Inverse Correlation Length Research Articles

Bragg glass signatures in PdxErTe3 with X-ray diffraction temperature clustering

AbstractThe Bragg glass phase is a nearly perfect crystal with glassy features predicted to occur in vortex lattices and charge-density-wave systems in the presence of disorder. Detecting it has been challenging, despite its sharp theoretical definition in terms of diverging correlation lengths. Here we present bulk probe evidence supporting a Bragg glass phase in the systematically disordered charge-density-wave material of PdxErTe3. We do this by using comprehensive X-ray data and a machine-learning-based analysis tool called X-ray diffraction temperature clustering (X-TEC). We establish a diverging correlation length in samples with moderate intercalation over a wide temperature range. To enable this analysis, we introduced a high-throughput measure of inverse correlation length that we call peak spread. The detection of Bragg glass order and the resulting phase diagram advance our understanding of the complex interplay between disorder and fluctuations. Moreover, the use of our analysis technique to target fluctuations through a high-throughput measure of peak spread can revolutionize the study of fluctuations in scattering experiments.

Finite size effects in the phase transition patterns of coupled scalar field systems

It is considered in this work the phase transition patterns for a coupled two-scalar field system model under the combined effects of finite sizes and temperature. The scalar fields are taken as propagating in a $D=4$ Euclidean space with the usual periodic compactification in the Euclidean time direction (with dimension given by the inverse of the temperature) and also under a compact dimension in the space direction, which is restricted to size $L$. In the latter case, a Dirichlet boundary condition is considered. Finite-size variation of the critical temperature for the cases of symmetry restoration and inverse symmetry breaking are studied. At fixed finite-temperature values, the variation of the inverse correlation lengths with the size $L$ might display a behavior analogous to reentrant phase transitions. Possible applications of our results to physical systems of interest are also discussed.

On the Two-Point Function of the Potts Model in the Saturation Regime

We consider the Random-Cluster model on {mathbb {Z}}^d with interactions of infinite range of the form J_x = psi (x){mathsf {scriptstyle e}}^{-rho (x)} with rho a norm on {mathbb {Z}}^d and psi a subexponential correction. We first provide an optimal criterion ensuring the existence of a nontrivial saturation regime (that is, the existence of beta _{textrm{sat}}(s)>0 such that the inverse correlation length in the direction s is constant on [0,beta _{textrm{sat}}(s))), thus removing a regularity assumption used in our previous work (Aoun et al. in Commun Math Phys 386:433–467, 2021). Then, under suitable assumptions, we derive sharp asymptotics (which are not of Ornstein–Zernike form) for the two-point function in the whole saturation regime (0,beta _{textrm{sat}}(s)). We also obtain a number of additional results for this class of models, including sharpness of the phase transition, mixing above the critical temperature and the strict monotonicity of the inverse correlation length in beta in the regime (beta _{textrm{sat}}(s), beta _{mathrm {scriptscriptstyle c}}).

2D Ising Field Theory in a magnetic field: the Yang-Lee singularity

We study Ising Field Theory (the scaling limit of Ising model near the Curie critical point) in pure imaginary external magnetic field. We put particular emphasis on the detailed structure of the Yang-Lee edge singularity. While the leading singular behavior is controlled by the Yang-Lee fixed point (= minimal CFT mathcal{M} 2/5), the fine structure of the subleading singular terms is determined by the effective action which involves a tower of irrelevant operators. We use numerical data obtained through the “Truncated Free Fermion Space Approach” to estimate the couplings associated with two least irrelevant operators. One is the operator Toverline{T} , and we use the universal properties of the Toverline{T} deformation to fix the contributions of higher orders in the corresponding coupling parameter α. Another irrelevant operator we deal with is the descendant L_4 overline{L} _4ϕ of the relevant primary ϕ in mathcal{M} 2/5. The significance of this operator is that it is the lowest dimension operator which breaks integrability of the effective theory. We also establish analytic properties of the particle mass M (= inverse correlation length) as the function of complex magnetic field.

Mass Scaling of the Near-Critical 2D Ising Model Using Random Currents

We examine the Ising model at its critical temperature with an external magnetic field \(h a^{\frac{15}{8}}\) on \(a\mathbb {Z}^2\) for \(a,h >0\). A new proof of exponential decay of the truncated two-point correlation functions is presented. It is proven that the mass (inverse correlation length) is of the order of \(h^\frac{8}{15}\) in the limit \(h \rightarrow 0\). This was previously proven with CLE-methods in Camia et al. in (Commun Pure Appl Math 73(7):1371–405, 2020). Our new proof uses instead the random current representation of the Ising model and its backbone exploration. The method further relies on recent couplings to the random cluster model (Aizenman et al. in Invent Math 216:661–743, 2018) as well as a near-critical RSW-result for the random cluster model (Duminil-Copin and Manolescu in Planar Random-Cluster Model: Scaling Relations, 2020).

Critical structure and emergent symmetry of Dirac fermion systems

Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross–Neveu–Yukawa (GNY) model. Using the first-order ε expansion in dimensions, we study the critical structure and emergent symmetry of the O(N)-GNY model with N f flavors of four-component Dirac fermions coupled strongly to an O(N) scalar field under a small O(N)-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general N and N f . Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for on the basis of O(N)-GNY model. It turns out that the O(N)-GNY universality class is physically meaningful if and only if . On this premise, the small O(N)-symmetry breaking perturbation is always irrelevant in the O(N)-GNY universality class. Our studies show that the emergent symmetry in Dirac systems has an upper limit , depending on the flavor numbers N f . As a result, the emergent-O(4) and O(5) symmetries are possible to be found in Dirac systems with fermion flavor , and the emergent-O(4), O(5), O(6) and O(7) symmetries are expected to be found in the systems with fermion flavor . Our result suggests some richer transitions with emergent- symmetry, and so on. Interestingly, in the O(4)-GNY universality class, we find that there is a new supersymmetric critical point which is expected to be found in Dirac systems with fermion flavor .

Chiral Ising Gross-Neveu Criticality of a Single Dirac Cone: A Quantum MonteCarlo Study.

We perform large-scale quantum MonteCarlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with N=2 spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength U_{c}=7.28±0.02 in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding N=2 chiral Ising Gross-Neveu universality class: the inverse correlation length exponent ν^{-1}=1.19±0.03, the order parameter anomalous dimension η_{ϕ}=0.31±0.01, and the fermion anomalous dimension η_{ψ}=0.136±0.005.

Damping of Pseudo-Goldstone Fields.

Approximate symmetries abound in nature. If these symmetries are also spontaneously broken, the would-be Goldstone modes acquire a small mass, or inverse correlation length, and are referred to as pseudo-Goldstones. At nonzero temperature, the effects of dissipation can be captured by hydrodynamics at sufficiently long scales compared to the local equilibrium. Here, we show that, in the limit of weak explicit breaking, locality of hydrodynamics implies that the damping of pseudo-Goldstones is completely determined by their mass and diffusive transport coefficients. We present many applications: superfluids, QCD in the chiral limit, Wigner crystal and density wave phases in the presence of an external magnetic field or not, nematic phases, and (anti)ferromagnets. For electronic density wave phases, pseudo-Goldstone damping generates a contribution to the resistivity independent of the strength of disorder, which can have a linear temperature dependence provided the associated diffusivity saturates a bound. This is reminiscent of the phenomenology of strange metal high-T_{c} superconductors, where charge density waves are observed across the phase diagram.

Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice

Within the tensor network framework, the (positive) thermal density operator can be approximated by a double layer of infinite Projected Entangled Pair Operator (iPEPO) coupled via ancilla degrees of freedom. To investigate the thermal properties of the spin-1/2 Heisenberg model on the square lattice, we introduce a family of fully spin-$SU(2)$ and lattice-$C_{4v}$ symmetric on-site tensors (of bond dimensions $D=4$ or $D=7$) and a plaquette-based Trotter-Suzuki decomposition of the imaginary-time evolution operator. A variational optimization is performed on the plaquettes, using a full (for $D=4$) or simple (for $D=7$) environment obtained from the single-site Corner Transfer Matrix Renormalization Group fixed point. The method is benchmarked by a comparison to quantum Monte Carlo in the thermodynamic limit. Although the iPEPO spin correlation length starts to deviate from the exact exponential growth for inverse-temperature $\beta \gtrsim 2$, the behavior of various observables turns out to be quite accurate once plotted w.r.t the inverse correlation length. We also find that a direct $T=0$ variational energy optimization provides results in full agreement with the $\beta\rightarrow\infty$ limit of finite-temperature data, hence validating the imaginary-time evolution procedure. Extension of the method to frustrated models is described and preliminary results are shown.

Generation of chiral asymmetry via helical magnetic fields

It is well known that helical magnetic fields undergo a so-called inverse cascade by which their correlation length grows due to the conservation of magnetic helicity in classical ideal magnetohydrodynamics (MHD). At high energies above approximately $10$ MeV, however, classical MHD is necessarily extended to chiral MHD and then the conserved quantity is $\langle\mathcal{H}\rangle + 2 \langle\mu_5\rangle / \lambda$ with $\langle\mathcal{H}\rangle$ being the mean magnetic helicity and $\langle\mu_5\rangle$ being the mean chiral chemical potential of charged fermions. Here, $\lambda$ is a (phenomenological) chiral feedback parameter. In this paper, we study the evolution of the chiral MHD system with the initial condition of nonzero $\langle\mathcal{H}\rangle$ and vanishing $\mu_5$. We present analytic derivations for the time evolution of $\langle\mathcal{H}\rangle$ and $\langle\mu_5\rangle$ that we compare to a series of laminar and turbulent three-dimensional direct numerical simulations. We find that the late-time evolution of $\langle\mathcal{H}\rangle$ depends on the magnetic and kinetic Reynolds numbers ${\rm Re}_{_\mathrm{M}}$ and ${\rm Re}_{_\mathrm{K}}$. For a high ${\rm Re}_{_\mathrm{M}}$ and ${\rm Re}_{_\mathrm{K}}$ where turbulence occurs, $\langle\mathcal{H}\rangle$ eventually evolves in the same way as in classical ideal MHD where the inverse correlation length of the helical magnetic field scales with time $t$ as $k_\mathrm{p} \propto t^{-2/3}$. For a low Reynolds numbers where the velocity field is negligible, the scaling is changed to $k_\mathrm{p} \propto t^{-1/2}\mathrm{ln}\left(t/t_\mathrm{log}\right)$. After being rapidly generated, $\langle\mu_5\rangle$ always decays together with $k_\mathrm{p}$, i.e. $\langle\mu_5\rangle \approx k_\mathrm{p}$, with a time evolution that depends on whether the system is in the limit of low or high Reynolds numbers.

Exponential Decay for the Near‐Critical Scaling Limit of the Planar Ising Model

AbstractWe consider the Ising model at its critical temperature with external magnetic field ha15/8 on the square lattice with lattice spacing a. We show that the truncated two‐point function in this model decays exponentially with a rate independent of a as a ↓ 0. As a consequence, we show exponential decay in the near‐critical scaling limit Euclidean magnetization field. For the lattice model with a = 1, the mass (inverse correlation length) is of order h8/15 as h ↓ 0; for the Euclidean field, it equals exactly Ch8/15 for some C. Although there has been much progress in the study of critical scaling limits, results on near‐critical models are far fewer due to the lack of conformal invariance away from the critical point. Our arguments combine lattice and continuum FK representations, including coupled conformal loop and measure ensembles, showing that such ensembles can be useful even in the study of near‐critical scaling limits. Thus we provide the first substantial application of measure ensembles. © 2020 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

Exact solution of the critical Ising model with special toroidal boundary conditions.

The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary conditions, which we call duality-twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the system, along noncontractible circles of the cylinder, before closing it into a torus. We derive exact expressions for the eigenvalues of a transfer matrix for the critical ferromagnetic Ising model on the M×N square lattice wrapped on the torus with a specific defect line. As a result we have obtained analytically the partition function for the Ising model with such boundary conditions. In the case of infinitely long cylinders of circumference L with duality-twisted boundary conditions we obtain the asymptotic expansion of the free energy and the inverse correlation lengths. We find that the ratio of subdominant finite-size correction terms in the asymptotic expansion of the free energy and the inverse correlation lengths should be universal. We verify such universal behavior in the framework of a perturbating conformal approach by calculating the universal structure constant C_{n1n} for descendent states generated by the operator product expansion of the primary fields. For such states the calculations of an universal structure constants is a difficult task, since it involves knowledge of the four-point correlation function, which in general is not fixed by conformal invariance except for some particular cases, including the Ising model.

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 $T>0$ при произвольной конечной ширине слоя $L<\infty$. 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.

Possible increase in the critical temperature of high-temperature superconductors based on the synthesis of new classes of HTSC compounds

The effect of exchange enhancement of electron-phonon interactions in high-temperature superconductor (HTSC) systems is examined and an upper bound is determined for applicability of the quasilinear equations. The spin-phonon interaction in the HTSC phase is described. It is found that if the resonance wave vector krez ≪ pF, then use of the quasilinear equations is justified, since krez is on the order of the inverse correlation length kc which, in turn, does not exceed the inverse coherence length (i.e., kc ≪ pF). Thus, the quasilinear calculation of Tc is correct when the spin-phonon coupling parameter ξ ≫ 1 and can be used to determine the synthesis characteristics for new HTSC materials with higher Tc.

On Cluster Properties of Classical Ferromagnets in an External Magnetic Field

Correlation functions of ferromagnetic spin systems satisfying a Lee-Yang property are studied. It is shown that, for classical systems in a non-vanishing uniform external magnetic field $h$, the connected correlation functions decay exponentially in the distances between the spins, i.e., the inverse correlation length ("mass gap"), $m(h)$, is strictly positive. Our proof is very short and transparent and is valid for complex values of the external magnetic field $h$, provided that $\text{Re} \, h \not= 0$. It implies a mean-field lower bound on $m(h)$, as $h \searrow 0$, first established by Lebowitz and Penrose for the Ising model. Our arguments also apply to some quantum spin systems.

The critical Ising model on a torus with a defect line

The critical Ising model in two dimensions with a specific defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically the partition function and the asymptotic expansions of the free energy and inverse correlation lengths for an infinitely long cylinder of circumference Lx. We find that finite-size corrections to scaling are of the form for the free energy f and and for inverse correlation lengths and , respectively, with integer values of k. By exact evaluation we find that the amplitude ratios and are universal and verify this universal behavior using a perturbative conformal approach.

Calculation of the spectral dependence of the Anderson localization criterion in a one-dimensional system with correlated diagonal disorder

We consider the problem of calculating the Anderson criterion for a one-dimensional disordered chain with correlated disorder. We solve this problem by the perturbation method with the inverse correlation length as the small parameter. We show that in a correlated system, the degree of localization not only naturally decreases but its spectral dependence also differs significantly from the spectral dependence in uncorrelated chains. The calculations are based on the method for constructing joint statistics of Green’s functions, which was previously used to analyze uncorrelated one-dimensional systems. We illustrate the theoretical calculations with a numerical experiment.

Fermi surface evolution in the ensemble of spin-polarized quasiparticles in La2 − x Sr x CuO4

For the spin-fermion model, it has been shown that the concept of spin polarons makes it possible to reproduce fine details of the Fermi surface evolution in the nodal direction of La2 − x Sr x CuO4 occurring with changes in the doping level x. The physics here is determined by the spin-correlated hopping of charge carriers and by the doping dependence of the inverse magnetic correlation length.

Universal corrections to the entanglement entropy in gapped quantum spin chains: A numerical study

We carry out a numerical study of the bi-partite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the anti-ferromagnetic XXZ model. The universal scaling limit of these models is described by the massive Ising field theory and the SU(2)-Thirring (sine-Gordon) model, respectively. We may therefore exploit quantum field theoretical results to predict the behaviour of the entropy. We numerically confirm that, in the scaling limit, corrections to the saturation of the entropy at large region size are proportional to the Bessel function K0(2mr) where m is a mass scale (the inverse correlation length) and r the length of the region under consideration. The proportionality constant is simply related to the number of particle types in the universal spectrum. This was originally predicted in publications involving two of the current authors for two-dimensional quantum field theories. Away from the universal region our numerics suggest an entropic behaviour following quite closely the quantum field theory prediction, except for extra dependencies on the correlation length.

Field effect on surface states in a doped Mott-insulator thin film

Surface effects of a doped thin film made of a strongly correlated material are investigated both in the absence and presence of a perpendicular electric field. We use an inhomogeneous Gutzwiller approximation for a single band Hubbard model in order to describe correlation effects. For low doping, the bulk value of the quasiparticle weight is recovered exponentially deep into the slab, but with increasing doping, additional Friedel oscillations appear near the surface. We show that the inverse correlation length has a power-law dependence on the doping level. In the presence of an electrical field, considerable changes in the quasiparticle weight can be realized throughout the system. We observe a large difference (as large as five orders of magnitude) in the quasiparticle weight near the opposite sides of the slab. This effect can be significant in switching devices that use the surface states for transport.