Nontrivial Crossover Research Articles

Nonrelativistic trace anomaly and equation of state in dense fermionic matter

We investigate theoretically a nonrelativistic trace anomaly and its impact on the low-temperature equation of state in spatially one-dimensional three-component fermionic systems with a three-body interaction, which exhibit a nontrivial three-body crossover from a bound trimer gas to dense fermionic matter with increasing density. By applying the G-matrix approach to the three-body interaction, we obtain the analytical expression for the ground-state equation of state relevant to the high-density degenerate regime and thereby address how the three-body contact or, equivalently, the trace anomaly emerges. The analytical results are compared with the recent quantum Monte Carlo data. Our study of the trace anomaly and the sound speed could have some relevance to the physics of hadron-quark crossover in compact stars. Published by the American Physical Society 2024

Non-trivial topological crossover in functionalized AlBi monolayer

The incorporation of spin–orbit coupling and altering the orbital composition close to the Fermi level via functionalization are two essential techniques for exploring topological insulators. We have shown through an ab-initio study that spin–orbit coupling transforms the fluorinated AlBi honeycomb monolayer from a normal insulator to a topological insulator with a large band gap. The combined effects of functionalization and spin–orbit coupling led to a band-inversion in the AlBi honeycomb monolayer. This monolayer has a nontrivial topological character, as confirmed by the reported s/p band inversion in the band structures, the Z2 topological invariant and the clear demonstration of the topological gapless edge states bridging the valence band and conduction band. In addition, it is found that compressing the fluorinated AlBi lattice by about 3 % triggered the topological phase transition, which results in a normal state. The reported nontrivial band gap of 0.36 eV in the fluorinated AlBi monolayer is sufficient to make them a suitable consideration for spintronic devices at room temperature.

Cooper triples in attractive three-component fermions: Implication for hadron-quark crossover

We investigate many-body properties of equally populated three-component fermions with attractive three-body contact interaction in one dimension. A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are three-body counterparts of Cooper pairs with a two-body attraction. We develop a minimal framework that bridges the crossover from tightly-bound trimers to Cooper triples with increasing chemical potential and show how the formation of Cooper triples occurs in the grand-canonical phase diagram. Moreover, we argue that this non-trivial crossover is similar to the hadron-quark crossover proposed in dense matter. A coexistence of medium-induced triples and the underlying Fermi sea at positive chemical potential is analogous to quarkyonic matter consisting of baryonic excitations and the underlying quark Fermi sea. The comparison with the existing quantum Monte Carlo results implies that the emergence of these kinds of three-body states can be a microscopic origin of the peak of the sound velocity along the crossover.

Quantitative spectroscopy of single molecule interaction times.

Single molecule fluorescence tracking provides information at nanometer-scale and millisecond-temporal resolution about the dynamics and interaction of individual molecules in a biological environment. While the dynamic behavior of isolated molecules can be characterized well, the quantitative insight is more limited when interactions between two indistinguishable molecules occur. We address this aspect by developing a theoretical foundation for a spectroscopy of interaction times, i.e., the inference of interaction from imaging data. A non-trivial crossover between a power law to an exponential behavior of the distribution of the interaction times is highlighted, together with the dependence of the exponential term upon the microscopic reaction affinity. Our approach is validated with simulated and experimental datasets.

Emptiness formation probability in one-dimensional Bose liquids

We study emptiness formation probability (EFP) in interacting 1D Bose liquids. That is the probability that a snapshot of its ground state reveals exactly zero number of particles within the interval $|x|<R$. For a weakly interacting liquid there is parametrically wide regime $n^{-1} < R <\xi$ (here $n$ is the average density and $\xi$ is the healing length), where EFP exhibits a non-trivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [A. Abanov, 2004] to study quantitative details of these regime and compare it with previously reported limited cases.

Spin transport in an electrically driven magnon gas near Bose-Einstein condensation: Hartree-Fock-Keldysh theory

An easy-plane ferromagnetic insulator in a uniform external magnetic field and in contact with a phonon bath and a normal metal bath is studied theoretically in the presence of dc spin current injection via the spin Hall effect in the metal. The Keldysh path integral formalism is used to model the magnon gas driven into a nonequilibrium steady state by mismatched bath temperatures and/or electrical injection, and we analyze the magnon system in the normal (uncondensed) state, but close to the instability to Bose-Einstein condensation (BEC), within the self-consistent Hartree-Fock approximation. We find that the steady state magnon distribution function generally has a non-thermal form that cannot be described by a single effective chemical potential and effective temperature. We also show that the BEC instability in the electrically-driven magnon system is signaled by a sign change in the imaginary part of the poles for long-wavelength magnon modes and by the divergence of the nonequilibrium magnon distribution function. In the presence of two bath temperatures, we find that the correlation length of the superfluid order parameter fluctuations exhibits nontrivial finite temperature crossover behaviors that are richer than the standard crossover behaviors obtained for the vacuum-superfluid transition in an equilibrium dilute Bose gas. We study the consequences of these thermal crossovers on the magnon spin conductivity and obtain an inverse square-root divergence in the spin conductivity in the vicinity of the electrically-induced BEC instability. A spintronics device capable of testing our spin transport predictions is discussed.

Noise-dependent optimal strategies for quantum metrology

We show that for some noisy channels, the optimal entanglement-assisted strategy depends on the noise level. We note that there is a non-trivial crossover between the parallel-entangled strategy and the ancilla-assisted strategy - in the former the probes are all entangled, the latter the probes are entangled with a noiseless ancilla but not amongst themselves. The transition can be explained by the fact that, separable states are more robust against noise and therefore are optimal in the high noise limit, but they are in turn outperformed by ancilla-assisted ones.

High-precision simulation of the height distribution for the KPZ equation

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2, respectively, are preserved also in the region of long times. We present some evidence for the predicted non-trivial crossover in the left tail from the tail exponent to the cubic tail of the Tracy-Widom distribution, although the details of the full scaling form remain beyond reach.

A nontrivial crossover in topological Hall effect regimes

We propose a new theory of the topological Hall effect (THE) in systems with non-collinear magnetization textures such as magnetic skyrmions. We solve the problem of electron scattering on a magnetic skyrmion exactly, for an arbitrary strength of exchange interaction and the skyrmion size. We report the existence of different regimes of THE and resolve the apparent contradiction between the adiabatic Berry phase theoretical approach and the perturbation theory for THE. We traced how the topological charge Hall effect transforms into the spin Hall effect upon varying the exchange interaction strength or the skyrmion size. This transformation has a nontrivial character: it is accompanied by an oscillating behavior of both charge and spin Hall currents. This hallmark of THE allows one to identify the chirality driven contribution to Hall response in the experiments.

Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion.

The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006)PHYADX0378-437110.1016/j.physa.2005.06.101] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.

The three-dimensional O(n) ϕ 4 model on a strip with free boundary conditions: Exact results for a nontrivial dimensional crossover in the limit n→∞

We briefly review recent results of exact calculations of critical Casimir forces of the O(n) ϕ4 model as n→∞ on a three-dimensional strip bounded by two planar free surfaces at a distance L. This model has long-range order below the critical temperature Tc of the bulk phase transition only in the limit L→∞ but remains disordered for all T > 0 for an arbitrary finite strip width L /< 0, and the low-temperature asymptotic behavior of the residual free energy and the Casimir force) by a combination of boundary-operator and short-distance expansions, proper extensions of the inverse scattering theory, new trace formulas, and semiclassical expansions.

Трехмерная $O(n)$-$\phi^4$-модель в плоско-параллельном слое со свободными граничными условиями: точные результаты для нетривиального размерного кроссовера в пределе $n\to\infty$

Дан краткий обзор недавних результатов точных расчетов критических сил Казимира в $O(n)$-$\phi^4$-модели при $n\to\infty$ для трехмерного слоя ширины $L$, ограниченного двумя параллельными плоскостями со свободными граничными условиями. В этой модели дальний порядок имеет место при температурах ниже критической точки $T_{\mathrm c}$ объемного фазового перехода только в пределе $L\to\infty$, однако дальний порядок в модели отсутствует при всех температурах $T&gt;0$ при произвольной конечной ширине слоя $L&lt;\infty$. Последовательное описание скейлингового поведения системы вблизи $T_{\mathrm c}$ оказывается весьма сложной задачей, так как наряду с объемным и поверхностным скейлингом, а также конечно-размерным скейлингом необходимо учитывать нетривиальный размерный кроссовер. Модель допускает точное решение в пределе $n\to\infty$ в терминах собственных значений и собственных функций самосогласованного уравнения Шредингера. Это решение содержит потенциал $v(z)$, который имеет при $z\to +0$ сингулярное поведение $v(z)\approx-1/(4z^2)+4m/(\pi^2z)$ в приграничном слое, где $m=1/\xi_+(|t|)$ - обратная корреляционная длина в объемной системе, $t\sim(T-T_{\mathrm c})/T_{\mathrm c}$, и аналогичная сингулярность имеет место вблизи второй граничной плоскости. В недавней работе нами совместно с соавторами численными методами с высокой точностью были вычислены потенциал $v(z)$, избыточная свободная энергия и сила Казимира. Дано объяснение того, как эти численные результаты могут быть дополнены точными аналитическими результатами для целого ряда величин (коэффициенты разложения потенциала $v(z)$, данные рассеяния для потенциала $v(z)$ в полубесконечной геометрии $L=\infty$ при всех значениях $m\gtreqless 0$, низкотемпературная асимптотика избыточной свободной энергии и силы Казимира). Эти аналитические результаты были получены сочетанием таких методов, как операторные разложения, обобщенная теория обратной задачи рассеяния, новая формула следов и квазиклассические (ВКБ) разложения.

Two-qubit separability probabilities as joint functions of the Bloch radii of the qubit subsystems

We detect a certain pattern of behavior of separability probabilities [Formula: see text] for two-qubit systems endowed with Hilbert–Schmidt (HS), and more generally, random induced measures, where [Formula: see text] and [Formula: see text] are the Bloch radii ([Formula: see text]) of the qubit reduced states ([Formula: see text]). We observe a relative repulsion of radii effect, that is [Formula: see text], except for rather narrow “crossover” intervals [Formula: see text]. Among the seven specific cases we study are, firstly, the “toy” seven-dimensional [Formula: see text]-states model and, then, the fifteen-dimensional two-qubit states obtained by tracing over the pure states in [Formula: see text]-dimensions, for [Formula: see text], with [Formula: see text] corresponding to HS (flat/Euclidean) measure. We also examine the real (two-rebit) [Formula: see text], the [Formula: see text]-states [Formula: see text], and Bures (minimal monotone)–for which no nontrivial crossover behavior is observed–instances. In the two [Formula: see text]-states cases, we derive analytical results; for [Formula: see text], we propose formulas that well-fit our numerical results; and for the other scenarios, rely presently upon large numerical analyses. The separability probability crossover regions found expand in length (lower [Formula: see text]) as [Formula: see text] increases. This report continues our efforts [P. B. Slater, arXiv:1506.08739] to extend the recent work of [S. Milz and W. T. Strunz, J. Phys. A 48 (2015) 035306.] from a univariate ([Formula: see text]) framework — in which they found separability probabilities to hold constant with [Formula: see text] — to a bivariate ([Formula: see text]) one. We also analyze the two-qutrit and qubit–qutrit counterparts reported in Quantum Inform. Process. 15 (2016) 3745 in this context, and study two-qubit separability probabilities of the form [Formula: see text]. A physics.stack.exchange link to a contribution by Mark Fischler addressing, in considerable detail, the construction of suitable bivariate distributions is indicated at the end of the paper.

Temperature dependence of the NMR relaxation rate1/T1for quantum spin chains

We present results of numerical simulations performed on one-dimensional spin chains in order to extract the so-called relaxation rate $1/T_1$ accessible through NMR experiments. Building on numerical tensor network methods using the Matrix Product States (MPS) formalism, we can follow the non-trivial crossover occurring in critical chains between the high-temperature diffusive classical regime and the low-temperature response described by the Tomonaga-Luttinger liquid (TLL) theory, for which analytical expressions are known. In order to compare analytics and numerics, we focus on a generic spin-$1/2$ XXZ chain which is a paradigm of gapless TLL, as well as a more realistic spin-$1$ anisotropic chain, modelling the DTN material, which can be either in a trivial gapped phase or in a TLL regime induced by an external magnetic field. Thus, by monitoring the finite temperature crossover, we provide quantitative limits on the range of validity of TLL theory, that will be useful when interpreting experiments on quasi one-dimensional materials.

Scaling properties of evolutionary paths in a biophysical model of protein adaptation

The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of fitness landscapes and evolutionary paths. We first consider evolution on a simple Mount Fuji fitness landscape, focusing on how the length and predictability of evolutionary paths scale with the coarse-grained sequence length and alphabet. We obtain simple scaling relations for both the weak- and strong-selection limits, with a non-trivial crossover regime at intermediate selection strengths. We apply these results to evolution on a biophysical fitness landscape that describes how proteins evolve new binding interactions while maintaining their folding stability. We combine the scaling relations with numerical calculations for coarse-grained protein sequences to obtain quantitative properties of the model for realistic binding interfaces and a full amino acid alphabet.

Crossover aspects in Ising strips under the influence of variable surface fields and a grain boundary.

I use an exact variational formulation of Mikheev and Fisher to study the critical Ising strip with a grain boundary and confining surfaces characterized by arbitrary and different surface magnetic fields. Energy density profiles that serve as order parameters of the system within the used method show strong nonmonotonous behavior in the vicinity of confining surfaces. I consider short-distance expansion of energy density profiles. New universal amplitudes associated with distant-wall corrections exhibit nontrivial crossover behaviors from positive to negative values as the field's variables are continuously varied. Casimir amplitudes calculated in a self-contained manner are characterized by complex manifolds which may comprise two disconnected positive wings separated by an area of negative values. I define and determine the generalized de Gennes-Fisher amplitude, which strongly suggests that a stress tensor is present within one of the distant-wall corrections. This is an unanticipated result given that a similar discovery for standard extraordinary (E) and ordinary (O) surface universality classes was based on the conformal invariance symmetry, which is broken under the present boundary conditions. A grain boundary essentially influences both energy density profiles and Casimir amplitudes, besides surface fields with a number of accompanying features that are examined in detail. We present closed analytic forms of energy density profiles for standard (N) and (O) BCs: ɛNN(x,g),ɛOO(x,g),ɛNO(x,g) [(N) is the normal surface universality class, g is the grain boundary's strength, x is the relative distance x:=z/L with L as a film width], thus enabling us to deduce their important symmetry properties and to have a detailed insight into their general behaviors.

Boundary crossover in semi-infinite non-equilibrium growth processes

The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk are analysed. The causal interactions of the interface with the boundary lead to a roughness larger near to the boundary than deep in the bulk. This is exemplified in the semi-infinite Edwards–Wilkinson model in one dimension, from both its exact solution and numerical simulations, as well as from simulations on the semi-infinite one-dimensional Kardar–Parisi–Zhang model. The non-stationary scaling of interface heights and widths is analysed and a universal scaling form for the local height profile is proposed.

Nonsteady relaxation and critical exponents at the depinning transition

We study the non-steady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units (GPUs). We compute the time-dependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, non-universal microscopic time-regime, we find a non-trivial long crossover towards the non-steady macroscopic critical regime. This "mesoscopic" time-regime is robust under changes of the microscopic disorder including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L~2^{25}) simulations for the non-steady dynamics of the continuum displacement quenched Edwards Wilkinson equation, getting accurate and consistent depinning exponents for this class: \beta = 0.245 \pm 0.006, z = 1.433 \pm 0.007, \zeta=1.250 \pm 0.005 and \nu=1.333 \pm 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent \beta) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.

Crossover behaviors in the Ising strips with changeable boundary conditions: Exact variational results

A critical Ising strip with confining boundaries characterized by arbitrary and different surface magnetic field variables is considered by the exact variational formulation of Mikheev and Fisher. As one of the most important scaling densities in films we study the universal functions of the energy density profiles which exhibit strong nonmonotonous behavior near the confining boundaries. We also examine their short-distance expansion that reveals novel universal amplitudes associated with the distant-wall corrections. They manifest nontrivial crossover behaviors from positive to negative values as the fields variables are freely varied. As an indispensable part of our new formulation of the generalized distant-wall correction de Gennes-Fisher universal amplitude we derive in a self-contained manner within the present approach the Casimir amplitudes that may change their nature twice under the strong influence of surface fields: from repulsive to attractive and vice versa along certain trajectories. Our findings strongly suggest a surprising role of the stress-tensor within one of the distant-wall corrections, given that similar discovery for standard extraordinary and ordinary surface universality classes was based on the conformal invariance symmetry which is broken under the present boundary conditions. We also show that a constituent part of the de Gennes-Fisher amplitude, defined in a generalized sense, is not hyperuniversal in two dimensions, contrary to earlier results for standard boundary conditions in this dimension.

Confinement and deconfinement in the potential of antidot arrays of a massless Dirac electron in magnetic fields

We have investigated the effect of inter-Landau level mixing on confinement/deconfinement in antidot potentials of states with energies less than the potential height of the antidot array. We find that, depending on the ratio between the size of the antidot R and the magnetic length , probability densities display confinement or deconfinement in antidot potentials (B is the magnetic field). When R/ℓ < 1 inter-Landau level mixing is strong and probability densities with energy less than the potential height are non-chiral and localized inside antidot potentials. However, in the strong magnetic field limit R/ℓ ≫ 1, where inter-Landau level mixing is small, they are delocalized outside antidot potentials, and are chiral for N = 0 Landau level (LL) states while non-chiral for N = 1. In the non-trivial crossover regime R/ℓ ∼ 1 localized and delocalized probability densities coexist. States that are delocalized outside antidots when R/ℓ > 1 form a nearly degenerate band and their probability densities are independent of k, in contrast to the case of R/ℓ < 1.