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1. Quantum scars of bosons with correlated hopping

   https://doi.org/10.1038/s42005-020-0364-9  

   Hudomal, Ana ; Vasić, Ivana ; Regnault, Nicolas ; Papić, Zlatko ( June 2020 , Communications Physics)

   Recent experiments on Rydberg atom arrays have found evidence of anomalously slow thermalization and persistent density oscillations, which have been interpreted as a many-body analog of the phenomenon of quantum scars. Periodic dynamics and atypical scarred eigenstates originate from a “hard” kinetic constraint: the neighboring Rydberg atoms cannot be simultaneously excited. Here we propose a realization of quantum many-body scars in a 1D bosonic lattice model with a “soft” constraint in the form of density-assisted hopping. We discuss the relation of this model to the standard Bose-Hubbard model and possible experimental realizations using ultracold atoms. We find that this model exhibits similar phenomenology to the Rydberg atom chain, including weakly entangled eigenstates at high energy densities and the presence of a large number of exact zero energy states, with distinct algebraic structure.

    

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2. Many-body spin rotation by adiabatic passage in spin-1/2 XXZ chains of ultracold atoms

   https://doi.org/10.1088/2058-9565/acd2fb  

   Dimitrova, Ivana ; Flannigan, Stuart ; Kyung Lee, Yoo ; Lin, Hanzhen ; Amato-Grill, Jesse ; Jepsen, Niklas ; Čepaitė, Ieva ; Daley, Andrew J ; Ketterle, Wolfgang ( May 2023 , Quantum Science and Technology)

   Abstract Quantum many-body phases offer unique properties and emergent phenomena, making them an active area of research. A promising approach for their experimental realization in model systems is to adiabatically follow the ground state of a quantum Hamiltonian from a product state of isolated particles to one that is strongly-correlated. Such protocols are relevant also more broadly in coherent quantum annealing and adiabatic quantum computing. Here we explore one such protocol in a system of ultracold atoms in an optical lattice. A fully magnetized state is connected to a correlated zero-magnetization state (an xy -ferromagnet) by a many-body spin rotation, realized by sweeping the detuning and power of a microwave field. The efficiency is characterized by applying a reverse sweep with a variable relative phase. We restore up to 50 % of the original magnetization independent of the relative phase, evidence for the formation of correlations. The protocol is limited by the many-body gap of the final state, which is inversely proportional to system size, and technical noise. Our experimental and theoretical studies highlight the potential and challenges for adiabatic preparation protocols to prepare many-body eigenstates of spin Hamiltonians. 

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3. Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm

   https://doi.org/10.1038/s41534-019-0240-1  

   Gard, Bryan T. ; Zhu, Linghua ; Barron, George S. ; Mayhall, Nicholas J. ; Economou, Sophia E. ; Barnes, Edwin ( January 2020 , npj Quantum Information)

   The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. We test our circuits in quantum simulations of the$${H}_{2}$$$H_2$and$$LiH$$$LiH$molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth.

    

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4. Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

   https://doi.org/10.21468/SciPostPhys.15.2.043  

   Tanhayi Ahari, Mostafa ; Bandyopadhyay, Sumanta ; Nussinov, Zohar ; Seidel, Alexander ; Ortiz, Gerardo ( January 2023 , SciPost Physics)

   We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor\nu=2/3$\nu =2/3$. The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-bodyM$M$-clustering property within any given number of Landau levels, that is, wave functions withM$M$th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for theM=3$M=3$case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.

    

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5. Quantum scarring in a spin-boson system: fundamental families of periodic orbits

   https://doi.org/10.1088/1367-2630/abd2e6  

   Pilatowsky-Cameo, Saúl ; Villaseñor, David ; Bastarrachea-Magnani, Miguel A. ; Lerma-Hernández, Sergio ; Santos, Lea F. ; Hirsch, Jorge G. ( March 2021 , New Journal of Physics)

   As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimentally realizable atom–photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits.

    

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