Signatures of rare states and thermalization in a theory with confinement
Signatures of rare states and thermalization in a theory with confinement
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DOI：
10.1103/physrevb.99.195108
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发表时间：
2019-05-06
影响因子：
3.7
通讯作者：
Konik, Robert M.
中科院分区：
文献类型：
--
作者：
Robinson, Neil J.;James, Andrew J. A.;Konik, Robert M.
量子多体系统的非平衡动力学存在二分法。在可积性存在的情况下，局部算子的期望值平衡到广义吉布斯系综所描述的值，广义吉布斯系综保留了关于系统初始状态的广泛记忆。另一方面，在一般系统中，这样的期望值松弛到由热系综所描述的固定值，仅由状态的能量来固定。在理解的核心，这种二分法是本征态热化假说(ETH)：不可积系统中的单个本征态是热的，在某种意义上，期望值与由本征态的能量设置的温度下的热预测一致。在违反ETH的系统中，可以避免热化。因此，确定ETH的有效范围对于理解给定的量子系统是否热是至关重要的。在这里，我们研究了一个简单的受限模型--纵场量子伊辛链，在这个模型中，Eth被破坏了。尽管没有可积性，但仍有稀有的(非热的)态一直存在到光谱的很远的地方。这些都是限制的直接结果：粒子对被限制，形成新的“介子”激发，其能量在系统大小中可能是广泛的。我们证明了这种态在相应晶格模型的连续谱和低能谱中都是非热的。我们强调，光谱中这种态的存在具有重要的后果，某些猝灭导致没有热化，局域可观测到的异常演化。
There is a dichotomy in the nonequilibrium dynamics of quantum many-body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding, this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus, establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here, we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new "meson" excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. We highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously.