@article {3055, title = {Non-Abelian eigenstate thermalization hypothesis}, journal = {Phys. Rev. Lett.}, volume = {130}, year = {2023}, month = {4/6/2023}, chapter = {140402}, abstract = {

The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity (\"charge\"), the ETH implies thermalization within a charge sector -- in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local observables\&$\#$39; time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we also find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.

}, keywords = {FOS: Physical sciences, High Energy Physics - Theory (hep-th), Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.140402}, url = {https://arxiv.org/abs/2206.05310}, author = {Murthy, Chaitanya and Babakhani, Arman and Iniguez, Fernando and Srednicki, Mark and Nicole Yunger Halpern} } @article {3194, title = {Non-Abelian symmetry can increase entanglement entropy}, journal = {Physical Review B}, volume = {107}, year = {2023}, month = {1/3/2023}, abstract = {

The pillars of quantum theory include entanglement and operators\&$\#$39; failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian {\textquoteleft}{\textquoteleft}charges\&$\#$39;\&$\#$39;). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the effects of charges\&$\#$39; noncommutation -- of a symmetry\&$\#$39;s non-Abelian nature -- on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges\&$\#$39; noncommutation can promote entanglement.

}, doi = {10.1103/physrevb.107.045102}, url = {https://arxiv.org/abs/2209.14303}, author = {Shayan Majidy and Aleksander Lasek and David A. Huse and Nicole Yunger Halpern} } @article {3366, title = {Noncommuting conserved charges in quantum thermodynamics and beyond}, journal = {Nature Reviews Physics}, year = {2023}, month = {9/7/2023}, abstract = {

Thermodynamic systems typically conserve quantities (\"charges\") such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on observables\&$\#$39; failure to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Charges\&$\#$39; noncommutation has been found to invalidate derivations of the thermal state\&$\#$39;s form, decrease entropy production, conflict with the eigenstate thermalization hypothesis, and more. This Perspective surveys key results in, opportunities for, and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: Evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.

}, doi = {10.1038/s42254-023-00641-9}, url = {https://arxiv.org/abs/2306.00054}, author = {Shayan Majidy and William F. Braasch and Aleksander Lasek and Twesh Upadhyaya and Amir Kalev and Nicole Yunger Halpern} } @article {3054, title = {Negative Quasiprobabilities Enhance Phase Estimation in Quantum-Optics Experiment}, journal = {Phys. Rev. Lett.}, volume = {128}, year = {2022}, month = {6/2/2022}, pages = {220504}, abstract = {

Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities\—quantum extensions of probabilities\—engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using PPA, we measure a wave plate\’s birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter\’s amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA\’s metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.

}, doi = {10.1103/PhysRevLett.128.220504}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.128.220504}, author = {Lupu-Gladstein, Noah and Yilmaz, Y. Batuhan and Arvidsson-Shukur, David R. M. and Brodutch, Aharon and Pang, Arthur O. T. and Steinberg, Aephraim M. and Nicole Yunger Halpern} } @article {2560, title = {Noncommuting conserved charges in quantum many-body thermalization}, journal = {Phys. Rev. E }, volume = {101}, year = {2020}, month = {4/15/2020}, abstract = {

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 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\&$\#$39;s long-time state was dubbed \“the non-Abelian thermal state (NATS).\” We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

}, doi = {https://doi.org/10.1103/PhysRevE.101.042117}, url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.042117}, author = {Nicole Yunger Halpern and Michael E. Beverland and Amir Kalev} }