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We study the non-equilibrium dynamics of the superconducting order parameter in the Hatsugai-Kohmoto (HK) model. In the absence of superconductivity, its ground state is a non-Fermi liquid, whose properties are controlled by the HK interaction. Our protocol involves quantum quenching the HK interaction but leaving the interaction responsible for superconductivity unchanged. We map out the non-equilibrium dynamical phase diagram of the interacting model which contains three phases where, at long times, the order parameter amplitude vanishes, approaches a constant value or persistently oscillates. We also investigate the Loschmidt echo in searching for dynamical quantum phase transition, and find no significant correlation between the three phases and the non-analytic temporal behaviour of the Loschmidt echo. The momentum space entanglement entropy between positive and negative momentum modes, relevant for Coopair pairing, is calculated. Counterintuitively, this momentum space entanglement does not change significantly during the quench dynamics and its value remains reasonably large even for vanishing superconducting order parameter. Nevertheless, its derivative with respect to the HK interaction signals the dynamical phase transition associated to the late time vanishing of superconductivity., Comment: 10 pages, 8 figures

We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two $XY$ spin chains that are coupled through Ising $ZZ$ interaction. The spin ladder model is then examined within the semiclassical limit using a spin-coherent state basis, where the dynamics is governed by a set of coupled Landau-Lifshitz-Gilbert equations. The non-Hermitian interactions in this model generate a spin-transfer torque term. We analyze the system's evolution toward several potential steady states, including a state of decoupled chains that is accessible when each chain has uniform initial conditions. Other possible steady states involve dimerized configurations with decoupled rungs, where the rung spins are either ferromagnetically or antiferromagnetically coupled, depending on the sign of the imaginary interactions. The spin dynamics is then studied in the infinite-temperature limit, which favors dimerized steady states. Despite the decoupled rungs, we observe the formation of ferromagnetic domains along each chain in the steady state. Additionally, we investigate the spin correlation functions and identify signatures of anomalous spin dynamics., Comment: 12 pages, 9 figures

We explore the near adiabatic dynamics in a non-Hermitian quantum many-body system by investigating a finite-time ramp of the imaginary vector potential in the interacting Hatano-Nelson model. The excess energy, the Loschmidt echo, and the density imbalance are analyzed using bosonization and exact diagonalization. The energy becomes complex valued, despite the instantaneous Hamiltonian having the same real spectrum throughout. The adiabatic limit is approached very slowly through damped oscillations. The decay scales with $\tau^{-1}$ with $\tau$ the ramp duration, while the oscillation period is $2L/v$ with $v$ the Fermi velocity and $L$ the system length. Yet, without the need for auxiliary controls, a shortcut to adiabaticity is found for ramp times commensurate with the period. Our work highlights the intricate interplay of adiabaticity and non-Hermitian many-body physics., Comment: 11 pages, 4 figures

Controlling many-body quantum systems is a highly challenging task required to advance quantum technologies. Here, we report progress in controlling gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). To do so, we investigate the exact dynamics of the TLL induced by an interaction quench, making use of the $SU(1,1)$ dynamical symmetry group and the Schr\"odinger picture. First, we demonstrate that this approach is useful to perform a shortcut to adiabaticity, that cancels the final non-adiabatic residual energy of the driven TLL and is experimentally implementable in the semiclassical limit of the sine-Gordon model. Second, we apply this framework to analyze various driving schemes in finite time, including linear ramps and smooth protocols., Comment: 14+11 pages, 10 figures

Parafermions are anyons with the potential for realizing non-local qubits that are resilient to local perturbations. Compared to Majorana zero modes, braiding of parafermions implements an extended set of topologically protected quantum gates. This, however, comes at the price that parafermionic zero modes can not be realized in the absence of strong interactions whose theoretical description is challenging. In the present work, we construct a simple lattice model for interacting spinful electrons with parafermionic zero energy modes. The explicit microscopic nature of the considered model highlights new realization avenues for these exotic excitations in recently fabricated quantum dot arrays. By density matrix renormalization group calculations, we identify a broad range of parameters, with well-localized zero modes, whose parafermionic nature is substantiated by their unique $8\pi$ periodic Josephson spectrum.

We focus on the biorthogonal work statistics of the interacting many-body Hatano-Nelson model after switching on the imaginary vector potential. We introduce a generalized Loschmidt echo $G(t)$ utilizing the biorthogonal metric operator. It is well suited for numerical analysis and its Fourier transform yields the probability distribution of work done. The statistics of work displays several universal features, including an exponential decay with the square of both the system size and imaginary vector potential for the probability to stay in the ground state. Additionally, its high energy tail follows a universal power law with exponent $-3$. This originates from the peculiar temporal power law decay of $G(t)$ with a time dependent exponent. The mean and the variance of work scale linearly and logarithmically with system size while all higher cumulants are non-extensive. Our results are relevant for non-unitary field theories as well., Comment: 7 pages, 3 figures

Based on our first detailed $^{181}$Ta nuclear quadrupole resonance (NQR) studies from 2017 on the Weyl semimetal TaP, we now extended our NQR studies to another Ta-based monopnictide TaAs. In the present work, we have determined the temperature-dependent $^{181}$Ta-NQR spectra, the spin-lattice relaxation time $T_{1}$, and the spin-spin relaxation time $T_{2}$. We found the following characteristic features that showed great contrast to what was found in TaP: (1) The quadrupole coupling constant and asymmetry parameter of EFG, extracted from three NQR frequencies, have a strong temperature dependence above $\sim$80 K that cannot be explained by the density functional theory calculation incorporating the thermal expansion of the lattice. (2) The temperature dependence of the spin-lattice relaxation rate, $1/T_{1} T$, shows a $T^{4}$ power law behavior above $\sim$30 K. This is a great contrast with the $1/T_{1} T \propto T^{2}$ behavior found in TaP, which was ascribed to the magnetic excitations at the Weyl nodes with a temperature-dependent orbital hyperfine coupling. (3) Regarding the nuclear spin-spin interaction, we found the spin-echo signal decays with the pulse separation simply by a Lorentzian function in TaAs, but we have observed spin-echo modulations in TaP that is most likely due to the indirect nuclear spin-spin coupling via virtually excited Weyl fermions. From our experimental findings, we conclude that the present NQR results do not show dominant contributions from Weyl fermion excitations in TaAs., Comment: 8 pages, 10 figures

We investigate the decay of spatial correlations of $\mathcal{PT}$-symmetric non-Hermitian one-dimensional models that host higher-order exceptional points. Beyond a certain correlation length, they develop anomalous power-law behavior that indicates strong suppression of correlations in the non-Hermitian setups as compared to the Hermitian ones. The correlation length is also reflected in the entanglement entropy where it marks a change from logarithmic growth at short distance to a constant value at large distance, characteristic of an insulator, despite the spectrum being gapless. Two different families of models are investigated, both having a similar spectrum constrained by particle-hole symmetry. The first model offers an experimentally attractive way to generate arbitrary higher-order exceptional points and represents a non-Hermitian extension of the Dirac Hamiltonian for general spin. At the critical point it displays a decay of the correlations $\sim 1/x^2$ and $1/x^3$ irrespective of the order of the exceptional point. The second model is constructed using unidirectional hopping and displays enhanced suppression of correlations $\sim 1/x^a$, $a\ge 2$ with a power law that depends on the order of the exceptional point., Comment: 19 pages, 11 figures

We investigate the quantum quench dynamics of the interacting Hatano-Nelson model with open boundary conditions using both abelian bosonization and numerical methods. Specifically, we follow the evolution of the particle density and current profile in real space over time by turning the imaginary vector potential on or off in the presence of weak interactions. Our results reveal spatio-temporal Friedel oscillations in the system with light cones propagating ballistically from the open ends, accompanied by local currents of equal magnitude for both switch off and on protocols. Remarkably, the bosonization method accurately accounts for the density and current patterns with a single overall fitting parameter. The continuity equation is satisfied by the long wavelength part of the density and current, despite the non-unitary time evolution when the Hatano-Nelson term is switched on., Comment: 9 pages, 4 figures

We study the dissipative dynamics of a one-dimensional bosonic system described in terms of the bipartite Bose-Hubbard model with alternating gain and loss. This model exhibits the $\mathcal{PT}$ symmetry under some specific conditions and features a $\mathcal{PT}$-symmetry phase transition. It is characterized by an order parameter corresponding to the population imbalance between even and odd sites, similar to the continuous phase transitions in the Hermitian realm. In the noninteracting limit, we solve the problem exactly and compute the parameter dependence of the order parameter. The interacting limit is addressed at the mean-field level, which allows us to construct the phase diagram for the model. We find that both the interaction and dissipation rates induce a $\mathcal{PT}$-symmetry breaking. On the other hand, periodic modulation of the dissipative coupling in time stabilizes the $\mathcal{PT}$-symmetric regime. Our findings are corroborated numerically on a tight-binding chain with gain and loss., Comment: 8 pages, 7 figures

We study the non-equilibrium dynamics of a Luttinger liquid after a simultaneous quantum quench of the interaction and dissipative quench to the environment within the realm of the Lindblad equation. When the couplings to environment satisfy detailed balance, the system is destined to thermalize, which we follow using bosonization. The thermodynamic entropy of the system, which also encodes information about the entanglement with the environment, either exhibits a maximum and minimum or grows monotonically before reaching its thermal value in a universal fashion. The single-particle density matrix reveals rich behaviour in the spatio-temporal "phase diagram", including thermal, prethermal and dissipation enhanced sudden quench Luttinger liquid behaviour as well as dissipation enhanced Fermi liquid response., Comment: 8 pages, 7 figures

Recent experiments demonstrated that single-particle quantum walks can reveal the topological properties of single-particle states. Here, we generalize this picture to the many-body realm by focusing on multiparticle quantum walks of strongly interacting fermions. After injecting $N$ particles with multiple flavors in the interacting SU$(N)$ Su-Schrieffer-Heeger chain, their multiparticle continuous-time quantum walk is monitored by a variety of methods. We find that the many-body Berry phase in the $N$-body part of the spectrum signals a topological transition upon varying the dimerization, similarly to the single-particle case. This topological transition is captured by the single- and many-body mean chiral displacement during the quantum walk and remains present for strong interaction as well as for moderate disorder. Our predictions are well within experimental reach for cold atomic gases and can be used to detect the topological properties of many-body excitations through dynamical probes., Comment: 7 pages, 3 figures, and Supplemental Material

Particle formation represents a central theme in various branches of physics, often associated to confinement. Here we show that dynamical hadron formation can be spectroscopically detected in an ultracold atomic setting within the most paradigmatic and simplest model of condensed matter physics, the repulsive $\textrm{SU}(N)$ Hubbard model. By starting from an appropriately engineered initial state of the ${{\textrm{SU}(3)}}$ Hubbard model, not only mesons (doublons) but also baryons (trions) are naturally generated during the time evolution. In the strongly interacting limit, baryons become heavy and attract each other strongly, and their residual interaction with mesons generates meson diffusion, as captured by the evolution of the equal time density correlation function. Hadrons remain present in the long time limit, while the system thermalizes to a negative temperature state. Our conclusions extend to a large variety of initial conditions, all spatial dimensions, and for SU($N>2$) Hubbard models., Comment: 7 pages, 5 figures

We perform a comparative study for the magnetization dynamics within linear response theory of one and two dimensional massive Dirac electrons, after switching on either a real (hermitian) or an imaginary (non-hermitian) magnetic field. While hermitian dc magnetic fields polarize the spins in the direction of the external magnetic field, non-hermitian magnetic fields induce only off diagonal response. An imaginary dc magnetic field perpendicular to the mass term induces finite magnetization in the third direction only according to the right hand rule. This can be understood by analyzing the non-hermitian equation of motion of the spin, which becomes analogous to a classical particle in crossed electric and magnetic fields. Therein, the spin expectation value, the mass term and imaginary magnetic field play the role of the classical momentum, magnetic and electric field, respectively. The latter two create a drift velocity perpendicular to them, which gives rise to the off-diagonal component of the dc spin susceptibility, similarly to how the Hall effect develops in the classical description., Comment: 8 pages, 2 figures

We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a hermitian Fermi gas. The fermionic Green's function decays in a power law fashion for large distances, as expected from gapless excitations, albeit the exponent is reduced from $-1$ due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT-symmetry, respectively. Our results challenge the concept of universality in non-hermitian systems, where quantum criticality can be masked due to non-hermiticity., Comment: 8 pages, 5 figures

The Lindhard function represents the basic building block of many-body physics and accounts for charge response, plasmons, screening, Friedel oscillation, RKKY interaction etc. Here we study its non-Hermitian version in one dimension, where quantum effects are traditionally enhanced due to spatial confinement, and analyze its behavior in various limits of interest. Most importantly, we find that the static limit of the non-Hermitian Lindhard function has no divergence at twice the Fermi wavenumber and vanishes identically for all other wavenumbers at zero temperature. Consequently, no Friedel oscillations are induced by a non-Hermitian, imaginary impurity to lowest order in the impurity potential at zero temperature. Our findings are corroborated numerically on a tight-binding ring by switching on a weak real or imaginary potential. We identify conventional Friedel oscillations or heavily suppressed density response, respectively., Comment: 6 pages, 3 figures

Close to the Fermi energy, nodal loop semimetals have a torus-shaped, strongly anisotropic Fermi surface which affects their transport properties. Here we investigate the non-equilibrium dynamics of nodal loop semimetals by going beyond linear response and determine the time evolution of the current after switching on a homogeneous electric field. The current grows monotonically with time for electric fields perpendicular to the nodal loop plane however it exhibits non-monotonical behavior for field orientations aligned within the plane. After an initial non-universal growth $\sim Et$, the current first reaches a plateau $\sim E$. Then, for perpendicular directions, it increases while for in-plane directions it decreases with time to another plateau, still $\sim E$. These features arise from interband processes. For long times or strong electric fields, the current grows as $\sim E^{3/2}t$ or $\sim E^3t^2$ for perpendicular or parallel electric fields, respectively. This non-linear response represents an intraband effect where the large number of excited quasiparticles responds to the electric field. Our analytical results are benchmarked by the numerical evaluation of the current from continuum and tight-binding models of nodal loop semimetals., Comment: 12 pages, 10 figures, 1 table

Linear response theory plays a prominent role in various fields of physics and provides us with extensive information about the thermodynamics and dynamics of quantum and classical systems. Here we develop a general theory for the linear response in non-Hermitian systems with non-unitary dynamics and derive a modified Kubo formula for the generalized susceptibility for arbitrary (Hermitian and non-Hermitian) system and perturbation. As an application, we evaluate the dynamical response of a non-Hermitian, one-dimensional Dirac model with imaginary and real masses, perturbed by a time-dependent electric field. The model has a rich phase diagram, and in particular, features a tachyon phase, where excitations travel faster than an effective speed of light. Surprisingly, we find that the dc conductivity of tachyons is finite, and the optical sum rule is exactly satisfied for all masses. Our results highlight the peculiar properties of the Kubo formula for non-Hermitian systems and are applicable for a large variety of settings.

Recently defect production was investigated during non-unitary dynamics due to non-Hermitian Hamiltonian. By ramping up the non-Hermitian coupling linearly in time through an exceptional point, defects are produced in much the same way as approaching a Hermitian critical point. A generalized Kibble--Zurek scaling accounted for the ensuing scaling of the defect density in terms of the speed of the drive and the corresponding critical exponents. Here we extend this setting by adding the recycling term and considering the full Lindbladian time evolution of the problem with quantum jumps. We find that by linearly ramping up the environmental coupling in time, and going beyond the steady-state solution of the Liouvillian, the defect density scales linearly with the speed of the drive for all cases. This scaling is unaffected by the presence of exceptional points of the Liouvillian, which can show up in the transient states. By using a variant of the adiabatic perturbation theory, the scaling of the defect density is determined exactly from a set of algebraic equations. Our study indicates the distinct sensitivity of the Lindbladian time evolution to exceptional points corresponding to steady states and transient states., Comment: 10 pages, 6 figures

We investigate a quantum quench from a critical to an exceptional point. The initial state, prepared in the ground state of a critical hermitian system, is time evolved with a non-hermitian SSH model, tuned to its exceptional point. The single particle density matrix exhibits supersonic modes and multiple light cones, characteristic to non-hermitian time evolution. These propagate with integer multiples of the original Fermi velocity. In the long time limit, the fermionic Green's function decays spatially as $1/x^2$, in sharp contrast to the usual $1/x$ decay of non-interacting fermions. The entanglement entropy is understood as if all these supersonic modes arise from independent quasiparticles (though they do not), traveling with the corresponding supersonic light cone velocity. The entropy production rate decreases with time and develops plateaus during the time evolution, signaling the distinct velocities in the propagation of non-local quantum correlations. At late times, the entanglement entropy saturates to a finite value, satisfying a volume law., Comment: 10 pages, 5 figures

We study the non-equilibrium dynamics and transport of a PT-symmetric Luttinger liquid (LL) after an interaction quench. The system is prepared in domain wall initial state. After a quantum quench to spatially homogeneous, PT-symmetric LL, the domain wall develops into a flat central region that spreads out ballistically faster than the conventional Lieb-Robinson maximal speed. By evaluating the current inside the regular lightcone, we find a universal conductance $e^2/h$, insensitive to the strength of the PT-symmetric interaction. On the other hand, by repeating the very same time evolution with a hermitian LL Hamiltonian, the conductance is heavily renormalized by the hermitian interaction as $e^2/hK$ with $K$ the LL parameter. Our analytical results are tested numerically, confirming the universality of the conductance in the non-hermitian realm., Comment: 5 pages, 2 figures, 2 pages of supplementary material

We investigate the stability of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The single particle density matrix reveals the fractionalization of fermionic excitations in the spatial correlations by retaining the initial non-integer power law exponents, accompanied by an exponential decay in time with interaction dependent rate. The spectrum of the time evolved density matrix is gapped, which collapses gradually as $-\ln(t)$. The von Neumann entropy crosses over from the early time $-t\ln(t)$ behaviour to $\ln(t)$ growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results could be tested experimentally in bosonic Luttinger liquids., Comment: 8 pages, 3 figures

Non-Hermitian descriptions of quantum matter have seen impressive progress recently, with major advances in understanding central aspects such as their topological properties or the physics of exceptional points, the non-Hermitian counterpart of critical points. Here, we use single-photon interferometry to reconstruct the non-Hermitian Kibble-Zurek mechanism and its distinct scaling behavior for exceptional points, by simulating the defect production upon performing slow parameter ramps. Importantly, we are able to realise also higher-order exceptional points, providing experimental access to their theoretically predicted characteristic Kibble-Zurek scaling behaviour. Our work represents a crucial step in increasing the experimental complexity of non-Hermitian quantum time-evolution. It thus also furthers the quest to move the frontier from purely single-particle physics towards increasingly complex settings in the many-body realm., Comment: 8 pages, 6 figures

We investigate quantum quenches and the Loschmidt echo in the two dimensional, three band $\alpha-T_3$ model, a close descendant of the dice lattice. By adding a chemical potential to the central site, the integral of the Berry curvature of the bands in different valleys is continously tunable by the ratio of the hopping integrals between the sublattices. By investigating one and two filled bands, we find that dynamical quantum phase transition (DQPT), i.e. nonanalytical temporal behaviour in the rate function of the return amplitude, occurs for a certain range of parameters, independent of the band filling. By focusing on the effective low energy description of the model, we find that DQPTs happen not only in the time derivative of the rate function, which is a common feature in two dimensional models, but in the rate function itself. This feature is not related to the change of topological properties of the system during the quench, but rather follows from population inversion for all momenta. This is accompanied by the appearance of dynamical vortices in the time-momentum space of the Pancharatnam geometric phase. The positions of the vortices form an infinite vortex ladder, i.e. a macroscopic phase structure, which allows us to identify the dynamical phases that are separated by the DQPT., Comment: 8 pages, 4 figures

Semiconductors in the proximity of superconductors have been proposed to support phases hosting Majorana bound states. When the systems undergo a topological phase transition towards the Majorana phase, the spectral gap closes, then reopens, and the quasiparticle band spin polarization is inverted. We focus on two paradigmatic semiconductor-superconductor heterostructures and propose an all-electrical spectroscopic probe sensitive to the spin inversion at the topological transition. Our proposal relies on the indirect coupling of a time-dependent electric field to the electronic spin due to the strong Rashba spin-orbit coupling in the semiconductor. We analyze within linear response theory the dynamical correlation functions and demonstrate that some components of the susceptibility can be used to detect the nontrivial topological phases.

We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a non-integer power law decay for late times, representing dissipation induced Luttinger liquid behaviour. However, the crossover between the two regions occurs due to dissipation induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as $-t\ln t$ initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems., Comment: 5 pages, 2 figures + supplementary material

Quantum information stored in local operators spreads over other degrees of freedom of the system during time evolution, known as scrambling. This process is conveniently characterized by the out-of-time-order commutators (OTOC), whose time dependence reveals salient aspects of the system's dynamics. Here we study the spatially local spin correlation function i.e., the expectation value of spin commutator and the corresponding OTOC of Dirac--Weyl systems in one, two, and three spatial dimensions. The OTOC can be written as the square of the expectation value of the commutator and the variance of the commutator. In principle, the problem features two energy scales, the chemical potential, and the high energy cutoff. We find that only the latter is dominant, therefore the time evolution is separated into only two different regions. The spin correlation function grows linearly with time initially and decays as $t^{-2}$ for late times. The OTOC reveals a universal $t^2$ initial growth from both the commutator and the variance while its late time decay, $t^{-2}$ originates from the variance of the commutator. This late time decay is identified as a characteristic signature or Dirac-Weyl fermions. These features remain present also at finite temperatures. Our results indicate that Dirac--Weyl systems are slow information scramblers and are essential when additional channels for scrambling, i.e., interaction or disorder are analyzed., Comment: 11 pages, 7 figures

For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogues of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, as well as the size of the end spins: for $S=1/2$ end spins their interaction is antiferromagnetic, while for $S>1/2$ it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations., Comment: 5 pages, 4 figures + supplementary material

A Luttinger liquid (LL) describes low energy excitations of many interacting one dimensional systems, and exhibits universal response both in and out of equilibrium. We analyze its behaviour in the non-hermitian realm after quantum quenching to a PT-symmetric LL by focusing on the fermionic single particle density matrix. For short times, we demonstrate the emergence of unique phenomena, characteristic to non-hermitian systems, that correlations propagate faster than the conventional maximal speed, known as the Lieb-Robinson bound. These emergent supersonic modes travel with velocities that are multiples of the conventional light-cone velocity. This behaviour is argued to be generic for correlators in non-hermitian systems. In the long time limit, we find typical LL behaviour, extending the LL universality to the non-equilibrium non-hermitian case. Our analytical results are benchmarked numerically and indicate that the dispersal of quantum information is much faster in non-hermitian systems., Comment: 6+1 pages, 3 figures

While much is known about repulsive quantum impurity models, significantly less attention has been devoted to their attractive counterparts. This motivated us to study the attractive SU(N) Anderson impurity model. While for the repulsive case, the phase diagram features mild N dependence and the ground state is always a Fermi liquid, in the attractive case a Kosterlitz-Thouless charge localization phase transition is revealed for N > 2. Beyond a critical value of attractive interaction an abrupt jump appears in the number of particles at the impurity site, and a singular Fermi liquid state emerges, where the scattering of quasiparticles is found to exhibit power law behavior with fractional power. The capacity diverges exponentially at the quantum critical point, signaling the Kosterlitz-Thouless transition., Comment: 5 pages, 4 figures, includes Supplemental Information

Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to non-adiabaticity. We study the optimal protocol for swithcing on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $\tau$, starting from the non-interacting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $\tau/2$, and can be expressed as a functional of the occupation numbers of the bosonic modes in the final state. For short quench durations, the optimal protocol exhibits fast oscillation and excites high energy modes. In the limit of large $\tau$, minimizing energy requires a smooth protocol while maximizing overlap requires a linear quench protocol. In this limit, the minimal energy and maximal overlap are both universal functions of the system size and the duration of the protocol., Comment: 8 pages, 5 figures

We investigate the light-matter interaction between the edge state of a 2D topological insulator and quantum electromagnetic field. The interaction originates from the Zeeman term between the spin of the edge electrons and the magnetic field, and also through the Peierls substition. The continuous U(1) symmetry of the system in the absence of the vector potential reduces into discrete time reversal symmetry in the presence of the vector potential. Due to light-matter interaction, a superradiant ground state emerges with spontaneously broken time reversal symmetry, accompanied by a net photocurrent along the edge, generated by the vector potential of the quantum light. The spectral function of the photon field reveals polariton continuum excitations above a threshold energy, corresponding to a Higgs mode and another low energy collective mode due to the phase fluctuations of the ground state. This collective mode is a zero energy Goldstone mode that arises from the broken continuous U(1) symmetry in the absence of the vector potential, and acquires finite a gap in the presence of the vector potential. The optical conductivity of the edge electrons is calculated using the random phase approximation by taking the fluctuation of the order parameter into account. It contains the collective modes as a Drude peak with renormalized effective mass, which moves to finite frequencies as the symmetry of the system is lowered by the inclusion of the vector potential., Comment: 11 pages, 7 figures

Exceptional points (EPs) are ubiquitous in non-hermitian systems, and represent the complex counterpart of critical points. By driving a system through a critical point at finite rate induces defects, described by the Kibble-Zurek mechanism, which finds applications in diverse fields of physics. Here we generalize this to a ramp across an EP. We find that adiabatic time evolution brings the system into an eigenstate of the final non-hermitian Hamiltonian and demonstrate that for a variety of drives through an EP, the defect density scales as $\tau^{-(d+z)\nu/(z\nu+1)}$ in terms of the usual critical exponents and $1/\tau$ the speed of the drive. Defect production is suppressed compared to the conventional hermitian case as the defect state can decay back to the ground state close to the EP. We provide a physical picture for the studied dynamics through a mapping onto a Lindblad master equation with an additionally imposed continuous measurement., Comment: 7 pages, 3 figures

In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a discretized characteristic function and derive formulas for its cumulants and moments. In the case of a non-interacting system, our scheme leads to the gauge-invariant cumulants known from polarization theory. We study the behavior of such cumulants for several interacting models. In a one-dimensional system of spinless fermions with nearest neighbor interaction the transition at which gap closure occurs can be clearly identified from the finite size scaling exponent of the variance. When next nearest neighbor interactions are turned on a model with a richer phase diagram emerges, but the finite size scaling exponent is still an effective way to identify the localization transition.

Motivated by recent experiments in ultracold gases, we focus on the properties of the center of mass coordinate of an interacting one dimensional Fermi gas, displaying several distinct phases. While the variance of the center of mass vanishes in insulating phases such as phase separated and charge density wave phases, it remains finite in the metallic phase, which realizes a Luttinger liquid. By combining numerics with bosonization, we demonstrate that the autocorrelation function of the center of mass coordinate is universal throughout the metallic phase. It exhibits persistent oscillations and its short time dynamics reveal important features of the quantum liquid, such as the Luttinger liquid parameter and the renormalized velocity. The full counting statistics of the center of mass follows a normal distribution already for small systems. Our results apply to non-integrable systems as well and are within experimental reach for e.g. carbon nanotubes and cold atomic gases., Comment: 6 pages, 3 figures

Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals host coexisting topological and trivial magnetic oscillations. These originate from mapping the topological properties of the extremal Fermi surface cross sections onto the physics of two dimensional semi Dirac systems, stemming from merging two massless Dirac cones. By tuning the chemical potential and the direction of magnetic field, a sharp transition is identified separating purely trivial oscillations, arising from the Landau levels of a normal two dimensional (2D) electron gas, to a phase where oscillations of topological and trivial origin coexist, originating from 2D massless Dirac and semi Dirac points, respectively. These could in principle be directly identified in current experiments., Comment: 7 pages, 5 figures. Almost matches the published version

Out-of-time-ordered (OTO) correlators have developed into a central concept quantifying quantum information transport, information scrambling and quantum chaos. In this work we show that such OTO correlator can also be used to dynamically detect equilibrium as well as nonequilibrium phase transitions in Ising chains. We study OTO correlators of an order parameter both in equilibrium and after a quantum quench for different variants of transverse-field Ising models in one dimension, including the integrable one as well as non-integrable and long-range extensions. We find for all the studied models that the OTO correlator in ground states detects the quantum phase transition. After a quantum quench from a fully polarized state we observe numerically for the short-range models that the asymptotic long-time value of the OTO correlator signals still the equilibrium critical points and ordered phases. For the long-range extension, the OTO correlator instead determines a dynamical quantum phase transition in the model. We discuss how our findings can be observed in current experiments of trapped ions or Rydberg atoms., Comment: 6+3 pages, 5+5 figures

A spin fractionalizes into matter and gauge fermions in Kitaev's spin liquid on the honeycomb lattice. This follows from a Jordan-Wigner mapping to fermions, allowing for the construction of minimal entropy ground state wavefunction on the cylinder. We use this to calculate the entanglement entropy by choosing several distinct partitionings. First, by partitioning an infinite cylinder into two, the $-\ln 2$ topological entanglement entropy is reconfirmed. Second, the reduced density matrix of the gauge sector on the full cylinder is obtained after tracing out the matter degrees of freedom. This allows for evaluating the gauge entanglement Hamiltonian, which contains infinitely long range correlations along the symmetry axis of the cylinder. The matter-gauge entanglement entropy is $(N_y-1)\ln 2$ with $N_y$ the circumference of the cylinder. Third, the rules for calculating the gauge sector entanglement of any partition are determined. Rather small correctly chosen gauge partitions can still account for the topological entanglement entropy in spite of long-range correlations in the gauge entanglement Hamiltonian., Comment: 7 pages, 5 figures

The two-channel Kondo impurity model realizes a local non-Fermi liquid state with finite residual entropy. The competition between the two channels drives the system to an impurity quantum critical point. We show that the out-of-time-ordered (OTO) commutator for the impurity spin reveals markedly distinct behaviour depending on the low energy impurity state. For the one channel Kondo model with Fermi liquid ground state, the OTO commutator vanishes for late times, indicating the absence of the butterfly effect. For the two channel case, the impurity OTO commutator is completely temperature independent and saturates quickly to its upper bound 1/4, and the butterfly effect is maximally enhanced. These compare favourably to numerics on spin chain representation of the Kondo model. Our results imply that a large late time value of the OTO commutator does not necessarily diagnose quantum chaos., Comment: 8 pages, 6 figures

We study the spin-relaxation time in materials where a large spin-orbit coupling (SOC) is present which breaks the spatial inversion symmetry. Such a spin-orbit coupling is realized in zincblende structures and heterostructures with a transversal electric field and the spin relaxation is usually described by the so-called D'yakonov-Perel' (DP) mechanism. We combine a Monte Carlo method and diagrammatic calculation based approaches in our study; the former tracks the time evolution of electron spins in a quasiparticle dynamics simulation in the presence of the built-in spin-orbit magnetic fields and the latter builds on the spin-diffusion propagator by Burkov and Balents [Burkov and Balents Phys. Rev. B. 69, 245312 (2004).]. Remarkably, we find a parameter free quantitative agreement between the two approaches and it also returns the conventional result of the DP mechanism in the appropriate limit. We discuss the full phase space of spin relaxation as a function of SOC strength, its distribution, and the magnitude of the momentum relaxation rate. This allows us to identify two novel spin-relaxation regimes; where spin relaxation is strongly non-exponential and the spin relaxation equals the momentum relaxation. A compelling analogy between the spin-relaxation theory and the NMR motional narrowing is highlighted.

Inspired by recent advances in cold atomic systems and non-equilibrium physics, we introduce a novel characterization scheme, the time of flight full counting statistics. We benchmark this method on an interacting one dimensional Bose gas, and show that there the time of flight image displays several universal regimes. Finite momentum fluctuations are observed at larger distances, where a crossover from exponential to Gamma distribution occurs upon decreasing momentum resolution. Zero momentum particles, on the other hand, obey a Gumbel distribution in the weakly interacting limit, characterizing the quantum fluctuations of the former quasi-condensate. Time of flight full counting statistics is demonstrated to capture thermalization processes after a quantum quench, and can be useful for characterizing exotic quantum states such as many-body localized systems or models of holography., Comment: 14 pages, 9 figures (including appendix), accepted version, new appendices

Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered (OTO) commutators through an exponential growth and large late time value. We show that the latter feature shows up in a strongly correlated many-body system, a Luttinger liquid, whose density fluctuations we study at long and short wavelengths, both in equilibrium and after a quantum quench. We find rich behaviour combining robustly universal and non-universal features. The OTO commutators display temperature and initial state independent behaviour, and grow as $t^2$ for short times. For the short wavelength density operator, they reach a sizeable value after the light cone only in an interacting Luttinger liquid, where the bare excitations break up into collective modes. We benchmark our findings numerically on an interacting spinless fermion model in 1D, and find persistence of central features even in the non-integrable case. As a non-universal feature, the short time growth exhibits a distance dependent power., Comment: 6 pages, 2 figures

While much is known about the entanglement characteristics of ground states, the properties of reduced thermal density matrices have received significantly less attention. Here we investigate the entanglement content of reduced thermal density matrices for momentum-space bipartitioning in Luttinger liquids using analytical and numerical methods. The low lying part of its spectrum contains an "entanglement gap", which persists up to temperatures comparable to the level spacing. With increasing temperature, the low energy modes acquire dispersion and resemble to those in the physical Hamiltonian with an enhanced effective temperature. The momentum-space entanglement is carried by high energy modes (compared to temperature), featuring a completely flat spectrum. The von-Neumann entropy increases with temperature with a universal Sommerfeld coefficient. The momentum-space entanglement Hamiltonian turns out to be as universal as the physical Hamiltonian., Comment: 6 pages, 2 figures

The electron-nuclear hyperfine interaction shows up in a variety of phenomena including e.g. NMR studies of correlated states and spin decoherence effects in quantum dots. Here we focus on the hyperfine coupling and the NMR spin relaxation time, $T_1$ in Weyl semimetals. Since the density of states in Weyl semimetals varies with the square of the energy around the Weyl point, a naive power counting predicts a $1/T_1T\sim E^4$ scaling with $E$ the maximum of temperature ($T$) and chemical potential. By carefully investigating the hyperfine interaction between nuclear spins and Weyl fermions, we find that while its spin part behaves conventionally, its orbital part diverges unusually with the inverse of energy around the Weyl point. Consequently, the nuclear spin relaxation rate scales in a graphene like manner as $1/T_1T\sim E^2\ln(E/\omega_0)$ with $\omega_0$ the nuclear Larmor frequency. This allows us to identify an effective hyperfine coupling constant, which is tunable by gating or doping, which is relevant for decoherence effect in spintronics devices and double quantum dots where hyperfine coupling is the dominant source of spin-blockade lifting., Comment: 7 pages, 2 figures