اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models
107
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We discuss how to locate critical points in the Berezinskii-Kosterlitz-Thouless (BKT) universality class by means of gap-scaling analyses. While accurately determining such points using gap extrapolation procedures is usually challenging and inaccurate due to the exponentially small value of the gap in the vicinity of the critical point, we show that a generic gap-scaling analysis, including the effects of logarithmic corrections, provides very accurate estimates of BKT transition points in a variety of spin and fermionic models. As a first example, we show how the scaling procedure, combined with density-matrix-renormalization-group simulations, performs extremely well in a non-integrable spin-$3/2$ XXZ model, which is known to exhibit strong finite-size effects. We then analyze the extended Hubbard model, whose BKT transition has been debated, finding results that are consistent with previous studies based on the scaling of the Luttinger-liquid parameter. Finally, we investigate an anisotropic extended Hubbard model, for which we present the first estimates of the BKT transition line based on large-scale density-matrix-renormalization-group simulations. Our work demonstrates how gap-scaling analyses can help to locate accurately and efficiently BKT critical points, without relying on model-dependent scaling assumptions.
قيم البحث
اقرأ أيضاً
In this Letter we will show that, in the presence of a properly modulated Dzyaloshinskii-Moriya (DM) interaction, a $U(1)$ vortex-antivortex lattice appears at low temperatures for a wide range of the DM interaction. Even more, in the region dominate
d by the exchange interaction, a standard BKT transition occurs. In the opposite regime, the one dominated by the DM interaction, a kind of inverse BKT transition (iBKT) takes place. As temperature rises, the vortex-antivortex lattice starts melting by annihilation of pairs of vortex-antivortex, in a sort of inverse BKT transition.
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. Such a topological phase transit
ion has long been sought yet undiscovered directly in magnetic materials. Here, we pin down two transitions that bound a BKT phase in an ideal 2D frustrated magnet TmMgGaO$_4$, via nuclear magnetic resonance under in-plane magnetic fields, which do not disturb the low-energy electronic states and allow BKT fluctuations to be detected sensitively. Moreover, by applying out-of-plane fields, we find a critical scaling behaviour of the magnetic susceptibility expected for the BKT transition. The experimental findings can be explained by quantum Monte Carlo simulations applied on an accurate triangular-lattice Ising model of the compound which hosts a BKT phase. These results provide a concrete example for the BKT phase and offer an ideal platform for future investigations on the BKT physics in magnetic materials.
We have considered two classical lattice-gas models, consisting of particles that carry multicomponent magnetic momenta, and associated with a two-dimensional square lattices; each site can host one particle at most, thus implicitly allowing for hard
-core repulsion; the pair interaction, restricted to nearest neighbors, is ferromagnetic and involves only two components. The case of zero chemical potential has been investigated by Grand--Canonical Monte Carlo simulations; the fluctuating occupation numbers now give rise to additional fluid-like observables in comparison with the usual saturated--lattice situation; these were investigated and their possible influence on the critical behaviour was discussed. Our results show that the present model supports a Berezinskii-Kosterlitz-Thouless phase transition with a transition temperature lower than that of the saturated lattice counterpart due to the presence of ``vacancies; comparisons were also made with similar models studied in the literature.
We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover)
at the same temperature $T_{rm u}=0.282 J$ as for static properties due to unbinding of $mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{rm u}$ the dynamic properties in the intermediate time range are similar to those of two-dimensional XY model below Berezinskii-Kosterlitz-Thouless transition. The interaction of $mathbb{Z}_2$-vortices with spin-wave degrees of freedom does not emerge until rather long times.
The celebrated Berezinskii-Kosterlitz-Thouless (BKT) phase transition refers to a topological transition characterized, e.g., by the dissociation of vortex-antivortex pairs in two-dimensional (2D) systems. Such unusual phase has been reported in vari
ous types of materials, but never in the new class of systems made by one-unit-cell-thick (1UC) ferroelectrics (also coined as 2D ferroelectrics). Here, the use of a first-principles-based effective Hamiltonian method leads to the discovery of many fingerprints of a BKT phase existing in-between the ferroelectric and paraelectric states of 1UC tin tellurium being fully relaxed. Moreover, epitaxial strain is found to have dramatic consequences on the temperature range of such BKT phase for the 1UC SnTe. Consequently, our predictions extend the playground of BKT theory to a novel class of functional materials, and demonstrate that strain is an effective tool to alter BKT characteristics there.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
