects on the correlation function in imaginary time and the free energy. The thermodynamic phase structures show the equivalence of the wormhole-black hole picture between non-Hermitian model and Hermitian model still holds under TT¯ deformation. The correlation function in Lorentz time, revival dynamic, and the deformed holography are also evaluated. Published by the American Physical Society 2024

Quasi-stationary alpha-states from non-Hermitian Hamiltonians of even-even heavy isotones

Three isotone groups (N=128,130,132) with alpha-decaying, short-lifetime even-even nuclei of large mass number are studied in order to show that the tunneling phase of the alpha decay process is appropriately describable by a specific non-hermitian mean-field model. In this model the mean-field lifetime of the alpha cluster is extracted directly by the complex diagonalization of the non-hermitian Hamiltonian of the system. In this paper, we demonstrate that by calculating the mean-field width of the alpha clusters, in each isotone groups, by non-perturbative complex spectral calculations, then, due to the distinct patterns the isotones are naturally organized into with respect to the half-life and proton number, the total width of the alpha-decay can be approximated by matching the calculated results to experimental data.

Non-hermitian Dirac theory from Lindbladian dynamics

This study investigates the intricate relationship between dissipative processes of open quantum systems and the non-Hermitian quantum field theory of relativistic fermionic systems. By examining the influence of dissipative effects on Dirac fermions via Lindblad formalism, we elucidate the effects of coupling relativistic Dirac particles with the environment and show the lack of manifest Lorentz invariance. Employing rigorous theoretical analysis, we generalize the collisionless Boltzmann equations for the relativistic dissipation-driven fermionic system and find the Lyapunov equation, which governs the stationary solutions. Using our formalism, one presents a simple non-Hermitian model that the relativistic fermionic particles and anti-particles are stable. Going further, using the solution to the Lyapunov equations, one analyses the effect of dissipation on the stationary charge imbalance of this non-Hermitian model and finds that the dissipation can induce a new kind of charge imbalance compared with the collisionless equilibrium case.

Periodicity alters topological states in thermal diffusion system

Topological edge states are a ubiquitous phenomenon across diverse wave systems, including electromagnetic, acoustic and quantum systems. In contrast to wave systems, thermal transport is a kind of diffusion system characterized by pure dissipation. The imposition of different boundary conditions can significantly influence the evolution of thermal system, leading to the appearance of different topological states, which haven't been systematically analyzed yet, especially in practical heat transfer structures. In this work, via a non-Hermitian thermal diffusion lattice model, we discuss the periodicity-dependent topological states. Through rigorous theoretical analysis and numerical simulations of the temperature field, the Hamiltonian is obtained whose eigenvalues are purely imaginary corresponding to the decay rate of the temperature field. Our work paves the way for the investigation of how periodicity alters topological states in thermal diffusion systems, potentially revolutionizing the design of thermal metamaterials for topological thermal protection in thermal management.

Linear response theory for transport in non-Hermitian [formula omitted]-symmetric models

We analyzed the influence of dissipative non-Hermitian terms on electrical transport in one-dimensional non-Hermitian PT-symmetric models, which presents chiral symmetry. The combination of periodic modulation and non-Hermitian effects opens up exciting avenues for exploring new phases of matter and understanding of the role of non-Hermitian physics in topological systems. The effective Hermitian Hamiltonian has always a higher dimension than the corresponding non-Hermitian one. We analyzed the effect of periodic hopping modulation on Su-Schrieffer-Heeger chain, that exhibits the non-Hermiticity in the presence of an complex staggered potential, where this dissipative non-Hermitian extension modifies the features of the topological trivial phase and the topological nontrivial phase.

Critical behavior of dirty free parafermionic chains

Abstract A family of $\mathbb Z_n$-symmetric non-Hermitian models of Baxter was shown by Fendley to be exactly solvable via a parafermionic generalization of the Clifford algebra. We study these models with spatially random couplings, and obtain several exact results on thermodynamic singularities as the distributions of couplings are varied. We find that these singularities, independent of $n$, are identical to those in the random transverse-field Ising chain; correspondingly the models host infinite-randomness critical points. Similarities in structure to exact methods for random Ising models, a strong-disorder renormalization group, and generalizations to other models with free spectra, are discussed.

Non-Hermitian linear-response theory for spin diffusion in quantum systems

Spin transport theory of non-Hermitian quantum systems, where the non-Hermiticity led to a series of exotic phenomena when the system experiences dissipation to an environment is proposed. The goal is a better understanding of the spin diffusion in the one-dimensional non-Hermitian XXZ model which allows the transport coefficients be computed analytically. Moreover, we analyzed the electric transport in the one-dimensional non-Hermitian Hubbard model which is a very important model of electrons strongly correlated, where we have investigated the effect of non-Hermitian parameters like the imaginary hopping on AC and DC conductivities of the system. We analyzed the large U limit of this model, where such non-Hermiticity contributes with a minus sign in the virtual exchange of quasiparticles and the behavior of the ground state energy and low-lying excitations is reversed.

One-way optomechanical interaction between nanoparticles

Within a closed system, physical interactions are reciprocal. However, the effective interaction between two entities of an open system may not obey reciprocity. Here, we describe a non-reciprocal interaction between nanoparticles which is one-way, almost insensitive to the interparticle distance, and scalable to many particles. The interaction we propose is based on the non-conservative optical forces between two nanoparticles with highly directional scattering patterns. However, we elucidate that scattering patterns can in general be very misleading about the interparticle forces. We introduce zeroth- and first-order non-reciprocity factors to precisely quantify the merits of any optomechanical interaction between nanoparticles. Our proposed one-way interaction could constitute an important step in the realization of mesoscopic heat pumps and refrigerators, the study of non-equilibrium systems, and the simulation of non-Hermitian quantum models.

Quantum correlation, entanglement in the kagome lattice non-Hermitian quantum systems

Quantum correlation in the antiferromagnetic XXZ model on kagome lattice and non-Hermitian tight binding model on kagome lattice are investigated. For the Hermitian XXZ model on kagome lattice, the calculations are performed for different extensions of the model with single-ion anisotropy and out-of-plane Dzyaloshinskii–Moriya interaction (DMI). We get the von Neumann entropy as a function of the DMI interaction, anisotropy and single-ion anisotropy with aim to verify the effect of these corrections that occurs in real magnetic systems on quantum correlation. Moreover, the effect of DMI interaction, anisotropy and single-ion anisotropy is investigated on concurrence and entanglement negativity as well. For the non-Hermitian tight binding model on kagome lattice, we analyzed quantum correlation using the entanglement negativity as entanglement measure which is more adequate in this case.

Non-Hermitian transport in Glauber-Fock optical lattices

The effect of a non-unitary transformation on an initial Hermitian operator is studied. The initial (Hermitian) optical system is a Glauber-Fock optical lattice. The resulting non-Hermitian Hamiltonian models an anisotropic (Glauber-Fock) waveguide array of the Hatano-Nelson-type. Several cases are analyzed and exact analytical solutions for both the Hermitian and non-Hermitian Schrödinger problems are given, as they are simply connected. Indeed, such transformation can be regarded as a non-unitary Supersymmetric transformation and the resulting non-Hermitian Hamiltonian can be considered as representing an open system that interchanges energy with the environment.

Machine learning of knot topology in non-Hermitian band braids

The deep connection among braids, knots and topological physics has provided valuable insights into studying topological states in various physical systems. However, identifying distinct braid groups and knot topology embedded in non-Hermitian systems is challenging and requires significant efforts. Here, we demonstrate that an unsupervised learning with the representation basis of su(n) Lie algebra on n-fold extended non-Hermitian bands can fully classify braid group and knot topology therein, without requiring any prior mathematical knowledge or any pre-defined topological invariants. We demonstrate that the approach successfully identifies different topological elements, such as unlink, unknot, Hopf link, Solomon ring, trefoil, and so on, by employing generalized Gell-Mann matrices in non-Hermitian models with n=2 and n=3 energy bands. Moreover, since eigenstate information of non-Hermitian bands is incorporated in addition to eigenvalues, the approach distinguishes the different parity-time symmetry and breaking phases, recognizes the opposite chirality of braids and knots, and identifies out distinct topological phases that were overlooked before. Our study shows significant potential of machine learning in classification of knots, braid groups, and non-Hermitian topological phases.

Non-Hermitian dynamical topological winding in photonic mesh lattices.

Topological winding in non-Hermitian systems is generally associated to the Bloch band properties of lattice Hamiltonians. However, in certain non-Hermitian models, topological winding naturally arises from the dynamical evolution of the system and is related to a new form of geometric phase. Here we investigate dynamical topological winding in non-Hermitian photonic mesh lattices, where the mean survival time of an optical pulse circulating in coupled fiber loops is quantized and robust against Hamiltonian deformations. The suggested photonic model could provide an experimentally accessible platform for the observation of non-Hermitian dynamical topological windings.

The funneling effect in a non-Hermitian Anderson model

The topological funneling effect, i.e., the motion of an arbitrary excitation to a focal point of the lattice no matter where the lattice is excited, is a dynamical effect due to the non-Hermitian skin effect. This effect disappears in the presence of strong disorder where the system is topologically trivial. In Anderson localized regime with complex spectrum, the motion shows jumpy behavior and the focal point can be any point along the lattice as it is not possible to say its exact place in an experiment a priori. We study transport phenomena in a non-Hermitian system, exhibiting both funneling effect and non-Hermitian jumps. We show that the competition between the skin and Anderson localizations may result in the creation of an extended eigenstate. This can lead to disorder-induced dynamical delocalization in topologically nontrivial region.

Gain-driven synchronization and asymmetric bound states in the continuum within non-Hermitian circuit model

The gain-driven emission in gain–loss coupling systems attains significant interest. In this work, we study the monochromatic oscillation of a gain–loss coupling system through a circuit model, where the monochromacy is manifested as the gain-driven synchronization of two coupled oscillators. The synchronized oscillation in this model is theoretically studied and experimentally manifested. Benefiting from the conceptual simplicity of a circuit model, a pair of asymmetric long-living states is found among the unstable gain-driven monochromatic oscillations, corresponding to bound states in the continuum of coupling physics.

Parsing skin effect in a non-Hermitian spinless BHZ-like model

This work comprehensively investigates the non-Hermitian skin effect (NHSE) in a spinless Bernevig-Hughes-Zhang -like model in one dimension. It is generally believed that a system with non-reciprocal hopping amplitudes demonstrates NHSE. However, we show that there are exceptions, and more in-depth analyses are required to decode the presence of NHSE or its variants in a system. The fascinating aspects of our findings, depending on the inclusion of non-reciprocity in the inter-orbital hopping terms, concede the existence of conventional NHSE or NHSE at both edges and even a surprising absence of NHSE. The topological properties and the (bi-orthogonal) bulk-boundary correspondence, enumerated via computation of the (complex) Berry phase and spatial localization of the edge modes, highlight the topological phase transitions occurring therein. Further, to facilitate a structured discussion of the non-Hermitian model, we split the results into PT symmetric and non- PT symmetric cases with a view to comparing the two.

Features, Paradoxes and Amendments of Perturbative Non-Hermitian Quantum Mechanics

Quantum mechanics of unitary systems is considered in quasi-Hermitian representation and in the dynamical regime in which one has to take into account the ubiquitous presence of perturbations, random or specific. In this paper, it is shown that multiple technical obstacles encountered in such a context can be circumvented via just a mild amendment of the so-called Rayleigh–Schrödinger perturbation–expansion approach. In particular, the quasi-Hermitian formalism characterized by an enhancement of flexibility is shown to remain mathematically tractable while, on the phenomenological side, opening several new model-building horizons. It is emphasized that they include, i.a., the study of generic random perturbations and/or of multiple specific non-Hermitian toy models. In parallel, several paradoxes and open questions are shown to survive.

Topological phase transitions in the non-Hermitian SSH model with long-range hopping terms induced by gains and losses

The latest progress in the one-dimensional chain SSH model provide the basic understanding of non-Hermitian topological phases. By periodically introducing the gains and losses of imaginary potential ig,-ig,-ig,ig with anti-PT symmetry, we have investigated the topological property of non-Hermitian SSH model with long-range hopping terms. We find that the gains and losses of imaginary potential causes the model to exhibit non-Hermiticity, and the non-Hermiticity induces system to undergo topological phase transitions from topologically trivial phase with non-Hermitian winding number 0 to topologically nontrivial phase with non-Hermitian winding number 1 and −1. The introduction of gains and losses greatly broadens the topological non-trivial region and play a non-trivial role in the model. We fully characterize the topological phase transitions by the band gap closing-reopening, the non-Hermitian winding numbers v and the hidden Chern number C.

Exploring the impact of fluctuation-induced criticality on non-Hermitian skin effect and quantum sensors

In this paper we present a concrete example comparing the results predicted by non-Hermitian quantum mechanics with those of a more comprehensive description that considers environment-induced fluctuations. Our results highlight inaccuracies in the non-Hermitian model. Specifically, we investigate the non-Hermitian skin effect and sensor in the Hatano-Nelson model, contrasting it with a more precise Lindblad description. Our analysis reveals that these phenomena can undergo breakdown when environmental fluctuations come to the forefront, resulting in a nonequilibrium phase transition from a localized skin phase to a delocalized phase. Beyond this specific case study, we engage in a broader discussion regarding the interpretations and implications of non-Hermitian quantum mechanics. This examination serves to broaden our understanding of these phenomena and their potential consequences. Published by the American Physical Society 2024