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The nonequilibrium dynamics of quantum many-body systems have attracted growing attention due to various intriguing phenomena absent in equilibrium physics. One famous example is the quantum Mpemba effect, where the subsystem symmetry is restored faster under a symmetric quench from a more asymmetric initial state. The quantum Mpemba effect has been extensively studied in integrable and chaotic systems. In this Letter, we investigate symmetry restoration and quantum Mpemba effect in many-body localized systems with various initial states. We reveal that the symmetry can still be fully restored in many-body localization phases without approaching thermal equilibrium. Furthermore, we demonstrate that the presence of the quantum Mpemba effect is universal for any initial tilted product state, contrasting to the cases in the chaotic systems where the presence of the quantum Mpemba effect relies on the choice of initial states. We also provide a theoretical analysis of symmetry restoration and quantum Mpemba effects with the help of the effective model for many-body localization. This Letter not only sheds light on extending the quantum Mpemba effect to more non-equilibrium settings but also contributes to a deeper understanding of the many-body localization., Comment: 23 pages (including supplemental materials), 11 figures

Proposed as an elegant symmetry relating bosons and fermions, spacetime supersymmetry (SUSY) has been actively pursued in both particle physics and emergent phenomena in quantum critical points (QCP) of topological quantum materials. However, how SUSY casts the light on nonequilibrium dynamics remains open. In this letter, we investigate the Kibble-Zurek dynamics across a QCP with emergent $\mathcal{N}=2$ spacetime SUSY between the Dirac semimetal and a superconductor through large-scale quantum Monte Carlo simulation. The scaling behaviors in the whole driven process are uncovered to satisfy the full finite-time scaling (FTS) forms. More crucially, we demonstrate that the emergent SUSY manifests in the intimate relation between the FTS behaviors of fermionic and bosonic observables, namely the fermions and bosons acquire the identical anomalous dimensions. Our work not only brings a fundamental new ingredient into the critical theory with SUSY, but also provide the theoretical guidance to experimental detect of QCP with emergent SUSY from the perspectives of Kibble-Zurek mechanism and FTS., Comment: 7+2 pages, 3 figures

In conventional quantum critical point (QCP) characterized by order parameter fluctuations, the celebrated Kibble-Zurek mechanism (KZM) and finite-time scaling (FTS) theory provide universal descriptions of the driven critical dynamics. However, in strongly correlated fermionic systems where gapless fermions are usually present in vicinity of QCP, the driven dynamics has rarely been explored. In this Letter, we investigate the driven critical dynamics in two-dimensional Dirac systems, which harbor semimetal and Mott insulator phases separated by the QCP triggered by the interplay between fluctuations of gapless Dirac fermions and order-parameter bosons. By studying the evolution of physical quantities for different driving rates through large-scale quantum Monte Carlo simulation, we confirm that the driven dynamics is described by the FTS form. Accordingly, our results significantly generalize the KZM theory by relaxing its requirement for a gapped initial state to the system accommodating gapless Dirac fermionic excitation. Through successfully extending the KZM and FTS theory to Dirac QCP, our work not only brings new fundamental perspective into the nonequilibrium critical dynamics, but also provides a novel theoretical approach to fathom quantum critical properties in fermionic systems., Comment: 9+3 pages, 5+2 figures

We study the imaginary-time relaxation critical dynamics of the Neel-paramagnetic quantum phase transition in the two-dimensional (2D) dimerized S = 1/2 Heisenberg model. We focus on the scaling correction in the short-time region. A unified scaling form including both short-time and finite-size corrections is proposed. According to this full scaling form, improved short-imaginary-time scaling relations are obtained. We numerically verify the scaling form and the improved short-time scaling relations for different initial states using projector quantum Monte Carlo algorithm., Comment: 10 pages, 8 figures

Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a proxy for thermalization, has recently been proposed and studied in the context of symmetry restoration for quantum many-body systems undergoing a quench. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits, particularly focusing on the U(1) symmetry case. In contrast to non-symmetric random circuits where the U(1) symmetry of a small subsystem can always be restored at late times, we reveal that symmetry restoration can fail in U(1)-symmetric circuits for certain weak symmetry-broken initial states in finite-size systems. In the early-time dynamics, we observe an intriguing quantum Mpemba effect implying that symmetry is restored faster when the initial state is more asymmetric. Furthermore, we also investigate the entanglement asymmetry dynamics for SU(2) and $Z_{2}$ symmetric circuits and identify the presence and absence of the quantum Mpemba effect for the corresponding symmetries, respectively. A unified understanding of these results is provided through the lens of quantum thermalization with conserved charges., Comment: 4.5 pages, 5 figures, and Supplemental Material

Different from usual critical point characterized by a single length scale, critical point with emergent symmetry exhibits intriguing critical properties characterized by two relevant length scales, attracting long-term investigations from both theoretical and experimental aspects. A natural question is how the critical dynamics is affected by the presence of two relevant length scales. Here we study the relaxation critical dynamics in the three-dimensional ($3$D) clock model, whose critical point has emergent $U(1)$ symmetry. We find that in contrast to the magnatization $M$, whose relaxation process is described by the usual dynamic exponent $z$ of the $3$D $XY$ universality class, the angular order parameter $\phi_q$ shows a two-stage evolution characterized by different dynamic critical exponents. While in the short-time stage the relaxation dynamics is governed by $z$, in the long-time stage the dynamics is controlled by a new dynamic exponent $z'$. We also show the off-critical-point effects in the critical relaxation. Our results may be experimentally detected in the hexagonal RMnO$_3$ (R$=$rare earth) materials., Comment: 7 pages, 4 figures

Quantum criticality within Dirac fermions harbors a plethora of exotic phenomena, attracting sustained attention in the past decades. Nevertheless, the nonequilibrium dynamics therein has rarely been studied. To fill in the gap, we explore the imaginary-time relaxation dynamics in a typical Dirac quantum criticality belonging to chiral Heisenberg universality class. Performing large-scale quantum Monte Carlo simulation, we unveil rich nonequilibrium critical phenomena from different initial states. Particularly, a new dynamic exponent characterizing the non-stationary evolution in the short-time state is determined as $\theta=-0.84(4)$, in sharp contrast with the prevalent belief that $\theta$ is positive as demonstrated in classical cases. Furthermore, we propose a universal dynamic scaling theory governing the fruitful nonequilibrium properties in Dirac quantum criticality. Armed with the scaling theory, we develop a new framework to investigate fermionic quantum criticality based on short-time dynamics, paving a promising avenue to fathoming quantum criticality in diverse fermionic systems with high efficiency., Comment: 7+5 pages,5+4 figures

While the zeros of complex partition functions, such as Lee-Yang zeros and Fisher zeros, have been instrumental in characterizing temperature-driven phase transitions, the extension of this concept to zero temperature remains an open and active topic. In this paper, we introduce the concept of Imaginary-Temperature Zeros (ITZs) by calculating the zeros of the imaginary-temperature partition function. We delve into the properties of ITZs for the transverse-field Ising chain, and find that the ITZs are distributed in sectorial structures, accompanied by universal singular behaviors for such quantities as the edge density of ITZs and the magnetization. These singularities remarkably differ from those in the Lee-Yang theory, and are demonstrated to be intimately related to quantum criticality and the Ising critical exponents. We further illuminate the correspondence between ITZs and the zeros of the spectrum form factor, which offers a practical way for detecting ITZs and zero-temperature phase transitions through quantum dynamics., Comment: 6 pages, 4 figures

The charge equilibration of laser-accelerated carbon ion beams in 2 mg/cm3 foam target was investigated experimentally. The ions were generated through target normal sheath acceleration mechanism in laser-foil interaction scheme. This allows to get the equilibrium charge state in wide energy range near Bragg peak within a single shot. By using foam, the charge equilibration measurement in density regime between gas and solid state was firstly reached out experimentally. It was found that the theoretical predictions with tabulated cross section data for gas target greatly underestimated the charge states. The experimental data are in close agreement with both semi-empirical formula as well as rate equation predictions based on ion-solid interactions. The important role of target density effects that increase the ionization probability and decrease the electron capture probability through frequent multi-collisions in foam are demonstrated. The double electron processes are shown to have little influence on the average charge states. The findings are essential for high energy density physics research where the foams are widely used, and have impacts on a broad range of applications in medical, biological and material fields. The method also provides a new approach to investigate the interaction mechanism of swift heavy ions in matter by taking advantage of the laser-accelerated short-pulse wide-energy range ions.

Quantum computers promise a highly efficient approach to investigate quantum phase transitions, which describe abrupt changes between different ground states of many-body systems. At quantum critical points, the divergent correlation length and entanglement entropy render the ground state preparation difficult. In this work, we explore the imaginary-time evolution for probing the universal critical behavior as the universal information of the ground state can be extracted in the early-time relaxation process. We propose a systematic and scalable scheme to probe the universal behaviors via imaginary-time critical dynamics on quantum computers and demonstrate the validness of our approach by both numerical simulation and quantum hardware experiments. With the full form of the universal scaling function in terms of imaginary time, system size, and circuit depth, we successfully probe the universality by scaling analysis of the critical dynamics at an early time and with shallower quantum circuit depth. Equipped with quantum error mitigation, we also confirm the expected scaling behavior from experimental results on a superconducting quantum processor which stands as the first experimental demonstration on universal imaginary-time quantum critical dynamics., Comment: 5 pages, 4 figures and supplemental materials

Local constraint in the lattice gauge theory provides an exotic mechanism that facilitates the disorder-free localization. However, the understanding of nonequilibrium dynamics in the non-Hermitian lattice gauge model remains limited. Here, we investigate the quench dynamics in a system of spinless fermions with nonreciprocal hopping in the $\mathbb{Z}_2$ gauge field. By employing a duality mapping, we systematically explore the non-Hermitian skin effect, localization-delocalization transition, and real-complex transition. Through the identification of diverse scaling behaviors of quantum mutual information for fermions and spins, we propose that the non-Hermitian quantum disentangled liquids exist both in the localized and delocalized phases, the former originates from the $\mathbb{Z}_2$ gauge field and the latter arises from the non-Hermitian skin effect. Furthermore, we demonstrate that the nonreciprocal dissipation causes the flow of quantum information. Our results provide valuable insights into the nonequilibrium dynamics in the gauge field, and may be experimentally validated using quantum simulators., Comment: 11+4pages, 6+4 figures; accepted by Communications Physics

Thoroughly understanding the transport and energy loss of intense ion beams in dense matter is essential for high-energy-density physics and inertial confinement fusion. Here, we report a stopping power experiment with a high-intensity laser-driven proton beam in cold, dense matter. The measured energy loss is one order of magnitude higher than the expectation of individual particle stopping models. We attribute this finding to the proximity of beam ions to each other, which is usually insignificant for relatively-low-current beams from classical accelerators. The ionization of the cold target by the intense ion beam is important for the stopping power calculation and has been considered using proper ionization cross section data. Final theoretical values agree well with the experimental results. Additionally, we extend the stopping power calculation for intense ion beams to plasma scenario based on Ohm's law. Both the proximity- and the Ohmic effect can enhance the energy loss of intense beams in dense matter, which are also summarized as the beam-density effect. This finding is useful for the stopping power estimation of intense beams and significant to fast ignition fusion driven by intense ion beams.

Deconfined quantum criticality (DQC) arises from fractionalization of quasi-particles and leads to fascinating behaviors beyond the Landau-Ginzburg-Wilson (LGW) description of phase transitions. The unusual aspects of DQC in equilibrium also suggest exotic phenomena out of equilibrium, which are still largely unexplored. Here we study manifestations of DQC when driving (quantum annealing) a two-dimensional quantum magnet through a critical point separating antiferromagnetic and spontaneously dimerized ground states. Numerical simulations show that the celebrated Kibble-Zurek scaling (KZS) mechanism is inadequate for describing the annealing process. To explain our results, we introduce the concept of dual asymmetric KZS, where a deconfinement time enters in addition to the conventional relaxation time and the scaling also depends on the direction in which the system is driven through the critical point according to a duality principle connecting the topological defects in the two phases. These defects -- spinons in the dimerized phase and space-time hedgehogs in the antiferromagnetic phase -- require a much longer time scale for equilibration than the amplitude of the order parameter. Beyond the new insights into DQC, our scaling approach provides a new window into out-of-equilibrium criticality with multiple length and time scales., Comment: 15 pages, 9 figures

In this work, we explore the driven dynamics of the one-dimensional ($1$D) localization transitions. By linearly changing the strength of disorder potential, we calculate the evolution of the localization length $\xi$ and the inverse participation ratio (IPR) in a disordered Aubry-Andr\'{e} (AA) model, and investigate the dependence of these quantities on the driving rate. At first, we focus on the limit in the absence of the quasiperiodic potential. We find that the driven dynamics from both ground state and excited state can be described by the Kibble-Zurek scaling (KZS). Then, the driven dynamics near the critical point of the AA model is studied. Here, since both the disorder and the quasiperiodic potential are relevant directions, the KZS should include both scaling variables. Our present work not only extends our understanding of the localization transitions but also generalize the application of the KZS., Comment: 7 pages, 6 figures

In this paper, we explore quantum criticality in the disordered Aubry-Andr\'{e} (AA) model. For the pure AA model, it is well-known that it hosts a critical point separating an extended phase and a localized insulator phase by tuning the strength of the quasiperiodic potential. Here we unearth that the disorder strength $\Delta$ contributes an independent relevant direction near the critical point of the AA model. Our scaling analyses show that the localization length $\xi$ scales with $\Delta$ as $\xi\propto\Delta^{-\nu_\Delta}$ with $\nu_\Delta$ a new critical exponent, which is estimated to be $\nu_\Delta\approx0.46$. This value is remarkably different from the counterparts for both the pure AA model and the Anderson model. Moreover, rich critical phenomena are discovered in the critical region spanned by the quasiperiodic and the disordered potentials. In particular, in the extended phase side, we show that the scaling theory satisfy a hybrid scaling form as a result of the overlap between the critical regions of the AA model and the Anderson localization., Comment: 7 pages, 7 figures

We explore the imaginary-time relaxation dynamics near quantum critical points with semi-ordered initial states. Different from the case with homogeneous ordered initial states, in which the order parameter $M$ decays homogeneously as $M\propto \tau^{-\beta/\nu z}$, here $M$ depends on the location $x$, showing rich scaling behaviors. Similar to the classical relaxation dynamics with an initial domain wall in Model A, which describes the purely dissipative dynamics, here as the imaginary time evolves, the domain wall expands into an interfacial region with growing size. In the interfacial region, the local order parameter decays as $M\propto \tau^{-\beta_1/\nu z}$, with $\beta_1$ being an additional dynamic critical exponent. Far away from the interfacial region the local order parameter decays as $M\propto \tau^{-\beta/\nu z}$ in the short-time stage, then crosses over to the scaling behavior of $M\propto \tau^{-\beta_1/\nu z}$ when the location $x$ is absorbed in the interfacial region. A full scaling form characterizing these scaling properties is developed. The quantum Ising model in both one and two dimensions are taken as examples to verify the scaling theory. In addition, we find that for the quantum Ising model the scaling function is an analytical function and $\beta_1$ is not an independent exponent., Comment: 7 pages, 5 figures

Background: Spinal cord injury triggers complex pathological cascades, resulting in destructive tissue damage and incomplete tissue repair. Scar formation is generally considered as a barrier for regeneration in central nervous system (CNS), while the intrinsic mechanism of scar-forming after spinal cord injury has not been completed deciphered. Methods: We assessed cholesterol hemostasis in spinal cord lesions and injured peripheral nerves using confocal reflection microscopy and real-time PCR analyses. The involvement of the proteins, which were predicted to promote cholesterol efflux in spinal cord lesions, were assessed with Liver X receptor (LXR) agonist and Apolipoprotein E (APOE) deficiency. The role of reverse cholesterol transport (RCT) in cholesterol clearance was examined in APOE KO mice injured sciatic nerves and myelin-overloaded macrophages in vitro. Finally, we determined the consequence of excess cholesterol accumulation in CNS by transplantation of myelin into neonatal spinal cord lesions. Results: We found that excess cholesterol accumulates in phagocytes and is inefficiently removed in spinal cord lesions in young-adult mice. Interestingly, we observed that excessive cholesterol also accumulates in injured peripheral nerves, but is subsequently removed by RCT. Meanwhile, preventing RCT led to macrophage accumulation and fibrosis in injured peripheral nerves. Furthermore, the neonatal mouse spinal cord lesions are devoid of myelin-derived lipids, and able to heal without excess cholesterol accumulation. We found that transplantation of myelin into neonatal lesions disrupts healing with excessive cholesterol accumulation, persistent macrophage activation and fibrosis, indicating myelin-derived cholesterol plays a critical role in impaired wound healing.

We report on charge state measurements of laser-accelerated carbon ions in the energy range of several MeV penetrating a dense partially ionized plasma. The plasma was generated by irradiation of a foam target with laser-induced hohlraum radiation in the soft X-ray regime. We used the tri-cellulose acetate (C$_{9}$H$_{16}$O$_{8}$) foam of 2 mg/cm$^{-3}$ density, and $1$-mm interaction length as target material. This kind of plasma is advantageous for high-precision measurements, due to good uniformity and long lifetime compared to the ion pulse length and the interaction duration. The plasma parameters were diagnosed to be T$_{e}$=17 eV and n$_{e}$=4 $\times$ 10$^{20}$ cm$^{-3}$. The average charge states passing through the plasma were observed to be higher than those predicted by the commonly-used semiempirical formula. Through solving the rate equations, we attribute the enhancement to the target density effects which will increase the ionization rates on one hand and reduce the electron capture rates on the other hand. In previsous measurement with partially ionized plasma from gas discharge and z-pinch to laser direct irradiation, no target density effects were ever demonstrated. For the first time, we were able to experimentally prove that target density effects start to play a significant role in plasma near the critical density of Nd-Glass laser radiation. The finding is important for heavy ion beam driven high energy density physics and fast ignitions., Comment: 7 pages, 4 figures, 35 conferences

In this paper, we investigate the driven dynamics of the localization transition in the non-Hermitian Aubry-Andr\'{e} model with the periodic boundary condition. Depending on the strength of the quasi-periodic potential $\lambda$, this model undergoes a localization-delocalization phase transition. We find that the localization length $\xi$ satisfies $\xi\sim \varepsilon^{-\nu}$ with $\varepsilon$ being the distance from the critical point and $\nu=1$ being a universal critical exponent independent of the non-Hermitian parameter. In addition, from the finite-size scaling of the energy gap between the ground state and the first excited state, we determine the dynamic exponent $z$ as $z=2$. The critical exponent of the inverse participation ratio (IPR) for the $n$th eigenstate is also determined as $s=0.1197$. By changing $\varepsilon$ linearly to cross the critical point, we find that the driven dynamics can be described by the Kibble-Zurek scaling (KZS). Moreover, we show that the KZS with the same set of the exponents can be generalized to the localization phase transitions in the excited states.

Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical point (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J$-$Q_3$ model. In this work, we study the nonequilibrium imaginary-time relaxation dynamics in the $J$-$Q_2$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point, but also investigate the breakdown and the vestige of the dual dynamic scaling when the tuning parameter is away from the critical point. We also discuss its possible experimental realizations in devices of quantum computers., Comment: 18 pages, 11 figures

We propose scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their combinations are studied. Relaxation times of both a usual power-law and an unusual power-law with a logarithmic factor are considered. Finite-size and finite-entanglement scaling forms somehow similar to a frequently employed ansatz are presented. The Kibble-Zurek scaling of topological defect density for a linear driving across the KT transition point is investigated in detail. An implicit equation for a rate exponent in the theory is derived and the exponent varies with the distance from the critical point and the driving rate consistent with relevant experiments. To verify the theories, we utilize the KT phase transition of a one-dimensional Bose-Hubbard model. The infinite time-evolving-block-decimation algorithm is employed to solve numerically the model for finite bond dimensions. Both a correlation length and an entanglement entropy in imaginary time and only the entanglement entropy in real-time driving are computed. Both the short-time critical dynamics in imaginary time and the finite-time scaling in real-time driving, both including the finite bond dimension, for the measured quantities are found to describe the numerical results quite well via surface collapses. The critical point is also estimated and confirmed to be $0.302(1)$ at the infinite bond dimension on the basis of the scaling form., Comment: 16 pages, 9 figures. A mistake in a finite-size scaling form corrected

In this paper, the interplay of the non-Herimiticity and the cascade of delocalization transition in the quasi-periodic chain is studied. The study is applied in a non-Hermitian interpolating Aubry-Andr{\'e}-Fibonacci (IAAF) model, which combines the non-Hermitian Aubry-Andr{\'e} (AA) model and the non-Hermitian Fibonacci model through a varying parameter, and the non-Hermiticity in this model is introduced by the non-reciprocal hopping. In the non-Hermitian AA limit, the system undergoes a delocalization transition by tuning the potential strength. At the critical point, the spatial distribution of the critical state shows a self-similar structure with the relative distance between the peaks being the Fibonacci sequence, and the finite-size scaling of the inverse participation ratios $({\rm IPRs})$ of the critical ground state with lattice size $L$ shows that ${\rm IPR}_g\propto L^{-0.1189}$. In the non-Hermitian Fibonacci limit, we find that the system is always in the extended phase. Along the continuous deformation from the non-Hermitian AA model into the non-Hermitian Fibonacci model in the IAAF model, the cascade of the delocalization transition is found, but only a few plateaux appear. Moreover, the self-similar structure of spatial distribution for the critical modes along the cascade transition is also found. In addition, we find that the delocalization transition and the real-complex transition for the excited states happen at almost the same parameter. Our results show that the non-Hermiticity provides an additional knob to control the cascade of the delocalization transition besides the on-site potential.

As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent symmetry. So far, great efforts have been spent on its equilibrium properties, but the nonequilibrium properties therein are largely unknown. Here we study the nonequilibrium dynamics of the DQCP via the imaginary-time evolution in the two-dimensional (2D) J-Q$_3$ model. We discover fascinating nonequilibrium scaling behaviors hinging on the process of fractionization and the dynamics of emergent symmetry associated with two length scales. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems., Comment: 19 pages, 14 figures

The fluctuations of massless Dirac fermion can not only turn a first-order bosonic phase transition (in the Landau sense) to a quantum critical point, but also work reversely to enhance the first-order transition itself, depending on the implementation of finite size effects in the coupling corrections. Here, we report a case study of the latter by employing quantum Monte Carlo simulation upon a lattice model in which the bosonic part featuring the Landau-Devonshire first-order phase transition and Yukawa coupled to the Dirac fermions. We find that the parameter range for the first-order phase transition becomes larger as the Yukawa coupling increases and the microscopic mechanism of this phenomena is revealed, at a quantitative level, as the interplay between the critical fluctuations and the finite-size effects. Moreover, the scaling behavior at the separation point between the first-order and the continuous phase transitions is found to belong to the chiral tricritical Gross-Neveu universality. Our result demonstrates that the interplay of massless Dirac fermions, critical fluctuations and the finite size effects could trigger a plethora of interesting phenomena and therefore great care is called for when making generalizations., Comment: 9 pages, 6 figures

We consider a heterostructure of semiconductor layers sandwiched between two superconductors, forming a two-dimensional Josephson junction. Applying a Zeeman field perpendicular to the junction can render a topological superconducting phase with chiral Majorana edge mode. We show that the phase difference between two superconductors can efficiently reduce the magnetic field required to achieve the chiral topological superconductivity, providing an experimentally feasible setup to realize chiral Majorana edge modes. We also construct a lattice Hamiltonian of the setup to demonstrate the chiral Majorana edge mode and the Majorana bound state localized in vortices., Comment: 10 pages, 6 figures

In the present study, the interplay among interaction, topology, quasiperiodicity, and non-Hermiticity is studied. The hard-core bosons model on a one-dimensional lattice with asymmetry hoppings and quasiperiodic onsite potentials is selected. This model, which preserves time-reversal symmetry (TRS), will exhibit three types of phase transition: real-complex transition of eigenenergies, topological phase transition and many-body localization (MBL) phase transition. For thereal-complex transition, it is found that the imaginary parts of the eigenenergies are always suppressed by the MBL. Moreover, by calculating the winding number, a topological phase transition can be revealed with the increase of potential amplitude, and we find that the behavior is quite different from the single-particle systems. Based on our numerical results, we conjecture that these three types of phase transition occur at the same point in the thermodynamic limit, and the MBL transition of quasiperiodic system and disordered system should belong to different universality classes. Finally, we demonstrate that these phase transitions can profoundly affect the dynamics of the non-Hermitian many-body system.

We study the short-imaginary-time quantum critical dynamics (SITQCD) in the J-Q$_3$ spin chain, which hosts a quasi-long-range-order phase to a valence bond solid transition. By using the scaling form of the SITQCD with a saturated ordered phase, we are able to locate the critical point at $q_{\rm c}=0.170(14)$. We also obtain the critical initial slip exponent $\theta=-0.507(3)$ and the static exponent $\beta/\nu=0.498(2)$. More strikingly, we find that the scaling dimension of the initial order parameter $x_{0}$ is close to zero, which suggests that the initial order parameter is a marginal operator. As a result, there is no initial increase behavior of the order parameter in the short-imaginary-time relaxation process for this model, which is very different from the relaxation dynamics in the Ising-type phase transitions. Our numerical results are realized by the projector quantum Monte Carlo algorithm., Comment: 8 pages, 8 figures

Dynamical phase transition (DPT) characterizes the abrupt change of dynamical properties in nonequilibrium quantum many-body systems. It has been demonstrated that extra quantum fluctuating modes besides the conventional order parameter field can drastically change the properties of equilibrium phase transitions. However, the counterpart phenomena in DPTs have rarely been explored. Here, we study the DPT in the Dirac system after a sudden quench, and find that the fermion fluctuations can round a putative first-order DPT into a dynamical critical point, which is referred to as a fermion-induced dynamical critical point (FIDCP). It is also a nonthermal critical point, in which the universal short-time scaling behavior emerges despite the system goes through a first-order transition after thermalization. In the novel scenario of FIDCP, the quantum Yukawa coupling $g_q$ is indispensable for inducing the FIDCP albeit irrelevant in the infrared scale. We call these variables {\it indispensable irrelevant scaling variables}. Moreover, a dynamical tricritical point which separates the first-order DPT and the FIDCP is discovered by tuning this indispensable irrelevant scaling variable. We further mention possible experimental realizations., Comment: 6+4 pages, 4+4 figures

Nonlinear mapping is an essential and common demand in online systems, such as sensor systems and mobile phones. Accelerating nonlinear mapping will directly speed up online systems. Previously the authors of this paper proposed a Dendrite Net (DD) with enormously lower time complexity than the existing nonlinear mapping algorithms; however, there still are redundant calculations in DD. This paper presents a DD with an acceleration module (AC) to accelerate nonlinear mapping further. We conduct three experiments to verify whether DD with AC has lower time complexity while retaining DD's nonlinear mapping properties and system identification properties: The first experiment is the precision and identification of unary nonlinear mapping, reflecting the calculation performance using DD with AC for basic functions in online systems. The second experiment is the mapping precision and identification of the multi-input nonlinear system, reflecting the performance for designing online systems via DD with AC. Finally, this paper compares the time complexity of DD and DD with AC and analyzes the theoretical reasons through repeated experiments. Results: DD with AC retains DD's excellent mapping and identification properties and has lower time complexity. Significance: DD with AC can be used for most engineering systems, such as sensor systems, and will speed up computation in these online systems. The code of DD with AC is available on https://github.com/liugang1234567/Gang-neuron, Comment: Published in Mathematics