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arXiv:1305.0985 · New Journal of Physics

Prethermalization and dynamic phase transition in an isolated trapped ion spin chain

Zhe-Xuan Gong, L-M Duan

Published Nov 26, 2013• 36 citations
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Abstract

We propose an experimental scheme to observe prethermalization and a dynamic phase transition in a one-dimensional XY spin chain with long-range interactions and inhomogeneous lattice spacing, which can be readily implemented with a recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at an intermediate timescale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is shown to result from a non-trivial structure in the lower half of the energy spectrum. The dynamic behavior of the system is shown to cross different phases when the interaction range is continuously tuned, indicating the existence of a dynamic phase transition.

DOI
10.1088/1367-2630/15/11/113051

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We propose an experimental scheme to observe prethermalization and a dynamic phase transition in a one-dimensional XY spin chain with long-range interactions and inhomogeneous lattice spacing, which can be readily implemented with a recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at an intermediate timescale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is shown to result from a non-trivial structure in the lower half of the energy spectrum. The dynamic behavior of the system is shown to cross different phases when the interaction range is continuously tuned, indicating the existence of a dynamic phase transition.
Abstract The prethermalizaiton phenomenon in long-range interacting spin chains has been predicted in Gong and Duan (2013 New J. Phys. 15 113051) and experimentally observed in Neyenhuis et al (2017 Sci. Adv. 3 e1700672). The phenomenon disappears in short-range interacting spin chains in their scenario. Here we propose a scheme to observe prethermalization in short-range interacting spin chains by applying additional site-dependent potentials with global parity symmetry in the system. We study the time evolution of an effective XY model with a single-particle initially pumped, and consider several typical potential forms for the emergence of prethermalization. Through numerical calculations, we find that (1) depending on different dephasing speeds of the coherence between eigenstates, the spin chain may evolve up to three prethermal states at different time scales before relaxing to the thermal state; (2) an interesting excitation spreading phenomenon may occur along with prethermalization; and (3) with a special form of potentials, the long-time evolution of the system undergoes a transition from the absence to the presence of prethermal states by controlling the potential strength.
Although statistical mechanics describes thermal equilibrium states, these states may or may not emerge dynamically for a subsystem of an isolated quantum many-body system. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale, and instead relax to quasi-stationary prethermal states that can be described by statistical mechanics, when approximately conserved quantities are included in a generalized Gibbs ensemble (GGE). We experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse-field Ising Hamiltonian following a sudden quench. For sufficiently long-range interactions, the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. However, the prethermal state in this case cannot be described by a standard GGE; it rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.
Abstract Nonequilibrium dynamics in an isolated quantum spin chain with long-range Ising interactions that decay as ( ) with the distance r is studied. It turns out that long-range interactions give rise to a big timescale separation, which causes prethermalization for all . This conclusion is deduced by comparing two important timescales relevant for relaxation dynamics; one is the relaxation time of local permutation operators, which are quasi-conserved quantities in this system, and the other is the timescale of the initial relaxation of local quantities due to the growth of quantum fluctuations. We also explore the entire nonequilibrium dynamics by using the discrete truncated Wigner approximation, which is consistent with the result mentioned above.
We consider a chain of trapped ions to interact with each other via long-range interactions. This system can be used to simulate the long-range Ising model. We study the dynamics of quantum coherence of a single spin in the chain, where the spins are initially prepared in their upper states. The relaxation dynamics exhibits due to the genuine long-range interaction. The degree of quantum coherence of a single spin rapidly decreases and vanishes in the steady state. However, our numerical result suggests that the conventional spin chain model, which truncates the interactions between the distant spins, cannot show the relaxation dynamics. This implies that the usual truncation in approximating the long-range interaction is not applicable to describing the non-equilibrium dynamics. The effect of the interaction range on the relaxation dynamics is studied. The higher relaxation rate will show if a system has a longer range of interaction. However, it takes a longer relaxation time in the vicinity of infinite interaction range. We also examine the dynamics of quantum coherence of a block of spins. Our result may shed light on the relationship between long-range interaction and the coherence dynamics of a quantum many-body system.
Abstract One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 232323 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.
Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.