We study the non-equilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model -- a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent experiments with Rydberg-atom arrays. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a "holographic" mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles. We discuss how this integrability is broken by geometric features of the bubbles and by corrections in inverse powers of the ferromagnetic coupling, and provide a lower bound to the timescale after which the bubble is ultimately expected to melt. Remarkably, we demonstrate that a symmetry-breaking longitudinal field gives rise to a robust ergodicity breaking in two dimensions, a phenomenon underpinned by Stark many-body localization of the emergent fermionic excitations of the interface.
The nature of the thermal melting process by which triangular-lattice Ising antiferromagnets lose their low-temperature ferrimagnetic three-sublattice order depends on the range of the interactions: It changes character when second and third neighbour ferromagnetic interactions become comparable to the nearest-neighbour antiferromagnetic coupling. We present a detailed numerical characterization of the corresponding threshold at which two-step melting of three-sublattice order gives way to a direct first-order transition at which this order is lost. The multicritical behaviour at this threshol…
Magnetic frustrations and dimensionality play an important role in determining the nature of the magnetic long-range order and how it melts at temperatures above the ordering transition $T_N$. In this work, we use large-scale Monte Carlo simulations to study these phenomena in a class of frustrated Ising spin models in two spatial dimensions. We find that the melting of the magnetic long-range order into an isotropic gas-like paramagnet proceeds via an intermediate stage where the classical spins remain anisotropically correlated. This correlated paramagnet exists in a temperature range $T_N <…
Frustrated magnets host the promises of material realizations of new paradigm of quantum matter, while direct comparison of unbiased model calculations with experimental measurements is still very challenging. Here, we design and implement a protocol of employing many-body computation methodologies for accurate model calculation -- both equilibrium and dynamical properties -- of a frustrated rare-earth magnet TmMgGaO$_4$ (TMGO), which perfectly explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic …
The melting of the corner of a crystal is a classical, real-world, non-equilibrium statistical mechanics problem which has shown several connections with other branches of physics and mathematics. For a perfect, classical crystal in two and three dimensions the solution is known: the crystal melts reaching a certain asymptotic shape, which keeps expanding ballistically. In this paper, we move onto the quantum realm and show that the presence of quenched disorder slows down severely the melting process. Nevertheless, we show that there is no many-body localization transition, which could impede…
Complex magnetic orders in frustrated magnets may exhibit rich melting processes when the magnet is heated toward the paramagnetic phase. We show that one may tune such melting processes by quantum fluctuations. We consider a kagome lattice dipolar Ising model subject to transverse field and focus on the thermal transitions out of its magnetic ground state, which features a $\sqrt{3}\times\sqrt{3}$ magnetic unit cell. Our quantum Monte Carlo (QMC) simulations suggest that, at weak transverse field, the $\sqrt{3}\times\sqrt{3}$ phase melts by way of an intermediate magnetic charge ordered phase…
We investigate the occurrence of many-body localization (MBL) on a spin-1/2 transverse-field Ising model defined on a Chimera connectivity graph with random exchange interactions and longitudinal fields. We observe a transition from an ergodic phase to a non-thermal phase for individual energy eigenstates induced by a critical disorder strength for the Ising parameters. Our result follows from the analysis of both the mean half-system block entanglement and the energy level statistics. We identify the critical point associated with this transition using the maximum variance of the block entang…
Determining the border between ergodic and localized behavior is of central interest for interacting many-body systems. We consider here the recently very popular spin-chain model that is periodically excited. A convenient description of such a many-body system is achieved by the dual operator that evolves the system in contrast to the time-evolution operator not in time but in particle direction. We identify in this paper the largest eigenvalue of a function based on the dual operator as a convenient tool to determine if the system shows ergodic or many-body localized features. By perturbatio…
The Ising one-dimensional (1D) chain with spin $S=1/2$ and magnetoelastic interactions is studied with the lattice contribution included in the form of elastic interaction and thermal vibrations simultaneously taken into account. The magnetic energy term and the elastic (static) energy term based on the Morse potential are calculated exactly. The vibrational energy is calculated in the Debye approximation, in which the anharmonicity is introduced by the Gr{ü}neisen parameter. The total Gibbs potential, including both the magnetic field, as well as the external force term, is constructed and fr…
The nonlinear effect of a driving force in periodically driven quantum many-body systems can be systematically investigated by analyzing the effective Floquet Hamiltonian. In particular, under an appropriate definition of the effective Hamiltonian, simple driving forces may result in non-local interactions. Here we consider a driven $ XXZ $ model to show that four-site interactions emerge owing to the driving force, which can produce state-selective localization, a phenomenon where some limited Ising-like product states become fixed points of dynamics. We first derive the effective Hamiltonian…
In a recent paper [Phys. Rev. Lett. 129, 120601] we have shown that the dynamics of interfaces, in the symmetry-broken phase of the two-dimensional ferromagnetic quantum Ising model, displays a robust form of ergodicity breaking. In this paper, we elaborate more on the issue. First, we discuss two classes of initial states on the square lattice, the dynamics of which is driven by complementary terms in the effective Hamiltonian and may be solved exactly: (a) strips of consecutive neighbouring spins aligned in the opposite direction of the surrounding spins, and (b) a large class of initial sta…
It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the infinite-temperature version of this "universal operator growth hypothesis" holds for the quantum Ising spin model in $d \ge 2$ dimensions, and for the chaotic Ising chain (with longitudinal and transverse fields) in one dimension. Moreover, the disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density decay as thermalizing models. Our argument is…
We analyze the out-of-equilibrium dynamics of a quantum particle coupled to local magnetic degrees of freedom that undergo a classical phase transition. Specifically, we consider a two-dimensional tight-binding model that interacts with a background of classical spins in thermal equilibrium, which are subject to Ising interactions and act as emergent, correlated disorder for the quantum particle. Particular attention is devoted to temperatures close to the ferromagnet-to-paramagnet transition. To capture the salient features of the classical transition, namely the effects of long-range correla…
Relaxation and Thermalization after a Quantum Quench: Why Localization is Important
我们研究了类自由费米子哈密顿量在突然量子猝灭后的幺正动力学和热化性质，推广了S。Ziraldo等人[Phys. Rev. Lett. 109，247205（2012）]。分析和数值参数，我们表明，一个稳定的状态和广义吉布斯系综（GGE）的描述的存在取决于至关重要的可观察到的考虑（本地与广泛）和本地化的最终哈密顿量的属性。我们给出了两个一维模型的结果，无序一维长程跳跃费米子链和无序Ising/XY自旋链。我们分析证明，虽然时间平均的一个机构运营商是完美的再现GGE（即使是有限大小的系统，如果时间积分扩展超出复兴），时间平均的多体运营商可能会显示出明显的偏离GGE预测时，无序诱导本地化的本征态是在发挥作用。
We explore the finite-temperature dynamics of the quasi-1D orbital compass and plaquette Ising models. We map these systems onto a model of free fermions coupled to strictly localized spin-1/2 degrees of freedom. At finite temperature, the localized degrees of freedom act as emergent disorder and localize the fermions. Although the model can be analyzed using free-fermion techniques, it has dynamical signatures in common with typical many-body localized systems: Starting from generic initial states, entanglement grows logarithmically; in addition, equilibrium dynamical correlation functions de…
Probing many-body localization crossover in quasiperiodic Floquet circuits on a quantum processor
RIKEN Center for Computational Science（理化学研究所计算科学中心）；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所交叉理论与数学科学中心）；RIKEN Pioneering Research Institute（理化学研究所先驱研究所）；Jožef Stefan Institute（约热·斯特凡研究所）；University of Ljubljana（卢布尔雅那大学）
Role of flavor degrees of freedom in quantum simulations of disorder-free localization
Ludwig Maximilian University of Munich（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics (ASC)（阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of Leeds（利兹大学）；University of Nottingham（诺丁汉大学）；Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems（量子非平衡系统数学与理论物理中心）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Kyung Hee University（庆熙大学）
