اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDynamics of correlations in two-dimensional quantum spin models with long-range interactions: A phase-space Monte-Carlo study
122
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case of spin models with short-range couplings. However, progress towards the development of a comparable understanding in long-range interacting models, in particular out-of-equilibrium, remains limited. In a recent work, we proposed a semiclassical numerical method to study spin models, the discrete truncated Wigner approximation (DTWA), and demonstrated its capability to correctly capture the dynamics of one- and two-point correlations in one dimensional (1D) systems. Here we go one step forward and use the DTWA method to study the dynamics of correlations in 2D systems with many spins and different types of long-range couplings, in regimes where other numerical methods are generally unreliable. We compute spatial and time-dependent correlations for spin-couplings that decay with distance as a power-law and determine the velocity at which correlations propagate through the system. Sharp changes in the behavior of those velocities are found as a function of the power-law decay exponent. Our predictions are relevant for a broad range of systems including solid state materials, atom-photon systems and ultracold gases of polar molecules, trapped ions, Rydberg, and magnetic atoms. We validate the DTWA predictions for small 2D systems and 1D systems, but ultimately, in the spirt of quantum simulation, experiments will be needed to confirm our predictions for large 2D systems.
قيم البحث
اقرأ أيضاً
We probe the superconducting gap in the zero temperature ground state of an attractively interacting spin-imbalanced two-dimensional Fermi gas with Diffusion Monte Carlo. A condensate fraction at nonzero pair momentum evidences a spatially non-unifor
m superconducting order parameter. Comparison with exact diagonalisation studies confirms that the nonzero condensate fraction across a range of nonzero fermion pair momenta is consistent with non-exclusive pairing between majority and minority fermions, an extension beyond FFLO theory.
Spin ensembles coupled to optical cavities provide a powerful platform for engineering synthetic quantum matter. Recently, we demonstrated that cavity mediated infinite range interactions can induce fast scrambling in a Heisenberg $XXZ$ spin chain (P
hys. Rev. Research {bf 2}, 043399 (2020)). In this work, we analyze the kaleidoscope of quantum phases that emerge in this system from the interplay of these interactions. Employing both analytical spin-wave theory as well as numerical DMRG calculations, we find that there is a large parameter regime where the continuous $U(1)$ symmetry of this model is spontaneously broken and the ground state of the system exhibits $XY$ order. This kind of symmetry breaking and the consequent long range order is forbidden for short range interacting systems by the Mermin-Wagner theorem. Intriguingly, we find that the $XY$ order can be induced by even an infinitesimally weak infinite range interaction. Furthermore, we demonstrate that in the $U(1)$ symmetry broken phase, the half chain entanglement entropy violates the area law logarithmically. Finally, we discuss a proposal to verify our predictions in state-of-the-art quantum emulators.
The approach to equilibrium is studied for long-range quantum Ising models where the interaction strength decays like r^{-alpha} at large distances r with an exponent $alpha$ not exceeding the lattice dimension. For a large class of observables and i
nitial states, the time evolution of expectation values can be calculated. We prove analytically that, at a given instant of time t and for sufficiently large system size N, the expectation value of some observable <A>(t) will practically be unchanged from its initial value <A>(0). This finding implies that, for large enough N, equilibration effectively occurs on a time scale beyond the experimentally accessible one and will not be observed in practice.
The non-equilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issu
e by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power-law with distance $propto r^{-alpha}$, $alpha>0$. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for $alpha>2$; weakly long-range for $1<alpha<2$ without a clear light cone but with a finite propagation speed of almost all excitations; and fully non-local for $alpha<1$ with instantaneous transmission of correlations. This last regime breaks generalized Lieb--Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasi-particles remains valid, allowing an intuitive interpretation of our findings via divergences of quasi-particle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.
Using an infinite Matrix Product State (iMPS) technique based on the time-dependent variational principle (TDVP), we study two major types of dynamical phase transitions (DPT) in the one-dimensional transverse-field Ising model (TFIM) with long-range
power-law ($propto1/r^{alpha}$ with $r$ inter-spin distance) interactions out of equilibrium in the thermodynamic limit -- textit{DPT-I}: based on an order parameter in a (quasi-)steady state, and textit{DPT-II}: based on non-analyticities (cusps) in the Loschmidt-echo return rate. We construct the corresponding rich dynamical phase diagram, whilst considering different quench initial conditions. We find a nontrivial connection between both types of DPT based on their critical lines. Moreover, and very interestingly, we detect a new DPT-II dynamical phase in a certain range of interaction exponent $alpha$, characterized by what we call textit{anomalous cusps} that are distinct from the textit{regular cusps} usually associated with DPT-II. Our results provide the characterization of experimentally accessible signatures of the dynamical phases studied in this work.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
