We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford'' algebras. We also introduce the ``defining representation'' for such algebras, and show that this representation actually coincides with the terms of the Hamiltonian in two relevant models: the XY model and the ``free fermions in disguise'' model of Fendley. Afterwards we study a particular anti-symmetric combination of commuting Hamiltonians; this is performed in a model independent way. We show that for this combination there exists a reference state, and few body eigenstates can be created by the fermionic operators. Concrete application is presented in the case of the ``free fermions in disguise'' model.
Generalized eigenstate typicality in translation-invariant quasifree fermionic models
我们证明了一个广义的概念，本征态热化的守恒准自由费米子模型：绝大多数的本征态满足有限数量的适当的约束（例如，固定的能量和粒子数）的属性，其约化密度矩阵的小的子系统近似于相应的广义吉布斯系综。为此，我们推广了Lai和Yang（Phys. Rev. B 91，081110（2015））的分析结果，并通过XX自旋链的Jordan-Wigner变换的例子来数值说明这一主张。
The recent discovery of quantum many-body scar states has revealed the possibility of having states with low entanglement that violate the eigenstate thermalization hypothesis in nonintegrable systems. Such states with low entanglement entropy are rare but naturally exist in the integrable system of free fermions. Here, we demonstrate analytically that these atypical states would be always eliminated when an arbitrary weak interaction is introduced between the fermions. In particular, we show that the probability of having a many-body scar state with entanglement entropy satisfying a sub-volum…
We study the nature of many-body eigenstates of a system of interacting chiral spinless fermions on a ring. We find a coexistence of fermionic and bosonic types of eigenstates in parts of the many-body spectrum. Some bosonic eigenstates, native to the strong interaction limit, persist at intermediate and weak couplings, enabling persistent density oscillations in the system, despite it being far from integrability.
Capacity of entanglement (CoE), an information-theoretic measure of entanglement, defined as the variance of modular Hamiltonian, is known to capture the deviation from the maximal entanglement. We derive an exact expression for the average eigenstate CoE in fermionic Gaussian states as a finite series, valid for arbitrary bi-partition of the total system. Further, we consider the complex SYK$_2$ model in the thermodynamic limit and we obtain a closed-form expression of average CoE. In this limit, the variance of the average CoE becomes independent of the system size. Moreover, when the subsys…
Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
We consider free fermion systems in arbitrary dimensions and represent the occupation pattern of each eigenstate as a classical binary string. We find that the Kolmogorov complexity of the string correctly captures the scaling behavior of its entanglement entropy (EE). In particular, the logarithmically-enhanced area law for EE in the ground state and the volume law for EE in typical highly excited states are reproduced. Since our approach does not require bipartitioning the system, it allows us to distinguish typical and atypical eigenstates directly by their intrinsic complexity. We reveal t…
In a recent Letter [Phys. Rev. Lett. 125, 180604 (2020)], we introduced a closed-form analytic expression for the average bipartite von Neumann entanglement entropy of many-body eigenstates of random quadratic Hamiltonians. Namely, of Hamiltonians whose single-particle eigenstates have random coefficients in the position basis. A paradigmatic Hamiltonian for which the expression is valid is the quadratic Sachdev-Ye-Kitaev (SYK2) model in its Dirac fermion formulation. Here we show that the applicability of our result is much broader. Most prominently, it is also relevant for local Hamiltonians…
Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
Indian Institute of Technology - Kanpur（坎普尔印度理工学院）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington（华盛顿大学物理系量子模拟孵化器）；Department of Physics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus（比拉理工学院皮拉尼分校K.K.比尔拉果阿校区物理系）；Center for Research in Quantum Information and Technology, Birla Institute of Technology and Science Pilani（比拉理工学院皮拉尼分校量子信息技术研究中心）
Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz within the eigenstate thermalization hypothesis (ETH). We study a quantum chaotic spin-fermion model in a one-dimensional lattice, which consists of a spin-1/2 XX chain coupled to a single itinerant fermion. In our study, we focus on translationally invariant observables including the charge and energy current, thereby also connecting the ETH with transport properties. Considering observables with a Hilbert-Schmidt norm of one, we first perform a comprehensive analysis of ETH in the mode…
Efficient computation of average subsystem Bures distance between fermionic Gaussian states
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices
在量子动力学的突现本征态解[Phys. Rev. X 7，021012（2017）]中，人们可以构造一个局部算符（突现哈密顿量），其时间演化态是本征态。在这里，我们表明，这样的解决方案存在的膨胀动力学的Tonks-Girardeau气体在光晶格后关闭幂律（例如，谐波或四次）限制势，其是不涉及升压算子的几何猝灭。对于系统，最初是在基态，并在膨胀过程中进行动态费米子化，我们表明，他们仍然在基态的紧急本地哈密顿量在任何时候。另一方面，对于非零初始温度下的系统，膨胀动力学可以描述为构造涌现局部哈密顿量的吉布斯系综（涌现吉布斯系综）。
Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common property of all quantum-chaotic quadratic Hamiltonians studied in this context so far is the presence of random terms that act as a source of disorder. Here we introduce tight-binding billiards in two dimensions, which are described by non-interacting spinless fermions on a disorder-free square lattice subject to curved open (hard-wall) boundaries. We show that many properties of tight-binding billiar…
Consider a generic quantum spin chain that can be mapped to free quadratic fermions via Jordan-Wigner (JW) transformation. In the presence of arbitrary boundary magnetic fields, this Hamiltonian is no longer a quadratic Hamiltonian after JW transformation. Using ancillary sites and enlarging the Hamiltonian we first introduce a bigger quadratic Hamiltonian. Then we diagonalize this enlarged Hamiltonian in its most generic form and show that all the states are degenerate because of the presence of a zero mode. The eigenstates of the original spin chain with boundary magnetic fields can be deriv…
