Quantum simulators have recently enabled experimental observations of quantum many-body systems' internal thermalization. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number - in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6-21 spins in an approximate microcanonical subspace, a generalization of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, whose predictions can now be tested.
In statistical mechanics, a small system exchanges conserved quantities---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the conserved quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed ``the non-Abelian thermal state (NATS).'' We propose an experimental protocol for observi…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented by operators that fail to commute. Whether such a system thermalizes and what form the thermal state has are questions about truly quantum thermodynamics. Here we investigate this thermal state from three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system-and-bath composite, tracing out the bat…
Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities -- energy, particles, electric charge, etc. -- that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries -- about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from ab…
The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum therm…
Generic ETH: Eigenstate Thermalization beyond the Microcanonical
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Pennsylvania State University（宾夕法尼亚州立大学）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Syracuse University（雪城大学）；Sarah Lawrence College（莎拉劳伦斯学院）
We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization process. We also show that this approach is useful to investigate thermalization based on a finite-size scaling of numerical data. The condition follows from an exact representation of the observable as a sum of a projection onto the local conserved charges of the system and a projection onto the non-local ones. We show that thermalization requires that the …
We investigate a weak version of subsystem eigenstate thermalization hypothesis (ETH) for a two-dimensional large central charge conformal field theory by comparing the local equivalence of high energy state and thermal state of canonical ensemble. We evaluate the single-interval Rényi entropy and entanglement entropy for a heavy primary state in short interval expansion. We verify the results of Rényi entropy by two different replica methods. We find nontrivial results at the eighth order of short interval expansion, which include an infinite number of higher order terms in the large central …
We report on low-temperature noise measurements of a single electron transistor (SET) immersed in superfluid $^4$He. The device acts as a charge sensitive electrometer able to detect the fluctuations of charged defects in close proximity to the SET. In particular, we measure telegraph switching of the electric current through the device originating from a strongly coupled individual two-level fluctuator. By embedding the device in a superfluid helium immersion cell we are able to systematically control the thermalizing environment surrounding the SET and investigate the effect of the superflui…
Previous studies of photon-assisted tunneling through normal-metal-insulator-superconductor junctions have exhibited potential for providing a convenient tool to control the dissipation of quantum-electric circuits in-situ. However, the current literature on such a quantum-circuit refrigerator (QCR) does not present a detailed description for the charge dynamics of the tunneling processes or the phase coherence of the open quantum system. Here we derive a master equation describing both quantum-electric and charge degrees of freedom, and discover that typical experimental parameters of low tem…
Bypassing eigenstate thermalization with experimentally accessible quantum dynamics
JILA and Center for Theory of Quantum Matter, Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系量子物质理论中心及JILA）；University of Colorado, Boulder（科罗拉多大学博尔德分校）
We study the quantum dynamics of a simple translation invariant, center-of-mass (CoM) preserving model of interacting fermions in one dimension (1D), which arises in multiple experimentally realizable contexts. We show that this model naturally displays the phenomenology associated with fractonic systems, wherein single charges can only move by emitting dipoles. This allows us to demonstrate the rich Krylov fractured structure of this model, whose Hilbert space shatters into exponentially many dynamically disconnected subspaces. Focusing on exponentially large Krylov subspaces, we show that th…
We review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents. We briefly discuss how interactions affect the picture. In the second part, we explore the effects of a localized defect. We show that the emergence of spontaneous currents near the defect undermines any description of the late-time dynamics by means of a stationary state in a finite chain. In particular, the diagonal ensemble does not work. Finally, we provide numerical evidence that simple generic localized defects are not sufficient to induce thermali…
Statistical Mechanics of Non-Abelian Learnability Transitions
Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；Department of Theoretical Physics, University of Geneva（日内瓦大学理论物理系）；Geneva Quantum Center, University of Geneva（日内瓦大学日内瓦量子中心）
Geometric fragmentation and anomalous thermalization in cubic dimer model
German Aerospace Center (DLR), Institute of Frontier Materials on Earth and in Space, Functional, Granular, and Composite Materials（德国航空航天中心前沿地球与空间材料研究所功能颗粒及复合材料部门）；University of Southampton（南安普顿大学）；Wake Forest University（维克森林大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；TNG Technology Consulting GmbH（TNG技术咨询有限公司）
The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergo…
