Plateau Transition Research Articles

Eigenstate plateau transition and equilibration in one-dimensional quantum lattice models

We report a remarkable spectral phenomenon in a generic quantum lattice gas model. As the interaction strength increases, eigenstates spontaneously reorganize, leading to plateaus in the interaction energy. Gaps between plateaus can emerge similarly to continuous phase transitions. Our perturbation analysis indicates that, aside from these gaps, the plateau structure of the spectrum remains stable in the thermodynamic limit. The structured spectrum naturally manifests in far-from-equilibrium dynamics, exhibiting multiple stages. Our findings reveal a connection between emergent properties in high-energy states and equilibration dynamics in closed quantum systems, offering insights into the impact of interactions across the entire energy spectrum. These results directly relate to experiments probing equilibration in quantum spin systems and lattice gases. Published by the American Physical Society 2024

KPZ scaling from the Krylov space

Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems, such as Heisenberg spin chains, has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp–plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling, or equivalently, the diffusion-superdiffusion transition at the critical Euclidean time tE∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {t}_E^{\\ast } $$\\end{document} = ccrK, for the Krylov chain of finite length K, and ccr = O(1). In particular, we find a scaling ~ K1/3 for fluctuations in the one-point correlation function and a dynamical scaling ~ K−2/3 associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is interesting outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise term of order O (1/N) is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography.

Non-Hermitian topology in a multi-terminal quantum Hall device

Quantum devices characterized by non-Hermitian topology are predicted to show highly robust and potentially useful properties for precision sensing and signal amplification. However, realizing them has remained a daunting experimental task, as non-Hermiticity is often associated with gain and loss, which would require precise tailoring to produce the signatures of non-trivial topology. Here, instead of gain and loss, we use the non-reciprocity of quantum Hall edge states to directly observe non-Hermitian topology in a multi-terminal quantum Hall ring. Our transport measurements evidence a robust, non-Hermitian skin effect, characterized by currents and voltages showing an exponential profile that persists across Hall plateau transitions away from the regime of maximum non-reciprocity. Our observation of non-Hermitian topology in a quantum device introduces a scalable experimental approach to construct and investigate generic non-Hermitian systems.

Performance and uncertainties of five popular satellite-based precipitation products in drought monitoring for different climate regions

Satellite-based precipitation products (SPPs) can provide crucial precipitation estimations for large-scale, near-real-time meteorological drought monitoring. However, the performances and uncertainties of SPPs in capturing drought information may vary greatly by product and climate region and are still poorly understood. In this study, we comprehensively evaluated the accuracy of five popular SPPs (MSWEP, TMPA 3B42, PERSIANN-CDR, CHIRPS, and COMRPH) in characterizing meteorological drought in mainland China. (1) Under global warming conditions, the standardized precipitation evapotranspiration index (SPEI) identified a significant decrease in drought associated with higher potential evapotranspiration (PET), which indicated the essential role of PET in determining drought evolution over different climate regions. (2) Among all the SPPs investigated, MSWEP, TMPA 3B42, and PERSIANN perform best in capturing the spatiotemporal pattern of the SPEI trend in the arid Tibetan Plateau regions, transition regions, and humid regions, respectively. In terms of drought category and drought characteristics, MSWEP and TMPA 3B42 perform very well for humid regions, and CHIRPS is better for cold and arid regions, with the poorest performance being found in CMORPH. However, no product performs well for all climate regions for drought monitoring. (3) The optimized parameters (OPs) are the dominant factor for drought uncertainties, followed by the interaction effect and SPPs, with great regional dependence. The OPs contributed the most to drought uncertainties over the relatively arid area of northern China, the interaction of OPs and SPPs did so in the humid area of China, and SPPs were found to contribute the most in the central Tibetan Plateau and some parts of humid regions. Our findings provide guidelines on the choice and application of existing SPP datasets for drought monitoring in different climate zones, as well as some clues to further improve the products over areas where they perform poorly.

Impurity effects on the zeroth pseudo-Landau level in twisted bilayer graphene

We theoretically study the impurity effects on the zeroth pseudo-Landau level (PLL) representation of the flat band in a twisted bilayer graphene (TBG) system. Our research investigates the impact of both short-range and long-range charged impurities on the PLL using the self-consistent Born approximation and random phase approximation. Our findings indicate that short-range impurities have a significant effect on the broadening of the flat band due to impurity scattering. In contrast, the impact of long-range charged impurities on the broadening of the flat band is relatively weak, and the primary impact of the Coulomb interaction is the splitting of the PLL degeneracy when a certain purity condition is satisfied. As a result, spontaneous ferromagnetic flat bands with nonzero Chern numbers emerge. Our work sheds light on the effect of impurities on the quantum Hall plateau transition in TBG systems.

Probing the percolation in the quantum anomalous Hall insulator

The percolation plays an essential role in the physics of plateau transition, localization, and breakdown in quantum Hall (QH) systems. In practice, it always exists probably due to sample imperfections and has to be addressed before realizing the full potentials of topological electronics and qubits. Here, we investigate the cause, distribution, and number of the percolation in a quantum anomalous Hall (QAH) insulator of an anti-Hall bar geometry with two perimeters, which allows for probing both the inter- and intra-perimeter percolations by injecting currents into either or both perimeters. We discover the dual-QAH effect with opposite chiralities from these two perimeters, which exhibits linear modulations by the currents applied to both perimeters. By solving the formulation of such modulations with the Landauer–Büttiker formalism, the distribution and number of the inter-perimeter percolative channels could be identified. Strikingly, a dissipative constituent is detected in the transport of the QAH state, as revealed by the linear scalings in longitudinal conductivities versus the sum of currents injected to both perimeters, similar to that in the trivial-insulating state. Such a behavior unveils the quasi-2D nature of the intra-perimeter percolation, which superimposes onto and perturbs the dissipationless chiral edge transport. The formation of percolations is ascribed to the joint effect of the electric field, finite conductivity, and sample imperfections.

Influence of an Oriented External Electric Field on the Mechanism of Double Proton Transfer between Pyrazole and Guanidine: from an Asynchronous Plateau Transition State to a Synchronous or Stepwise Mechanism.

The double proton transfer (DPT) reaction between pyrazole and guanidine, a concerted reaction but strongly asynchronous and presenting a "plateau transition region", has been theoretically reinvestigated in the presence of an external uniform electric field. First, we computed the reaction path by DFT and proposed a very detailed description of the constitutive electronic events, based on the ELF topology and the bond evolution theory. Then, we studied the effect of an oriented external electric field (OEEF) on the reaction mechanism, for an OEEF oriented along the proton transfer axis. We observe that in one direction, the DPT reaction can be transformed into a stepwise reaction, going through a stabilized single proton transferred intermediate. Contrarily, the two proton transfers occur simultaneously when the electric field is applied in the opposite direction. In the latter case, the order in which the two protons are transferred in the same elementary step can even be reversed if the OEEF is intense enough. Finally, it has been shown that the evolution of the double proton transfer reaction in the presence of an electric field could be quantitatively anticipated by analyzing the ELF value at the bifurcation point between V(A, H) proton donor and V(B) proton acceptor of the double hydrogen bonded complex in the entrance channel.

Cenozoic drainage reversal on the southern margin of the Colorado Plateau, east-central Arizona, USA

Laramide northeast-flowing streams from the ancestral Mogollon highland beveled gently northeast-dipping Late Proterozoic to Cretaceous strata across the southern Colorado Plateau Transition Zone. Late Eocene renewed uplift rejuvenated northeast-flowing streams incising paleocanyons. Apache paleocanyon was incised into the Mogollon highland, including the north-trending Laramide Apache uplift bounded by major reverse faults/monoclines. The Mogollon Rim sequence aggraded in Apache paleocanyon and on a broad alluvial plain to the east. Middle Cenozoic tectonic subsidence of the Transition Zone, aridification, and volcanism combined to aggrade Apache paleocanyon with sedimentary and volcanic rocks from 37.6 to 18.63 Ma. Emplacement of the Mogollon-Datil caldera complex and Chuska erg on the southeastern Colorado Plateau forced streamflow to northwest-dispersal of fluvio-eolian sediment from 34 to 26 Ma. Following erosion by northwest-flowing streams on the southern Colorado Plateau from ~26 to 16 Ma, lake sediments of the lower Bidahochi Fm were deposited. Southwestward reactivation of Laramide faults was underway by ~25 Ma coeval with extensive 25 to 20 Ma Natanes Plateau basalt flows and extreme crustal thinning southwest of the Transition Zone. As northeastward streamflow gradually diminished, a Superstition field ash flow tuff ended northeastward flow at 18.63 Ma and was followed by a period of sluggish southwest stream flow and ponding until after ~14.84 Ma. Southwestward structural subsidence and possible spillover from ancestral Lake Hopi on the Colorado Plateau southern margin caused incision of the southwest-directed Dagger Canyon paleovalley after 14.84, which followed the path of the earlier Apache paleocanyon and possibly to the Sespe delta on the California coast before opening of Gulf of California. Structural collapse of the Tonto Basin to the west induced deposition of the Dagger Canyon Conglomerate in the Dagger Canyon paleovalley before the modern Salt River incised all previous deposits and became integrated with the Gila River during the Plio-Pleistocene.

Superuniversality of dimerized SU(N+M) spin chains

We explore the physics of the quantum Hall effect using the Haldane mapping of dimerised $SU(N+M)$ spin chains, the large $N$ expansion and the density matrix renormalization group technique. We show that while the transition is first order for $N+M >2$, the system at zero temperature nevertheless displays a continuously diverging length scale $\xi$ (correlation length). The numerical results for $(M, N) = (1,3), ~ (2, 2),~(1, 5)$ and $(1, 7)$ indicate that $\xi$ is a directly observable physical quantity, namely the spatial width of the edge states. We relate the physical observables of the quantum spin chain to those of the quantum Hall system (and, hence, the $\vartheta$ vacuum concept in quantum field theory). Our numerical investigations provide strong evidence for the conjecture of super universality which says the dimerised spin chain quite generally displays all the basic features of the quantum Hall effect, independent of the specific values of $M$ and $N$. For the cases at hand we show that the singularity structure of the quantum Hall plateau transitions involves a universal function with two scale parameters that may in general depend on $M$ and $N$. This includes not only the Hall conductance but also the ground state energy as well as the correlation length $\xi$ with varying values of $\vartheta \sim \pi$.

Emergence of 1/3 magnetization plateau and successive magnetic transitions in Zintl phase Eu3InAs3

Single crystals of ${\mathrm{Eu}}_{3}{\mathrm{InAs}}_{3}$ have been successfully synthesized by indium flux reactions. ${\mathrm{Eu}}_{3}{\mathrm{InAs}}_{3}$ crystallizes in the ${\mathrm{Ca}}_{3}\mathrm{Al}{\mathrm{As}}_{3}$-type structure with an orthorhombic space-group $Pnma$. Theoretical calculations indicate that ${\mathrm{Eu}}_{3}{\mathrm{InAs}}_{3}$ is a semiconductor with a direct band gap of 0.3 eV. ${\mathrm{Eu}}_{3}{\mathrm{InAs}}_{3}$ has large negative Seebeck coefficients in the range of 300--450 \ensuremath{\mu}V/K at room temperature. ${\mathrm{Eu}}_{3}{\mathrm{InAs}}_{3}$ displays two antiferromagnetic transitions (${T}_{N1}=13$ and ${T}_{N2}=10$ K) for both $H\ensuremath{\parallel}b$ and $H\ensuremath{\perp}b$ which can be suppressed by magnetic fields. At 2 K, field-induced ferromagnetic states are reached for both $H\ensuremath{\parallel}b$ and $H\ensuremath{\perp}b$. Particularly, the $H\ensuremath{\parallel}b$ magnetization curves show a plateau at 1/3 of the saturated magnetization and an anomaly at 2/3 of the saturated magnetization. ${\mathrm{Eu}}_{3}{\mathrm{InAs}}_{3}$ is a Zintl phase material showing a 1/3 magnetization plateau here.

Reprint of: Marginal CFT perturbations at the integer quantum Hall transition

According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess–Zumino–Novikov–Witten model with Riemannian target space inside a complex Lie supergroup GL. After a summary of that proposal and some of its predictions, the leading irrelevant and relevant perturbations of the proposed CFT are discussed. Argued to be marginal, these result in a non-standard renormalization group (RG) flow near criticality, which calls for modified finite-size scaling analysis and may explain the long-standing inability of numerical work to reach agreement on the values of critical exponents. The technique of operator product expansion is used to compute the RG-beta functions up to cubic order in the couplings. The mean value of the dissipative conductance at the RG-fixed point is calculated for a cylinder geometry with any aspect ratio.

Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model

An extended Bose-Hubbard model (EBHM) with three- and four-body constraints can be feasible in cold atoms in an optical lattice. A rich phase structure including various symmetry-protected topological (SPT) phases is obtained numerically with suitable parameter settings and particle filling. The SPT phase is characterized by the Berry phase as a local topological order parameter and the structure of the entanglement spectrum (ES). Based on the presence of various topological phases, separated by gapless phase boundaries, the EBHM exhibits various bosonic topological pumps, which are constructed by connecting the different SPT phases without gap closing. The bulk topological pumps exhibit the plateau transitions characterized by many-body Chern numbers. For the system with boundary, the center of mass (CoM) under grand canonical ensemble elucidates the contributions of multiple edge states and reveals the topology of the system. We demonstrate that the interacting bosonic pumps obey the bulk-edge-correspondence.

Composite fermion nonlinear sigma models

We study the integer quantum Hall plateau transition using composite fermion mean-field theory. We show that the topological $\theta = \pi$ term in the associated nonlinear sigma model [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] is stable against a certain particle-hole symmetry violating perturbation, parameterized by the composite fermion effective mass. This result, which applies to both the Halperin, Lee, and Read and Dirac composite fermion theories, represents an emergent particle-hole symmetry. For a disorder ensemble without particle-hole symmetry, we find that $\theta$ can vary continuously within the diffusive regime. Our results call for further study of the universality of the plateau transition.

Thermal dissipation in the quantum Hall regime in graphene

It is widely accepted that both backscattering and dissipation cannot occur in topological systems because of the topological protection. Here we show that the thermal dissipation can occur in the quantum Hall (QH) regime in graphene in the presence of dissipation sources, although the Hall plateaus and the zero longitudinal resistance still survive. Dissipation appears along the downstream chiral flow direction of the constriction in the Hall plateau regime, but it occurs mainly in the bulk in the Hall plateau transition regime. In addition, dissipation processes are accompanied with the evolution of the energy distribution from non-equilibrium to equilibrium. This indicates that topology neither prohibits the appearance of dissipation nor prohibits entropy increasing, which opens a new topic on the dissipation in topological systems.

Plateau transitions of a spin pump and bulk-edge correspondence

Sequential plateau transitions of quantum spin chains ($S=1$, 3/2, 2, and 3) are demonstrated by a spin pump using dimerization and a staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as the time. It counts the number of critical points in the loop that is specified by the ${Z}_{2}$ Berry phases. With an open boundary condition, the discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk-edge correspondence. It requires extra level crossings in the pump as a superselection rule that is consistent with the valence bond solid picture.

Marginal CFT perturbations at the integer quantum Hall transition

According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess–Zumino–Novikov–Witten model with Riemannian target space inside a complex Lie supergroup GL. After a summary of that proposal and some of its predictions, the leading irrelevant and relevant perturbations of the proposed CFT are discussed. Argued to be marginal, these result in a non-standard renormalization group (RG) flow near criticality, which calls for modified finite-size scaling analysis and may explain the long-standing inability of numerical work to reach agreement on the values of critical exponents. The technique of operator product expansion is used to compute the RG-beta functions up to cubic order in the couplings. The mean value of the dissipative conductance at the RG-fixed point is calculated for a cylinder geometry with any aspect ratio.

Phase transition beyond the monolayer collapse – The case of stearic acid spread at the air/water interface

The paper presents a detailed characterization of stearic acid film in various experimental conditions, recorded both in the pre- and post-collapse region, using – in addition to π–Α isotherms – visualization of film structure and thickness measurements (using Brewster angle microscope, BAM) supplemented with a precise analysis of compressibility modulus versus area (Cs−1- A) plots. π–Α isotherms recorded for unionized molecules exhibit a liquid-condensed (LC) state where the thickness (th) and the compressibility modulus (Cs−1) remain constant with monolayer compression along a plateau region, where a tilt angle of 73.5°, in respect to the water surface, was calculated for stearic acid molecule. Films subjected to subsequent compressions (beyond the collapse) and expansions show semi-reversible behavior as proved with BAM images. Upon the increase of carboxylic group ionization in alkaline pHs and increasing the speed of compression, the “spike” at the collapse changed its shape from sharp to rounded. Upon further compression, a long plateau transition has been observed. Within this post-collapse plateau, a three-fold increase in film thickness was observed, confirming the previously suggested model of trilayer formation. However, the visualization of film structure with BAM revealed that this process does not occur homogeneously, but through the nucleation of trilayer structures in the form of domains that undergo a continuous process of growth and coalescence within the post-collapse plateau region. The application of the adapted Clausius-Clapeyron equation indicates that the process of trilayer formation is endothermic and implies an increase of entropy, which has been additionally proven by PM-IRRAS.

Doping the chiral spin liquid: Topological superconductor or chiral metal

We point out that there are two different chiral spin liquid states on the triangular lattice and discuss the conducting states that are expected on doping them. These states labeled CS1 and CS2 are associated with two distinct topological orders with different edge states, although they both spontaneously break time reversal symmetry and exhibit the same quantized spin Hall conductance. While CSL1 is related to the Kalmeyer-Laughlin state, CSL2 is the $\nu =4$ member of Kitaev's 16 fold way classification. Both states are described within the Abrikosov fermion representation of spins, and the effect of doping can be accessed by introducing charged holons. On doping CSL2, condensation of charged holons leads to a topological d+id superconductor. However on doping CSL1 , in sharp contrast , two different scenarios can arise: first, if holons condense, a chiral metal with doubled unit cell and finite Hall conductivity is obtained. However, in a second novel scenario, the internal magnetic flux adjusts with doping and holons form a bosonic integer quantum Hall (BIQH) state. Remarkably, the latter phase is identical to a $d+id$ superconductor. In this case the Mott insulator to superconductor transition is associated with a bosonic variant of the integer quantum Hall plateau transition for the holon. We connect the above two scenarios to two recent numerical studies of doped chiral spin liquids on triangular lattice. Our work clarifies the complex relation between topological superconductors, chiral spin liquids and quantum criticality .

Critical Behavior and Universal Signature of an Axion Insulator State.

Recently, the search for an axion insulator state in the ferromagnetic-3D topological insulator (TI) heterostructure and MnBi_{2}Te_{4} has attracted intense interest. However, its detection remains difficult in experiments. We systematically investigate the disorder-induced phase transition of the axion insulator state in a 3D TI with antiparallel magnetization alignment surfaces. It is found that there exists a 2D disorder-induced phase transition on the surfaces of the 3D TI which shares the same universality class with the quantum Hall plateau to plateau transition. Then, we provide a phenomenological theory which maps the random mass Dirac Hamiltonian of the axion insulator state into the Chalker-Coddington network model. Therefore, we propose probing the axion insulator state by investigating the universal signature of such a phase transition in the ferromagnetic-3D TI heterostructure and MnBi_{2}Te_{4}. Our findings not only show a global phase diagram of the axion insulator state, but also stimulate further experiments to probe it.

Kinetic Processes in Fermi–Luttinger Liquids

In this work we discuss extensions of the pioneering analysis by Dzyaloshinskii and Larkin of correlation functions for one-dimensional Fermi systems, focusing on the effects of quasiparticle relaxation enabled by a nonlinear dispersion. Throughout the work we employ both, the weakly interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe attenuation of excitations and explore the fermion-boson duality between both approaches. Special attention is devoted to the role of spin-exchange processes, effects of interaction screening, and integrability. Thermalization rates for electron- and hole-like quasiparticles, as well as the decay rate of collective plasmon excitations and the momentum space mobility of spin excitations are calculated for various temperature regimes. The phenomenon of spin-charge drag is considered and the corresponding momentum transfer rate is determined. We further discuss how momentum relaxation due to several competing mechanisms, viz. triple electron collisions, electron-phonon scattering, and long-range inhomogeneities affect transport properties, and highlight energy transfer facilitated by plasmons from the perspective of the inhomogeneous Luttinger liquid model. Finally, we derive the full matrix of thermoelectric coefficients at the quantum critical point of the first conductance plateau transition, and address magnetoconductance in ballistic semiconductor nanowires with strong Rashba spin-orbit coupling.